On Testing Sample Selection Bias Under the Multicollinearity Problem

ABSTRACT

This paper reviews and extends the literature on the finite sample behavior of tests for sample selection bias. Monte Carlo results show that, when the “multicollinearity problem” identified by Nawata (1993 Nawata , K. ( 1993 ). A note on the estimation of models with sample-selection biases . Economics Letters 42 : 15 – 24 . [CSA] [CROSSREF] [Crossref], [Web of Science ®] , [Google Scholar]) is severe, (i) the t-test based on the Heckman–Greene variance estimator can be unreliable, (ii) the Likelihood Ratio test remains powerful, and (iii) nonnormality can be interpreted as severe sample selection bias by Maximum Likelihood methods, leading to negative Wald statistics. We also confirm previous findings (Leung and Yu, 1996 Leung , S. F. , Yu , S. ( 1996 ). On the choice between sample selection and two-part models . Journal of Econometrics 72 : 197 – 229 . [CSA] [CROSSREF] [Crossref], [Web of Science ®] , [Google Scholar]) that the standard regression-based t-test (Heckman, 1979 Heckman , J. J. ( 1979 ). Sample selection bias as a specification error . Econometrica 47 : 153 – 161 . [CSA] [Crossref], [Web of Science ®] , [Google Scholar]) and the asymptotically efficient Lagrange Multiplier test (Melino, 1982 Melino , A. ( 1982 ). Testing for sample selection bias . Review of Economic Studies 49 : 151 – 153 . [CSA] [Crossref], [Web of Science ®] , [Google Scholar]), are robust to nonnormality but have very little power.     

From Ordinary to Shrinkage Square-Root Estimators

Consider a skewed population. Suppose an intelligent guess could be made about an interval that contains the population mean. There may exist biased estimators with smaller mean squared error than the arithmetic mean within such an interval. This article indicates when it is advisable to shrink the arithmetic mean towards a guessed interval using root estimators. The goal is to obtain an estimator that is better near the average of natural origins. An estimator proposed. This estimator contains the Thompson (1968 Thompson , J. R. ( 1968 ). Accuracy borrowing in the estimation of the mean by shrinkage towards an interval . J. Amer. Statist. Assoc. 63 : 953 – 963 . [CSA] [CROSSREF] [Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) ordinary shrinkage estimator, the Jenkins et al. (1973 Jenkins , O. C. , Ringer , L. J. , Hartley , H. O. ( 1973 ). Root estimators . J Amer. Statist. Assoc. 68 : 414 – 419 . [CSA] [CROSSREF] [Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) square-root estimator, and the arithmetic sample mean as special cases. The bias and the mean squared error of the proposed more general estimator is compared with the three special cases. Shrinkage coefficients that yield minimum mean squared error estimators are obtained. The proposed estimator is considerably more efficient than the three special cases. This remains true for highly skewed populations. The merits of the proposed shrinkage square-root estimator are supported by the results of numerical and simulation studies.     

Generalized Scrambling in Quantitative Optional Randomized Response Models

Huang (2010 Huang , K. C. ( 2010 ). Unbiased estimators of mean, variance and sensitivity level for quantitative characteristics in finite population sampling . Metrika 71 : 341 – 352 .[Crossref], [Web of Science ®] , [Google Scholar]) proposed an optional randomized response model using a linear combination scrambling which is a generalization of the multiplicative scrambling of Eichhorn and Hayre (1983 Eichhorn , B. H. , Hayre , L. S. ( 1983 ). Scrambled randomized response methods for obtaining sensitive quantitative data . J. Statist. Plann. Infer. 7 : 307 – 316 .[Crossref], [Web of Science ®] , [Google Scholar]) and the additive scrambling of Gupta et al. (2006, 2010). In this article, we discuss two main issues. (1) Can the Huang (2010 Huang , K. C. ( 2010 ). Unbiased estimators of mean, variance and sensitivity level for quantitative characteristics in finite population sampling . Metrika 71 : 341 – 352 .[Crossref], [Web of Science ®] , [Google Scholar]) model be improved further by using a two-stage approach?; (2) Does the linear combination scrambling provide any benefit over the additive scrambling of Gupta et al. (2010 Gupta , S. N. , Shabbir , J. , Sehra , S. ( 2010 ). Mean and sensitivity estimation in optional randomized response models . J. Statist. Plann. Infer. 140 : 2870 – 2874 .[Crossref], [Web of Science ®] , [Google Scholar])? We will note that the answer to the first question is “yes” but the answer to the second question is “no.”     

