A Simulation Study on the Probability of Correct Selection for Large k Populations

An increasing number of contemporary datasets are high dimensional. Applications require these datasets be screened (or filtered) to select a subset for further study. Multiple testing is the standard tool in such applications, although alternatives have begun to be explored. In order to assess the quality of selection in these high-dimensional contexts, Cui and Wilson (2008b Cui , X. , Wilson , J. ( 2008b ). On the probability of correct selection for large k populations with application to microarray data . Biometrical Journal 50 ( 5 ): 870 – 883 .[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]) proposed two viable methods of calculating the probability that any such selection is correct (PCS). PCS thereby serves as a measure of the quality of competing statistics used for selection. The first simulation study of this article investigates the two PCS statistics of the above article. It shows that in the high-dimensional case PCS can be accurately estimated and is robust under certain conditions. The second simulation study investigates a nonparametric estimator of PCS.     

Selecting a Good Stochastic System for the Large Number of Alternatives

In this article, we present the problem of selecting a good stochastic system with high probability and minimum total simulation cost when the number of alternatives is very large. We propose a sequential approach that starts with the Ordinal Optimization procedure to select a subset that overlaps with the set of the actual best m% systems with high probability. Then we use Optimal Computing Budget Allocation to allocate the available computing budget in a way that maximizes the Probability of Correct Selection. This is followed by a Subset Selection procedure to get a smaller subset that contains the best system among the subset that is selected before. Finally, the Indifference-Zone procedure is used to select the best system among the survivors in the previous stage. The numerical test involved with all these procedures shows the results for selecting a good stochastic system with high probability and a minimum number of simulation samples, when the number of alternatives is large. The results also show that the proposed approach is able to identify a good system in a very short simulation time.     

A Class of Two-Stage Selection Procedures Using L-Statistics

Summary: A class of selection procedures for selecting the least dispersive distribution from k available distributions has been proposed. This problem finds applications in reliability and engineering. In engineering, for example, the goal of the experimenter is to select a firm whose components have least dispersive distribution from the available set of competing firms manufacturing the components of the desired specifications meant for the same purpose. The proposed procedures can be used even when the underlying distributions belong to different families. Applications of the proposed selection procedures are discussed by taking exponential, gamma and Lehmann type distributions. Performance of the proposed selection procedures is assessed through simulation study. Implementation of the proposed selection procedure is illustrated through an example. * The authors are very grateful to the editor and referees for their valuable comments.     

Multinomial Selection in the Presence of Infinite Alternatives

We propose a new procedure for the multinomial selection problem to solve a real problem of any modern Air Force: the elaboration of better air-to-air tactics for Beyond Visual Range air-to-air combat that maximize its aircraft survival probability H(θ, ω), as well as enemy aircraft downing probability G(θ, ω). In this study, using a low-resolution simulator with generic parameters for the aircraft and missiles, we could increase an average success rate of 16.69% and 16.23% for H(θ, ω) and G(θ, ω), respectively, to an average success rate of 76.85% and 79.30%. We can assure with low probability of being wrong that the selected tactic has greater probability of yielding greater success rates in both H(θ, ω) and G(θ, ω) than any simulated tactic.     

Treatment Evaluation in the Presence of Sample Selection

Sample selection and attrition are inherent in a range of treatment evaluation problems such as the estimation of the returns to schooling or training. Conventional estimators tackling selection bias typically rely on restrictive functional form assumptions that are unlikely to hold in reality. This paper shows identification of average and quantile treatment effects in the presence of the double selection problem into (i) a selective subpopulation (e.g., working—selection on unobservables) and (ii) a binary treatment (e.g., training—selection on observables) based on weighting observations by the inverse of a nested propensity score that characterizes either selection probability. Weighting estimators based on parametric propensity score models are applied to female labor market data to estimate the returns to education.     

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.     

