A two-stage procedure for selecting the best of k exponential distributions

The problem of selecting the best of k exponential distributions with different guarantee times and the same unknown variance is considered. A two-stage procedure, similar to the one considered by Bechhofer, Dunnett and Sobel (1954), is given. Some specific guidelines for selecting the first-stage sample size are also given.     

Confidence sets based on sequential Tests

For given (small) a and β a sequential confidence set that covers the true parameter point with probability at least 1 - a and one or more specified false parameter points with probability at most β can be generated by a family of sequen-tial tests. Several situations are described where this approach would be a natural one. The following example is studied in some detail: obtain an upper (1 - α)-confidence interval for a normal mean μ (variance known) with β-protection at μ - δ(μ), where δ(.) is not bounded away from 0 so that a truly sequential procedure is mandatory. Some numerical results are presented for intervals generated by (1) sequential probability ratio tests (SPRT's), and (2) generalized sequential probability ratio tests (GSPRT's). These results indicate the superiority of the GSPRT-generated intervals over the SPRT-generated ones if expected sample size is taken as performance criterion     

A four-moment approach and other practical solutions to the behrens-f1sher problem

Fixed sample size approximately similar tests for the Behrens-Fisher problem are studied and compared with various other tests suggested in current sttistical methodelogy texts. Several fourmoment approxiamtely similar tests are developed and offered as alternatives. These tests are shown to be good practical solutions which are easily implemented in practice.     

A method of power assessment for tests comparing several treatments with a control

A method of power assessment for the problem of comparing several treatments with a control is considered. Power assessment is based on the power function of a two-sided hypothesis test that none of the treatment is different from the control. Normally distributed data and binary response data are considered. Minimum power levels are found under certain easily interpretable range conditions on the treatment and control means or success probabilities. Expressions are provided allowing simple computer evaluation of minimum guaranteed power levels, and some illustrative tables of power levels are given.     

Use of ranks in probability propoetional to size sampling

Use of ranks in unequal probability sampling is examined for sample selection, stratification as well as determining the strata boundaries. A few sampling schemes are proposed and investigated, For samples of size two, two sampling schemes and their 1PPS versions are discussed, An extension of these schemes to general sample sizes is outlined. Nonnegative unbiased variance estimators are proposed in each case, An empirical comparison is included.     

On the sample breakdown robustness of some nonparametric tests

In this paper, relying on the sample breakdown points, we investigate the sample breakdown properties of some nonparametric tests. It is shown that the sample breakdown points of the sign test asymptotically dominate those of the Wilcoxon test for one–sided hypotheses, However, the different conclusion is derived in the case of testing some shrinking neighborhood hypotheses. The breakdown behaviors of the Kolmogorov test and X²–test are also explored. These studies unify or refine some existing breakdown analyses of tests.     

Sliced inverse regression under linear constraints

We consider the semiparametric regression model introduced by Li (1991) and add to this model some linear constraints on the slope parameters. These constraints can be identifiability conditions or they may carry additional in¬formations on the slope parameters. Using a geometric argument, we develop a method to estimate the slope parameters. This link-free and distribution-free method splits in two steps: the first is a Sliced Inverse Regression (SIR); Canonical Analysis is used at the second step to transform the SIR estimates so that they satisfy the constraints. We establish yn-consistency and obtain the asymptotic distribution of the estimates.

This estimation method is applied to the general sample selection model which is very useful in Econometrics. A simulation study shows that the method performs well in the example considered.     

Estimation of Laspeyres Price Indexes Using the Prediction Approach for Finite Population Sampling

Estimators of chain and fixed-base Laspeyres price indexes are studied using the prediction approach to finite population sampling. The estimators include some that are based on those used in several U.S. government index programs and others derived from prediction models. Biases and variances of the estimators are studied for a case in which the reference period index weights are unknown for nonsample items. Under a model for a one-period price change in which items have common within-stratum means, unbiased estimators can be constructed, but under a more general regression model, special sample balance conditions are needed for unbiasedness of those estimators. The theory for the estimators of fixed-base indexes is illustrated in an empirical study using a population of items priced for the U.S. Consumer Price Index.     

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.