Improved Bar-Lev,Bobovitch, and Boukai Randomized Response Models

In this article, two new improved randomized response models have been proposed. The proposed models are found to be more efficient than the recent randomized response model studied by Bar-Lev et al. (2004 Bar-Lev , S. K. , Bobovitch , E. , Boukai , B. ( 2004 ). A note on randomized response models for quantitative data . Metrika 60 : 255 – 260 .[Crossref], [Web of Science ®] , [Google Scholar]). The relative efficiency of the proposed models has been studied with respect to the Bar-Lev et al. (2004 Bar-Lev , S. K. , Bobovitch , E. , Boukai , B. ( 2004 ). A note on randomized response models for quantitative data . Metrika 60 : 255 – 260 .[Crossref], [Web of Science ®] , [Google Scholar]) model under different situations.     

A Similarity Measure Based on Species Proportions

ABSTRACT

There are several indices for measuring the similarity of two populations, including the ratio of the number of shared species to the number of distinct species (Jaccard's index) and the conditional probability of observing a shared species (Smith et al., 1996 Smith , W. , Solow , A. R. , Preston , P. E. ( 1996 ). An estimator of species overlap using a modified beta-binomial model. Biometrics 52 : 1472 – 1477 . [CSA] [CROSSREF] [Crossref], [Web of Science ®] , [Google Scholar]). However, these indices only take into account the number of species and species proportions of shared species. In this article, we propose a new similarity index which includes the species proportions of both the shared and non shared species in each population, and also propose a Nonparametric Maximum Likelihood Estimator (NPMLE) for this index. Bootstrap and delta methods are used to evaluate the standard errors of the NPMLE. Based on a loss function, we also compare a class of nonparametric estimators for the proposed index in various situations.     

The Modified Pulak and Al-Sultan's Model for Determining the Optimum Process Parameters

Economic selection of process parameters has been an important topic in modern statistical process control. The optimum process parameters setting have a major effect on the expected profit/cost per item. There are some concerns on the problem of setting process parameters. Boucher and Jafari (1991 Boucher , T. O. , Jafari , M. A. ( 1991 ). The optimum target value for single filling operations with quality sampling plans . J. Qual. Technol. 23 : 44 – 47 . [CSA] [Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) first considered the attribute single sampling plan applied in the selection of process target. Pulak and Al-Sultan (1996 Pulak , M. F. S. , Al-Sultan , K. S. ( 1996 ). The optimum targeting for a single filling operation with rectifying inspection . Omega 24 : 727 – 733 . [CSA] [CROSSREF] [Crossref], [Web of Science ®] , [Google Scholar]) extended Boucher and Jafari's model and presented the rectifying inspection plan for determining the optimum process mean. In this article, we further propose a modified Pulak and Al-Sultan model for determining the optimum process mean and standard deviation under the rectifying inspection plan with the average outgoing quality limit (AOQL) protection. Taguchi's (1986 Taguchi , G. ( 1986 ). Introduction to Quality Engineering . Asian Productivity Organization . [Google Scholar]) symmetric quadratic quality loss function is adopted for evaluating the product quality. By solving the modified model, we can obtain the optimum process parameters with the maximum expected profit per item and the specified quality level can be reached.     

Use of Two Decks of Cards in Randomized Response Techniques for Complex Survey Designs