Entropy-Based Moment Selection in the Presence of Weak Identification

Hall et al. (2007 Hall , A. R. , Inoue , A. , Jana , K. , Shin , C. (2007). Information in generalized method of moments estimation and entropy based moment selection. Journal of Econometrics 138:488–512.[Crossref] , [Google Scholar]) propose a method for moment selection based on an information criterion that is a function of the entropy of the limiting distribution of the Generalized Method of Moments (GMM) estimator. They establish the consistency of the method subject to certain conditions that include the identification of the parameter vector by at least one of the moment conditions being considered. In this article, we examine the limiting behavior of this moment selection method when the parameter vector is weakly identified by all the moment conditions being considered. It is shown that the selected moment condition is random and hence not consistent in any meaningful sense. As a result, we propose a two-step procedure for moment selection in which identification is first tested using a statistic proposed by Stock and Yogo (2003 Stock , J. H. , Yogo , M. ( 2003 ). Testing for weak instruments in linear IV regression . Discussion paper, Kennedy School of Government, Harvard University, Cambridge, MA . [Google Scholar]) and then only if this statistic indicates identification does the researcher proceed to the second step in which the aforementioned information criterion is used to select moments. The properties of this two-step procedure are contrasted with those of strategies based on either using all available moments or using the information criterion without the identification pre-test. The performances of these strategies are compared via an evaluation of the finite sample behavior of various methods for inference about the parameter vector. The inference methods considered are based on the Wald statistic, Anderson and Rubin's (1949 Anderson , T. W. , Rubin , H. ( 1949 ). Estimation of the parameters of a single equation in a complete system of stochastic equations . Annals of Mathematical Statistics 20 : 46 – 63 .[Crossref] , [Google Scholar]) statistic, Kleibergen (2002 Kleibergen , F. ( 2002 ). Pivotal statistics for testing structural parameters in instrumenatl variables regression . Econometrica 70 : 1781 – 1803 .[Crossref], [Web of Science ®] , [Google Scholar]) K statistic, and combinations thereof in which the choice is based on the outcome of the test for weak identification.     

Data-Based Choice of the Number of Pilot Stages for Plug-in Bandwidth Selection

The choice of the bandwidth is a crucial issue for kernel density estimation. Among all the data-dependent methods for choosing the bandwidth, the direct plug-in method has shown a particularly good performance in practice. This procedure is based on estimating an asymptotic approximation of the optimal bandwidth, using two “pilot” kernel estimation stages. Although two pilot stages seem to be enough for most densities, for a long time the problem of how to choose an appropriate number of stages has remained open. Here we propose an automatic (i.e., data-based) method for choosing the number of stages to be employed in the plug-in bandwidth selector. Asymptotic properties of the method are presented and an extensive simulation study is carried out to compare its small-sample performance with that of the most recommended bandwidth selectors in the literature.     

Variable Selection via Regression Trees in the Presence of Irrelevant Variables

Many tree algorithms have been developed for regression problems. Although they are regarded as good algorithms, most of them suffer from loss of prediction accuracy when there are many irrelevant variables and the number of predictors exceeds the number of observations. We propose the multistep regression tree with adaptive variable selection to handle this problem. The variable selection step and the fitting step comprise the multistep method.

The multistep generalized unbiased interaction detection and estimation (GUIDE) with adaptive forward selection (fg) algorithm, as a variable selection tool, performs better than some of the well-known variable selection algorithms such as efficacy adaptive regression tube hunting (EARTH), FSR (false selection rate), LSCV (least squares cross-validation), and LASSO (least absolute shrinkage and selection operator) for the regression problem. The results based on simulation study show that fg outperforms other algorithms in terms of selection result and computation time. It generally selects the important variables correctly with relatively few irrelevant variables, which gives good prediction accuracy with less computation time.     

Lag Length Selection for Unit Root Tests in the Presence of Nonstationary Volatility

A number of recent papers have focused on the problem of testing for a unit root in the case where the driving shocks may be unconditionally heteroskedastic. These papers have, however, taken the lag length in the unit root test regression to be a deterministic function of the sample size, rather than data-determined, the latter being standard empirical practice. We investigate the finite sample impact of unconditional heteroskedasticity on conventional data-dependent lag selection methods in augmented Dickey–Fuller type regressions and propose new lag selection criteria which allow for unconditional heteroskedasticity. Standard lag selection methods are shown to have a tendency to over-fit the lag order under heteroskedasticity, resulting in significant power losses in the (wild bootstrap implementation of the) augmented Dickey–Fuller tests under the alternative. The proposed new lag selection criteria are shown to avoid this problem yet deliver unit root tests with almost identical finite sample properties as the corresponding tests based on conventional lag selection when the shocks are homoskedastic.     

