Coherent Frequentism: A Decision Theory Based on Confidence Sets

By representing fair betting odds according to one or more pairs of confidence set estimators, dual parameter distributions called confidence posteriors secure the coherence of actions without any prior distribution. This theory reduces to the maximization of expected utility when the pair of posteriors is induced by an exact or approximate confidence set estimator or when a reduction rule is applied to the pair. Unlike the p-value, the confidence posterior probability of an interval hypothesis is suitable as an estimator of the indicator of hypothesis truth since it converges to 1 if the hypothesis is true or to 0 otherwise.     

Unification of Dirichlet Methodology

In this article we provide a unified framework for solving Dirichlet related probability and waiting time problems. We consider a Pólya sampling scheme in which each time an object is selected, it is put back into the population along with c additional objects of the same type. By considering both fixed sample size and inverse sampling procedures, we unify the Dirichlet I, J, C, and D functions with their hypergeometric counterparts by extending these functions to Pólya sampling. We then use these functions to unify and extend the corresponding expected waiting time results.     

Nonparametric Predictive Inference for Ordinal Data

Nonparametric predictive inference (NPI) is a powerful frequentist statistical framework based only on an exchangeability assumption for future and past observations, made possible by the use of lower and upper probabilities. In this article, NPI is presented for ordinal data, which are categorical data with an ordering of the categories. The method uses a latent variable representation of the observations and categories on the real line. Lower and upper probabilities for events involving the next observation are presented, and briefly compared to NPI for non ordered categorical data. As application, the comparison of multiple groups of ordinal data is presented.     

An Improved Procedure of Estimating the Finite Population Mean Using Auxiliary Information in the Presence of Random Non Response

This article deals with the problem of estimation of the finite population mean using auxiliary information in the presence of random non response. Three different situations where random non response occurs either in study variate, or in auxiliary variate, or in both the variates, have been discussed. The asymptotically optimum estimators (AOEs) for each strategy are also identified. Expressions of biases and mean squared errors of the proposed estimators have been derived up to the first degree of approximation. Proposed estimators have been compared with the usual unbiased estimator, ratio estimator, and product estimator in the presence of random non response. Empirical studies are also carried out to show the performance of the proposed estimators over other estimators.     

A Discussion of Permutation Tests Conditional to Observed Responses in Unreplicated 2 M Full Factorial Designs

ABSTRACT

In this article we present a new solution to test for effects in unreplicated two-level factorial designs. The proposed test statistic, in case the error components are normally distributed, follows an F random variable, though our attention is on its nonparametric permutation version. The proposed procedure does not require any transformation of data such as residualization and it is exact for each effect and distribution-free. Our main aim is to discuss a permutation solution conditional to the original vector of responses. We give two versions of the same nonparametric testing procedure in order to control both the individual error rate and the experiment-wise error rate. A power comparison with Loughin and Noble's test is provided in the case of a unreplicated 2⁴ full factorial design.     

Estimators for the Finite Mixture of Rayleigh Model Based on Progressively Censored Data

In this article, based on progressively Type-II censored samples from a heterogeneous population that can be represented by a finite mixture of two-component Rayleigh lifetime model, the problem of estimating the parameters and some lifetime parameters (reliability and hazard functions) are considered. Both Bayesian and maximum likelihood estimators are of interest. A class of natural conjugate prior densities is considered in the Bayesian setting. The Bayes estimators are obtained using both the symmetric (squared error) loss function, and the asymmetric (LINEX and General Entropy) loss functions. It has been seen that the estimators obtained can be easily evaluated for this type of censoring by using suitable numerical methods. Finally, the performance of the estimates have been compared on the basis of their simulated maximum square error via a Monte Carlo simulation study.     

Asymptotic Behavior of the Hazard Rate Kernel Estimator Under Truncated and Censored Data

In this article, we give the asymptotic mean integrated squared error and the mean squared error for the kernel estimator of the hazard rate from truncated and censored data. Martingale techniques and combinatory calculus are used to obtain these results. A probability bound and the optimal bandwidth choice are also given.     

An Enhanced Double MEWMA Controller for Drifted MIMO Systems

For a drifted multiple-input and multiple-output (MIMO) system, the double multivariate exponentially weighted moving average (dMEWMA) controller is a popular run-to-run (RTR) controller for adjusting the process mean to a desired target. The stability and performance of dMEWMA controller had been widely studied in literature. Although the dMEWMA controller (with suitable discount matrices) can guarantee long-term stability, it usually requires a moderately large number of runs to bring the process output to approach its desired target if the initial recipe is not chosen appropriately. Due to the initial recipe possibly having an infinite number of feasible solutions for MIMO systems, “how to determine an optimal setting for the initial recipe” turns out to be an interesting research topic. In this article, by solving a constrained optimization problem, we first obtain an optimal initial setting for the input recipe. Then, motivated by this setting, we propose an enhanced dMEWMA controller. The long-term stability conditions and short-term performance of the proposed controller are also addressed. Given a fixed and finite production run, it reveals that the proposed controller has the ability of reducing total mean squared error (TMSE) better than the conventional dMEWMA controller.     

Estimation and Prediction for Exponentiated Family of Distributions Based on Records

In this article, a family of distributions, namely the exponentiated family of distributions, is defined and for the unknown parameters, different point estimates are derived based on record statistics. Prediction for future record values is presented from a Bayesian view point. Two numerical examples and a Monte Carlo simulation study are presented to illustrate the results.     

Mathematical forms of the distribution of the product of two normal variables

This paper finds the mathematical forms of the distribution of the product where x and x follow a bivariate normal distribution In this paper the distribution when PT0 is expressed as an integral, a new, fundamental result. From this general form, six different cases can be distinguished depending on what is known about the parameters and p. The special cases are Aroian $year:1959 and (6) Additionally, we prove that if and as the distribution of the product approaches the Type III distribution. When p=0# Aroian $year:1959 and Aroian and Meeker $year:1977, give tables for various values of 6., 6 . The results in this paper will be used to provide brief tables for p^O in a separate paper