The randomized response (RR) technique with two decks of cards proposed by Odumade and Singh (2009 Odumade , O. , Singh , S. ( 2009 ). Efficient use of two deck of cards in randomized response sampling . Commun. Statist. Theor. Meth. 38 : 439 – 446 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) can always be made more efficient than the RR techniques proposed by Warner (1965 Warner , S. L. ( 1965 ). Randomize response: A survey technique for eliminating evasive answer bias . J. Amer. Statist. Assoc. 60 : 63 – 69 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]), Mangat and Singh (1990 Mangat , N. S. , Singh , R. ( 1990 ). An alternative randomized response procedure . Biometrika 77 : 349 – 442 .[Crossref], [Web of Science ®] , [Google Scholar]), and Mangat (1994 Mangat , N. S. ( 1994 ). An improved randomized response strategy . J. Roy. Statist. Soc. B 56 : 93 – 95 . [Google Scholar]) by adjusting the proportion of cards in the decks. The proposed method of Odumade and Singh (2009 Odumade , O. , Singh , S. ( 2009 ). Efficient use of two deck of cards in randomized response sampling . Commun. Statist. Theor. Meth. 38 : 439 – 446 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) is limited to simple random sampling with replacement (SRSWR) sampling only. In this article, generalization of Odumade and Singh strategy is provided for complex survey designs and a wider class of estimators. The results of Odumade and Singh (2009 Odumade , O. , Singh , S. ( 2009 ). Efficient use of two deck of cards in randomized response sampling . Commun. Statist. Theor. Meth. 38 : 439 – 446 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) can be derived from the proposed method as a special case.     

A stratified Tracy and Osahan's two-stage randomized response model

ABSTRACT

This paper proposes an alternative two-stage stratified randomized response model based on Tracy and Osahan (1999 Tracy, D.S., Osahan, S.S. (1999). An improved randomized response technique. Pak. J. Stat. 15(1):1–6. [Google Scholar]) model that has an optimal allocation and large gain in precision. It is also shown that the proposed model is more efficient than Kim and Warde (2004 Kim, J., Warde, W. (2004). A stratified Warner randomized response model. J. Stat. Plan. Infer. 120:155–165.[Crossref], [Web of Science ®] , [Google Scholar]) and Kim and Elam (2005 Kim, J.M., Elam, M.E. (2005). A two-stage stratified Warner's randomized response model using optimal allocation. Metrika 61:1–7.[Crossref], [Web of Science ®] , [Google Scholar]) stratified randomized response models under the conditions presented in both the cases of completely truthful reporting and that of not completely truthful reporting by the respondents. Numerical illustrations and graphs are also given in support of the present study.     

On the Feasibility of Basing Horvitz and Thompson's Estimator on a Sample by Rao,Hartley, and Cochran's Scheme

Formulae for the first and second order inclusion probabilities for the Rao et al. (1962 Rao , J. N. K. , Hartley , H. O. , Cochran , W. G. ( 1962 ). On a simple procedure of unequal probability sampling without replacement . J. Roy. Statist. Soc. B 24 : 482 – 491 . [CSA]  [Google Scholar]) (RHC) scheme of sampling are derived. They enable one to evaluate, for a sample drawn according to the RHC scheme, the Horvitz and Thompson's (1952 Horvitz , D. G. , Thompson , D. J. ( 1952 ). A generalization of sampling without replacement from a finite universe . J. Amer. Statist. Assoc. 47 : 663 – 685 . [CSA] [Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) estimator (HTE) along with its unbiased variance estimator given by Yates and Grundy (1953 Yates , F. , Grundy , P. M. ( 1953 ). Selection without replacement from within strata with probability proportional to size . J. Amer. Statist. Assoc. 75 : 206 – 211 . [CSA]  [Google Scholar]). So, for a sample at hand thus drawn one may choose between the RHCE and the HTE for use on finding which one has the smaller coefficient of variation.     

An Efficiency and Protection Degree-Based Comparison Among the Quantitative Randomized Response Strategies