A Characterization For Gpsd Signals In Additive Noise

In this paper we consider a convoluted generalized power series distibution and characterize the distributions by soiutions to system of differential equations. Characterization results are derived for Poisson, binomial, geometric and Pascal (negative binomial) as special cases and later unified with Samaniego [1976, 1980] and Samaniego and Gong [1979]

receiveddate="Oct1985" reviseddate="Jun1986"     

A Subset Selection Procedure for Selecting the Exponential Population Having the Longest Mean Lifetime When the Guarantee Times are the Same

ABSTRACT

Consider k(≥ 2) independent exponential populations Π₁, Π₂, …, Π _k , having the common unknown location parameter μ ∈ (?∞, ∞) (also called the guarantee time) and unknown scale parameters σ₁, σ₂, …σ _k , respectively (also called the remaining mean lifetimes after the completion of guarantee times), σ _i  > 0, i = 1, 2, …, k. Assume that the correct ordering between σ₁, σ₂, …, σ _k is not known apriori and let σ_[i], i = 1, 2, …, k, denote the ith smallest of σ _j s, so that σ_[1] ≤ σ_[2] ··· ≤ σ_[k]. Then Θ _i  = μ + σ _i is the mean lifetime of Π _i , i = 1, 2, …, k. Let Θ_[1] ≤ Θ_[2] ··· ≤ Θ_[k] denote the ranked values of the Θ _j s, so that Θ_[i] = μ + σ_[i], i = 1, 2, …, k, and let Π_(i) denote the unknown population associated with the ith smallest mean lifetime Θ_[i] = μ + σ_[i], i = 1, 2, …, k. Based on independent random samples from the k populations, we propose a selection procedure for the goal of selecting the population having the longest mean lifetime Θ_[k] (called the “best” population), under the subset selection formulation. Tables for the implementation of the proposed selection procedure are provided. It is established that the proposed subset selection procedure is monotone for a general k (≥ 2). For k = 2, we consider the loss measured by the size of the selected subset and establish that the proposed subset selection procedure is minimax among selection procedures that satisfy a certain probability requirement (called the P*-condition) for the inclusion of the best population in the selected subset.     

Selecting the normal population with the largest mean when the variances are bounded

A multiple decision approach to the problem of selecting the population with the largest mean was formulated by Bechhofer (1954), where a single-sample solution was presented for the case of normal populations with known variances. In this paper the problem of selecting the normal population with the largest mean is considered when the population variances are unequal and unknown but are constrained only to be less than a specified upper bound. It is demonstrated that a slight modification of Bechhofer' s procedure will suffice to ensure the probability requirements under this simple constraint for cases of practical interest.     

A Bayesian Approach for Multiple Response Surface Optimization in the Presence of Noise Variables

An approach for the multiple response robust parameter design problem based on a methodology by Peterson (2000) is presented. The approach is Bayesian, and consists of maximizing the posterior predictive probability that the process satisfies a set of constraints on the responses. In order to find a solution robust to variation in the noise variables, the predictive density is integrated not only with respect to the response variables but also with respect to the assumed distribution of the noise variables. The maximization problem involves repeated Monte Carlo integrations, and two different methods to solve it are evaluated. A Matlab code was written that rapidly finds an optimal (robust) solution in case it exists. Two examples taken from the literature are used to illustrate the proposed method.     

Operating Characteristics of a Subset Selection Procedure Applied to a Hybrid Randomized Response Model

The operating characteristics (OCs) of a subset ranking and selection procedure are derived for the hybrid randomized response model developed by Jia and McDonald (2009 Jia, F., McDonald, G. (2009). Analyzing hybrid randomized response data with a binomial selection procedure. Commun. Statist. Theor. Meth. 38:784807.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]). The OCs include the probability of a correct P(CS), the individual selection probability γ_i, and the expected subset size E(S), under the slippage configuration or the equi-spaced configuration. An example comparing failure rates of contraceptive methods is used to illustrate the use of these new results.     

Tuning Parameter Selection in Cox Proportional Hazards Model with a Diverging Number of Parameters

Regularized variable selection is a powerful tool for identifying the true regression model from a large number of candidates by applying penalties to the objective functions. The penalty functions typically involve a tuning parameter that controls the complexity of the selected model. The ability of the regularized variable selection methods to identify the true model critically depends on the correct choice of the tuning parameter. In this study, we develop a consistent tuning parameter selection method for regularized Cox's proportional hazards model with a diverging number of parameters. The tuning parameter is selected by minimizing the generalized information criterion. We prove that, for any penalty that possesses the oracle property, the proposed tuning parameter selection method identifies the true model with probability approaching one as sample size increases. Its finite sample performance is evaluated by simulations. Its practical use is demonstrated in The Cancer Genome Atlas breast cancer data.     

A Selection Procedure for Selecting the Least Increasing Failure Rate Average Distribution

For k independent absolutely continuous increasing failure rate average (IFRA) life distributions F_i, i = 1, 2, …, k, Link (1989 Link, W.A. (1989). Testing for exponentiality against monotone failure rate average alternatives. Commun. Statist. Theor. Meth. 18(8): 3009–3017.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) considered a measure of departure of against monotone failure rate average alternatives. In this paper, we use the measure defined by Link for detection of IFRA-ness of life distribution F_i. A two-stage selection procedure to select the least IFRA distribution is proposed. This selection procedure is based on a U-statistic which is an estimator of the measure and can be implemented even when the IFRA life distributions belong to different families. The applications of this procedure are discussed for some well known distributions.     

