Subset Selection Toward Optimizing the Best Performance at a Second Stage

In the search for the best of n candidates, two-stage procedures of the following type are in common use. In a first stage, weak candidates are removed, and the subset of promising candidates is then further examined. At a second stage, the best of the candidates in the subset is selected. In this article, optimization is not aimed at the parameter with largest value but rather at the best performance of the selected candidates at Stage 2. Under a normal model, a new procedure based on posterior percentiles is derived using a Bayes approach, where nonsymmetric normal (proper and improper) priors are applied. Comparisons are made with two other procedures frequently used in selection decisions. The three procedures and their performances are illustrated with data from a recent recruitment process at a Midwestern university.     

A Nonparametric Test for Deviation from Randomness with Applications to Stock Market Index Data

The proposed test detects deviations from randomness, without a priori distributional assumption, when observations are not independent and identically distributed (i.i.d.), which is suitable for our motivating stock market index data. Departures from i.i.d. are tested by subdividing data into subintervals and then using a conditional probability measure within intervals as a binomial test. This nonparametric test is designed to detect deviations of neighboring observations from randomness when the dataset consists of time series observations. Simulation results and a comparison with Lo and MacKinlay's (1988 Lo, A. W. and MacKinlay, A. C. 1988. Stock market prices do not follow random walks: Evidence from a simple specification test. The Review of Financial Studies, 1: 41–66. [Crossref], [Web of Science ®] , [Google Scholar]) variance ratio test showed that our proposed test is a competitive alternative.     

Fishery and Forestry Management

There are a large number of different definitions used for sample quantiles in statistical computer packages. Often within the same package one definition will be used to compute a quantile explicitly, while other definitions may be used when producing a boxplot, a probability plot, or a QQ plot. We compare the most commonly implemented sample quantile definitions by writing them in a common notation and investigating their motivation and some of their properties. We argue that there is a need to adopt a standard definition for sample quantiles so that the same answers are produced by different packages and within each package. We conclude by recommending that the median-unbiased estimator be used because it has most of the desirable properties of a quantile estimator and can be defined independently of the underlying distribution.     

Simulation-Based Tests that Can Use Any Number of Simulations

Conventional procedures for Monte Carlo and bootstrap tests require that B, the number of simulations, satisfy a specific relationship with the level of the test. Otherwise, a test that would instead be exact will either overreject or underreject for finite B. We present expressions for the rejection frequencies associated with existing procedures and propose a new procedure that yields exact Monte Carlo tests for any positive value of B. This procedure, which can also be used for bootstrap tests, is likely to be most useful when simulation is expensive.     

A Viable Alternative to Resorting to Statistical Tables

It is shown in this article that, given the moments of a distribution, any percentage point can be accurately determined from an approximation of the corresponding density function in terms of the product of an appropriate baseline density and a polynomial adjustment. This approach, which is based on a moment-matching technique, is not only conceptually simple but easy to implement. As illustrated by several applications, the percentiles so obtained are in excellent agreement with the tabulated values. Whereas statistical tables, if at all available or accessible, can hardly ever cover all the potentially useful combinations of the parameters associated with a random quantity of interest, the proposed methodology has no such limitation.     

A New Family of Nonparametric Quantile Estimators

A new core methodology for creating nonparametric L-quantile estimators is introduced and three new quantile L-estimators (SV1 _p , SV2 _p , and SV3 _p ) are constructed using the new methodology. Monte Carlo simulation was used in order to investigate the performance of the new estimators for small and large samples under normal distribution and a variety of light and heavy-tailed symmetric and asymmetric distributions. The new estimators outperform, in most of the cases studied, the Harrell–Davis quantile estimator and the weighted average at X _([np]) quantile estimator.     

An adaptive estimatcr frequently used in material fatigue testing

Small sample sizes in material fatigue tests give rise to an adaptive estimator of the 100(1-P)% normal percentile, which is the 100P% survival load. The mean squared relative efficiency of the best invariant estimator of normal percentiles to the adaptive estimator is dependent upon the unknown parameters only through the coefficient of variation. The adaptive estimator is shown to be more locally efficient than tl-:ebest invariant estimator over a subset of the parameter space. However, in the extreme values of P the coverage probabilities of the adaptive estimator provide little more protection than a traditional point estimator over the range of preference based on mean squared relative efficiency.     

A characterization of the Burr Type III and Type XII distributions through the method of percentiles and the Spearman correlation

A characterization of Burr Type III and Type XII distributions based on the method of percentiles (MOP) is introduced and contrasted with the method of (conventional) moments (MOM) in the context of estimation and fitting theoretical and empirical distributions. The methodology is based on simulating the Burr Type III and Type XII distributions with specified values of medians, inter-decile ranges, left-right tail-weight ratios, tail-weight factors, and Spearman correlations. Simulation results demonstrate that the MOP-based Burr Type III and Type XII distributions are substantially superior to their (conventional) MOM-based counterparts in terms of relative bias and relative efficiency.     

Discriminating among Weibull,log-normal,and log-logistic distributions

In this article, we consider the problem of the model selection/discrimination among three different positively skewed lifetime distributions. All these three distributions, namely; the Weibull, log-normal, and log-logistic, have been used quite effectively to analyze positively skewed lifetime data. In this article, we have used three different methods to discriminate among these three distributions. We have used the maximized likelihood method to choose the correct model and computed the asymptotic probability of correct selection. We have further obtained the Fisher information matrices of these three different distributions and compare them for complete and censored observations. These measures can be used to discriminate among these three distributions. We have also proposed to use the Kolmogorov–Smirnov distance to choose the correct model. Extensive simulations have been performed to compare the performances of the three different methods. It is observed that each method performs better than the other two for some distributions and for certain range of parameters. Further, the loss of information due to censoring are compared for these three distributions. The analysis of a real dataset has been performed for illustrative purposes.     

Nonparametric Shewhart-Type Sign Control Charts Based on Runs

Nonparametric control charts are considered for the median and other percentiles based on runs of sign statistics above and below the control limits. It is noted that the sign charts are advantageous in certain practical situations. Expressions for the run-length distributions are derived using Markov chain theory; several examples are given. The in-control (IC) and the out-of-control (OOC) performance of these charts are studied and compared to the existing nonparametric Wilcoxon signed-ranked charts of Chakraborti and Eryilmaz (2007 Chakraborti , S. , Eryilmaz , S. ( 2007 ). A nonparametric Shewhart-type signed-rank control chart based on runs . Commun. Statist. Simul. Computat. 36 ( 2 ): 335 – 356 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) under the normal, the double exponential and the Cauchy distributions, using the average run-length (ARL), the standard deviation of the run-length (SDRL), the false alarm rate (FAR) and some percentiles of the run-length, including the median run-length (MDRL). It is shown that the proposed “runs-rules enhanced” sign charts offer more practically desirable IC ARL (ARL ₀) and FAR values and perform better for some heavy-tailed distributions. Some concluding remarks are offered.