There have been many alternative strategies for implementing sampling survey on quantitative characteristic of sensitive issues by using randomized response (RR) technique. The efficiency of most of those strategies has been improved by choosing the suitable design parameters of model. However, the two different procedures with pre-assigned design parameter values cannot ensure that they possess the same protection degree to the respondents. Some earlier comparisons of those strategies are inadequate (as in Eichhorn and Hayre, 1983 Eichhorn , B. H. , Hayre , L. S. ( 1983 ). Scrambled randomized response methods for obtaining sensitive quantitative data . J. Statist. Plann. Infer. 7 : 307 – 316 .[Crossref], [Web of Science ®] , [Google Scholar]; Gupta et al., 2002 Gupta , S. , Gupta , B. , Singh , S. ( 2002 ). Estimation of sensitivity level of personal interview survey questions . J. Statist. Plann. Infer. 100 ( 2 ): 239 – 247 .[Crossref], [Web of Science ®] , [Google Scholar]). Some literature contains a more comprehensive comparison based on efficiency and protection degree to the respondents among the qualitative characteristic RR techniques (see Bhargava and Singh, 2002 Bhargava , M. , Singh , R. ( 2002 ). On the efficiency comparison of certain randomized response strategies . Metrika 55 : 191 – 197 .[Crossref], [Web of Science ®] , [Google Scholar]; Nayak, 1994 Nayak , T. K. ( 1994 ). On randomized response surveys for estimating a proportion . Commun. Statist. Theor. Meth. 23 ( 11 ): 3303 – 3321 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]; Zaizai and Zankan, 2004 Zaizai , Y. , Zankan , N. ( 2004 ). A fair comparison of the randomized response strategies . Acta Mathematica Scientia 24A ( 3 ): 362 – 368 . [Google Scholar]). As far as the comparisons are concerned that are based on efficiency and protection degree to the respondents among the quantitative characteristic RR techniques, very few related studies have been found so far. The purpose of this article is to give a more adequate comparison among those earlier quantitative characteristic RR strategies. It is found that several important differences between the results obtained in this article and some known results exist. Therefore, these earlier RR strategies should be reevaluated.     

Improved strategy to collect sensitive data by using geometric distribution as a randomization device

Abstract

In this article, we improvise Singh and Grewal (2013 Singh, S., and I. S. Grewal. 2013. Geometric distribution as a randomization device implemented in the Kuk’s model. International Journal of Contemporary Mathematical Sciences 8:243–8.[Crossref] , [Google Scholar]) and Hussain et al. (2016 Hussain, Z., J. Shabbir, Z. Pervez, S. F. Shah, and M. Khan. 2016. Generalized geometric distribution of order k: A flexible choice to randomize the response. Communications in Statistics: Simulation and Computation 46:4708–21.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) techniques by introducing a new two-stage randomization response process. Using the proposed new technique, we achieve better efficiency and increasing protection of privacy of respondents than the Kuk (1990 Kuk, A. Y. C. 1990. Asking sensitive questions indirectly. Biometrika 77 (2):436–8.[Crossref], [Web of Science ®] , [Google Scholar]), Singh and Grewal (2013 Singh, S., and I. S. Grewal. 2013. Geometric distribution as a randomization device implemented in the Kuk’s model. International Journal of Contemporary Mathematical Sciences 8:243–8.[Crossref] , [Google Scholar]) and Hussain et al. (2016 Hussain, Z., J. Shabbir, Z. Pervez, S. F. Shah, and M. Khan. 2016. Generalized geometric distribution of order k: A flexible choice to randomize the response. Communications in Statistics: Simulation and Computation 46:4708–21.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) models. The relative efficiency and protection of the respondents of the proposed two-stage randomization device have been investigated through simulation study, and the situations are reported where the proposed estimator performs better than its competitors. The SAS code used to investigate the performance of the proposed strategy are also provided.     

Stratification: Measuring and Inference

ABSTRACT

Stratification of distribution functions is an important issue in the area of income distributions. Two distribution functions form a perfect stratification if they occupy disjoint ranges on the horizontal axis. Otherwise, there is overlapping. A measure which quantifies the amount of stratification is introduced by Yitzhaki (1994 Yitzhaki , S. ( 1994 ). Economic distance and overlapping of distributions . J. Econometrics 61 : 147 – 159 . [CSA] [CROSSREF] [Crossref], [Web of Science ®] , [Google Scholar]), but no procedure for drawing inference is suggested. We develop a consistent estimator of the degree of overlapping and offer a nonparametric procedure for inference. Its limiting distribution, properly standardized, is normal. The asymptotic variance can be estimated using the jackknife method, and simulations show that the suggested procedure works well for sample sizes of 50 (100 for some cases).     