A Consistent Method for the Selection of Relevant Instruments

Abstract

In many applications, a researcher must select an instrument vector from a candidate set of instruments. If the ultimate objective is to perform inference about the unknown parameters using conventional asymptotic theory, then we argue that it is desirable for the chosen instrument vector to satisfy four conditions which we refer to as orthogonality, identification, efficiency, and non‐redundancy. It is impossible to verify a priori which elements of the candidate set satisfy these conditions; this can only be done using the data. However, once the data are used in this fashion it is important that the selection process does not contaminate the limiting distribution of the parameter estimator. We refer to this requirement as the inference condition. In a recent paper, Andrews [[Andrews, D. W. K. (1999)] Andrews, D. W.K. 1999. Consistent moment selection procedures for generalized method of moments estimation. Econometrica, 67: 543–564. [Crossref], [Web of Science ®] , [Google Scholar]. Consistent moment selection procedures for generalized method of moments estimation. Econometrica67:543–564] has proposed a method of moment selection based on an information criterion involving the overidentifying restrictions test. This method can be shown to select an instrument vector which satisfies the orthogonality condition with probability one in the limit. In this paper, we consider the problem of instrument selection based on a combination of the efficiency and non‐redundancy conditions which we refer to as the relevance condition. It is shown that, within a particular class of models, certain canonical correlations form the natural metric for relevancy, and this leads us to propose a canonical correlations information criterion (CCIC) for instrument selection. We establish conditions under which our method satisfies the inference condition. We also consider the properties of an instrument selection method based on the sequential application of [Andrews, D. W. K. (1999)] Andrews, D. W.K. 1999. Consistent moment selection procedures for generalized method of moments estimation. Econometrica, 67: 543–564. [Crossref], [Web of Science ®] , [Google Scholar]. Consistent moment selection procedures for generalized method of moments estimation. Econometrica67:543–564 method and CCIC.     

Selecting the best exponential population under Type-II progressive censoring scheme via empirical Bayes approach

The problem of selecting a population according to “selection and ranking” is an important statistical problem. The ideas in selecting the best populations with some demands having optimal criterion have been suggested originally by Bechhofer (1954 Bechhofer, R. E. (1954). A single-sample multiple-decision procedure for ranking means of normal populations with known variances. The Annals of Mathematical Statistics 25:16–39. [Google Scholar]) and Gupta (1956 Gupta, S. S. (1956). On a decision rule for a problem in ranking means. Mimeograph Series No. 150. Chapel Hill, North Carolina: University of North Carolina. [Google Scholar], 1965 Gupta, S. S. (1965). On some multiple decision (selection and ranking) rules. Technometrics 7:225–245. [Google Scholar]). In the area of ranking and selection, the large part of literature is connected with a single criterion. However, this may not satisfy the experimenter’s demand. We follow methodology of Huang and Lai (1999 Huang, W. T., Lai, Y. T. (1999). Empirical Bayes procedures for selecting the best population with multiple criteria. Annals of the Institute of Statistical Mathematics 51:281–299. [Google Scholar]) and the main focus of this article is to select a best population under Type-II progressively censored data for the case of right tail exponential distributions with a bounded and unbounded supports for μ_i. We formulate the problem and develop a Bayesian setup with two kinds of bounded and unbounded prior for μ_i. We introduce an empirical Bayes procedure and study the large sample behavior of the proposed rule. It is shown that the proposed empirical Bayes selection rule is asymptotically optimal.     

One stage multiple comparisons of k-1 treatment mean lifetimes with the control for exponential distributions under heteroscedasticity

Abstract

In survival or reliability data analysis, it is often useful to estimate the quantiles of the lifetime distribution, such as the median time to failure. Different nonparametric methods can construct confidence intervals for the quantiles of the lifetime distributions, some of which are implemented in commonly used statistical software packages. We here investigate the performance of different interval estimation procedures under a variety of settings with different censoring schemes. Our main objectives in this paper are to (i) evaluate the performance of confidence intervals based on the transformation approach commonly used in statistical software, (ii) introduce a new density-estimation-based approach to obtain confidence intervals for survival quantiles, and (iii) compare it with the transformation approach. We provide a comprehensive comparative study and offer some useful practical recommendations based on our results. Some numerical examples are presented to illustrate the methodologies developed.