A Note on Bootstrap for Gupta’s Subset Selection Procedure

A zero‐inflated proportional odds (ZIPO) regression model is proposed as an alternative for analyzing ordinal categorical response data characterized by an excess of zeros beyond what a proportional odds regression model accounts for. To address the challenge of parameter estimation in the ZIPO regression model when covariates are missing at random, we recommend the use of the inverse probability weighting method and the nonparametric multiple imputation method. Variance estimation is conducted through Rubin‐type and two proposed bootstrap methods. Simulations are carried out to assess the finite‐sample performances of the Rubin‐type method and the two proposed bootstrap methods. The results of the simulations suggest that the performances of the two proposed bootstrap methods are comparable and generally superior to the Rubin‐type method, as indicated by the agreement between empirical standard deviation and empirical (or mean) asymptotic standard error. To illustrate the practical application of the proposed estimation methods, we utilize a survey data set capturing violations of traffic rules among motorcyclist respondents in Taiwan.

On the Accuracy of Gaussian Approximation to the Distribution Functions of Sums of Independent Variables

In this paper, the origin of selection and ranking problems is discussed. The two basic approaches to the selection problem—the indifference zone approach and the subset selection approach—are reviewed briefly. Gupta's subset selection procedure is applied to motor vehicle fatality data which fit into a two-way layout.

On the Chebyshev-Cramér Asymptotic Expansions

Confidence interval localization of pipeline leakage via the bootstrap method

Bootstrap is a widely applicable computational statistical method. The focus of this paper lies in developing a bootstrap method for linear mixed models under homoscedasticity violation (heteroscedasticity) in variance of errors. We assume that the form of heteroscedasticity is unknown. To generate bootstrap response data as close as possible to the actual response data, we transform the marginal residuals to ensure that the variance of the modified marginal residuals in bootstrap samples is an unbiased estimator for the variance of the response variable in the linear mixed models. The consistency is proved, implying that the parameter estimators by the proposed method are asymptotically unbiased. The simulations are conducted with varying error terms and sample sizes to show improvement of the proposed method in parameter estimation. The simulation results are compared to demonstrate that the proposed method outperforms the other considered approaches including the wild method in the heteroscedastic linear mixed models under small samples and performs competitively with the parametric method and both methods outperform the other considered methods in homoscedastic linear mixed models. The proposed bootstrap method is applied to squid data for illustration of its effectiveness.

In this article, multiple comparison procedures with the average of scale parameters for normal and exponential populations are proposed. A subset selection procedure and a confidence interval procedure are investigated. These procedures will have broad applicability in identifying groups of treatments with smaller than the average, larger than the average and not different from the average variability in various fields. Bonferroni inequality is used to bound the probability of a correct selection and the coverage probability of confidence intervals. The Pearson’s approximation to the sampling distribution of the log chi-square ratio utilized in both subset selection and confidence intervals is shown to be satisfactory compared with the simulation results. Statistical tables to implement these procedures for the case of equal sample sizes are provided for use in practice.

: It is well over three decades since statistical inference problems were first posed in the now familiar selection and ranking framework. This paper deals with the subset selection theory mainly developed by Gupta and his associates. Our aim is to provide a historical perspective, and trace the major developments that took place in the subset selection theory over the years 1950- 1980 which is divided into three periods representing early developments, years of main growth and years of further strides. We also discuss recent developments and briefly assess the impact of these developments of the users.

Reliability estimation of the selected exponential populations

In this paper we propose a bootstrap method for quasi-maximum likelihood (QML) estimators in GARCH(1,1) models. The wild bootstrap is used to bootstrap GARCH(1,1) processes and construct bootstrap QML estimators. It is shown that this bootstrap procedure “works” in the sense that it is consistent. Simulation results demonstrate the small sample behaviour of the proposed bootstrap method.

A common question in biological experimentation is concerned with finding an optimal level for a treatment using data obtained from a designed experiment. For example, an experiment might concern a group of hyperactive adolescent males that have been grouped into blocks according to some relevant factors. Within each group the subjects are randomly assigned to several treatments for hyperactivity. An important aspect of the study would then be determining which of the treatment options is most effective in reducing hyperactivity in the subjects. Basing such a determination directly on the estimated treatment effects may be unreliable because of the inherent variability associated with the estimates. Other methods, such as multiple comparison procedures and best subset selection procedures can also be applied to this problem. Unfortunately, such procedures are often difficult to interpret and rely on assumptions that may not be appropriate for the experiment under consideration. In this paper we develop a method of assigning a confidence level to each treatment that measures how confident we are that each treatment is optimal. The method for assigning the confidence levels is based on a more general methodology developed for the problem of regions, where one assigns levels of confidence that an unknown parameter is within specified subsets of the parameter space. The actual computation of the confidence levels is based on the bootstrap. The method is applied to an example and is studied empirically.

This paper considers a stochastic system simulation with unknown input distribution parameters and assumes the availability of a limited amount of historical data for parameter estimation. We investigate how to account for parameter uncertainty - the uncertainty that is due to the estimation of the input distribution parameters from historical data of finite length - in a subset selection procedure that identifies the stochastic system designs whose sample means are within a user-specified distance of the best mean performance measure. We show that even when the number of simulation replications is large enough for the stochastic uncertainty to be negligible, the amount of parameter uncertainty in output data imposes a threshold on the user-specified distance for an effective use of the subset selection procedure for simulation. We demonstrate the significance of this effect of parameter uncertainty for a multi-item inventory system simulation in the presence of short demand histories.

Market structure models are used to identify submarkets or to test for the presence of submarkets where within-group competition is much stronger than across group competition. The implicit assumption in such models is that the brands in a submarket compete on the basis of their shared product features. However, if significant variety-seeking effect exist in the market, such an assumption may not be valid. We present a model based on a subset selection procedure for analyzing competitive market structures and develop tests of significance for variety-seeking effects present in the market. For each brand in the market, the subset selection procedure identifies sets (submarkets) of brands that are in “close” competition. The competitive market structure is defined by the possibly overlapping submarkets that are identified for each brand and the model provides insights on whether the brands in a submarket are of a reinforcing or a variety-seeking kind. The application of our model to two different consumer packaged goods markets highlights its contribution relative to extant methods.

This chapter deals with applications of the input selection strategies introduced in Chapter 15. First, a static process whose characteristics are well-known is studied. Some variables influence the output in a linear way, others in nonlinear ways. The sophisticated local model network-based input selection strategy successfully assigned the linear variable to the consequent space only, while the nonlinear variables are assigned to the premise space as well. This is in perfect alignment with the best-case scenario. This theoretically optimal result was achieved based on the information in the data only. Second, the efficiencies of two fans were modeled by computational fluid dynamics (CFD) – an axial and a radial fan. With local model networks metamodels were built approximating the CFD simulation results. Input selection could automatically discover the inputs considered most relevant by experts. They were selected as the most important ones by the subset selection procedure. Finally, a dynamic process HVAC process has been modeled as a basis for predictive control design. Here the input selection automatically discovered not only the relevant physical inputs but also the orders and dead times. This corresponds to an extremely high-dimensional input selection problem since 6 physical inputs/outputs with a time delay between 1 and 10 acted as potential input variables for the premises and consequents of the local model network.

Enumerating maximal-order abelian groups within a set of eligible elements