Estimation of Ordered Means of Two Poisson Distributions

In this article, we discuss the estimation of linear functions of two Poisson means, on which an order restriction is given. We give a necessary and sufficient condition on the coefficients of the linear function for the maximum likelihood estimator (MLE) which satisfies the order restriction to dominate the unbiased estimator under squared error loss. Furthermore, simultaneous estimation of two ordered Poisson means is considered and we suggest the Clevenson–Zidek type modification of MLE which dominates the MLE under normalized squared error loss. We also improve the estimator proposed by Clevenson and Zidek (1975 Clevenson , M. , Zidek , J. ( 1975 ). Simultaneous estimation of the means of independent Poisson laws . J. Amer. Statist. Assoc. 70 : 698 – 705 . [CSA] [CROSSREF] [Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) which ignores the order restriction.     

A New Estimator of Population Mean in Stratified Sampling

Kadilar and Cingi (2005 Kadilar , C. , Cingi , H. ( 2005 ). A new ratio estimator in stratified sampling . Comm. Statist. Theory Meth. 34 : 1 – 6 . [CSA] [Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) have suggested a new ratio estimator in stratified sampling. The efficiency of this estimator is compared with the traditional combined ratio estimator on the basis of mean square error (MSE). We propose another estimator by utilizing a simple transformation introduced by Bedi (1996 Bedi , P. K. ( 1996 ). Efficient utilization of auxiliary information at estimation stage . Biomet. J. 38 ( 8 ): 973 – 976 . [CSA] [Crossref], [Web of Science ®] , [Google Scholar]). The proposed estimator is found to be more efficient than the traditional combined ratio estimator as well as the Kadilar and Cingi (2005 Kadilar , C. , Cingi , H. ( 2005 ). A new ratio estimator in stratified sampling . Comm. Statist. Theory Meth. 34 : 1 – 6 . [CSA] [Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) ratio estimator.     

Inferences on partial linear models with right censored data by empirical likelihood

ABSTRACT

This article considers inference for partial linear models with right censored data. We use empirical likelihood based on the Buckley and James (1979 Buckley, J., James, I. (1979). Linear regression with censored data. Biometrika 66:429–436.[Crossref], [Web of Science ®] , [Google Scholar]) estimating equation to derive the confidence region for the regression parameter. We introduce an adjusted empirical likelihood ratio statistic for the parameter of interest and show that its limiting distribution is standard chi-square. A simulation is carried out to compare our method with the synthetic data approach in Wang and Li (2002 Wang, Q.-H., Li, G. (2002). Empirical Likelihood Semiparametric Regression Analysis under Random Censorship. J. Multivariate Anal. 83:469–486.[Crossref], [Web of Science ®] , [Google Scholar]).     

On Simultaneous Estimation of the Number of Signals and Frequencies of Multiple Sinusoids When Some Observations Are Missing

In an earlier article (Bai et al., 1999 Bai , Z. D. , Rao , C. R. , Wu , Y. H. , Zen , M. M. , Zhao , L. C. ( 1999 ). The simultaneous estimation of the number of signals and frequencies of multiple sinusods when some observations are missing: I. Asymptotics . Proc. Natl. Acad. Sci. 96 : 11,106 – 11,110 . [CSA] [Crossref], [Web of Science ®] , [Google Scholar]), the problem of simultaneous estimation of the number of signals and frequencies of multiple sinusoids is considered in the case that some observations are missing. The number of signals is estimated with an information theoretic criterion and the frequencies are estimated with eigenvariation linear prediction. Asymptotic properties of the procedure are investigated but the Monte Carlo simulation is not performed. In this article, a slightly different but scale invariant criterion for detection is proposed and the estimation of frequencies remains the same. Asymptotic properties of this new procedure are provided. Monte Carlo Simulation for both procedures is carried out. Furthermore, comparison on the real signals is also given.     

Revisiting Beal's Confidence Intervals for the Difference of Two Binomial Proportions

Confidence interval construction for the difference of two independent binomial proportions is a well-known problem with a full panoply of proposed solutions. In this paper, we focus largely on the family of intervals proposed by Beal (1987 Beal , S. ( 1987 ). Asymptotic confidence intervals for the difference between two binomial parameters for use with small samples . Biometrics 43 : 941 – 950 . [CSA] [CROSSREF] [Crossref], [PubMed], [Web of Science ®] , [Google Scholar]). This family, which includes the Haldane and Jeffreys–Perks intervals as special cases, assumes a symmetric prior distribution for the population proportions p ₁ and p ₂. We propose new methods that allow the currently observed data to set the prior distribution by taking a parametric empirical-Bayes approach; in addition, we also provide an investigation of the new interval' behaviors in small-sample situations. Unlike other solutions, our intervals can be used adaptively for experiments conducted in multiple stages over time. We illustrate this notion using data from an Argentinean study involving the Mal Rio Cuarto virus and its transmission to susceptible maize crops.     

Some Modifications for Choosing Ridge Parameters

Standard least square regression can produce estimates having a large mean squares error (MSE) when predictor variables are highly correlated or multicollinear. In this article, we propose four modifications to choose the ridge parameter (K) when multicollinearity exists among the columns of the design matrix. The proposed new estimators are extended versions of that suggested by Khalaf and Shukur (2005 Khalaf , G. , Shukur , G. ( 2005 ). Choosing ridge parameter for regression problems . Commun. Statist. A 34 : 1177 – 1182 . [CSA] [Taylor & Francis Online] , [Google Scholar]). The properties of these estimators are compared with those of Hoerl and Kennard (1970a Hoerl , A. E. , Kennard , R. W. ( 1970a ). Ridge regression: biased estimation for non-orthogonal problems . Tech. . 12 : 55 – 67 . [CSA] [Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) and the OLS using the MSE criterion. All estimators under consideration are evaluated using simulation techniques under certain conditions where a number of factors that may affect their properties have been varied. In addition, it is shown that at least one of the proposed estimators either has a smaller MSE than the others or is the next best otherwise.     

Methods for Bivariate Survival Data with Mismeasured Covariates Under an Accelerated Failure Time Model

Accelerated failure time models are useful in survival data analysis, but such models have received little attention in the context of measurement error. In this paper we discuss an accelerated failure time model for bivariate survival data with covariates subject to measurement error. In particular, methods based on the marginal and joint models are considered. Consistency and efficiency of the resultant estimators are investigated. Simulation studies are carried out to evaluate the performance of the estimators as well as the impact of ignoring the measurement error of covariates. As an illustration we apply the proposed methods to analyze a data set arising from the Busselton Health Study (Knuiman et al., 1994 Knuiman , M. W. , Cullent , K. J. , Bulsara , M. K. , Welborn , T. A. , Hobbs , M. S. T. ( 1994 ). Mortality trends, 1965 to 1989, in Busselton, the site of repeated health surveys and interventions . Austral. J. Public Health 18 : 129 – 135 . [CSA] [Crossref], [PubMed] , [Google Scholar]).     

Parametric Nonlinear Regression with Endogenous Switching

Based on the insightful work of Olsen (1980 Olsen , R. J. ( 1980 ). A least squares correction for selectivity bias . Econometrica 48 : 1815 – 1820 .[Crossref], [Web of Science ®] , [Google Scholar]) for the linear context, a generic and unifying framework is developed that affords a simple extension of the classical method of Heckman (1974 Heckman , J. ( 1974 ). Shadow prices, market wages, and labor supply . Econometrica 42 : 679 – 694 .[Crossref], [Web of Science ®] , [Google Scholar], 1976 Heckman , J. ( 1976 ). The common structure of statistical models of truncation sample selection and limited dependent variables and a simple estimator for such models . Annals of Economic and Social Measurement 5 : 475 – 492 . [Google Scholar], 1978 Heckman , J. ( 1978 ). Dummy endogenous variables in a simultaneous equation system . Econometrica 46 : 931 – 959 .[Crossref], [Web of Science ®] , [Google Scholar], 1979 Heckman , J. ( 1979 ). Sample selection bias as a specification error . Econometrica 47 : 153 – 161 .[Crossref], [Web of Science ®] , [Google Scholar]) to a broad class of nonlinear regression models involving endogenous switching and its two most common incarnations, endogenous sample selection and endogenous treatment effects. The approach should be appealing to applied researchers for three reasons. First, econometric applications involving endogenous switching abound. Secondly, the approach requires neither linearity of the regression function nor full parametric specification of the model. It can, in fact, be applied under the minimal parametric assumptions—i.e., specification of only the conditional means of the outcome and switching variables. Finally, it is amenable to relatively straightforward estimation methods. Examples of applications of the method are discussed.