Testing for Unit Root Against Stationarity Using the Likelihood Ratio Test

In a first-order autoregressive model with drift, we derive the likelihood ratio test for a unit root against the stationary alternative. We also derive the test in a state space model with trend. Finite sample and asymptotic critical values are obtained by Monte Carlo simulations. A simulation study investigates the power performance of the likelihood ratio test and we also examine how a bias correction of the test affects the results.     

Statisticians Can Matter

Statisticians fall far short of their potential as guides to enlightened decision making in business. Two important explanations are: (1) Decision makers are often more easily convinced by concrete examples, however fragmentary and misleading, than by competent statistical analysis. (2) The effective use of statistics in the process of decision making requires hard thinking by decision makers, thinking that cannot be delegated entirely to the statistical specialist. Modern developments in interactive statistical computing may help to reduce the force of these limitations on exploitation of statistics; used properly, computing can encourage, almost force, the student or business user of statistics to think statistically.     

Asymptotically Optimal Nonparametric Empirical Bayes Via Predictive Recursion

An empirical Bayes problem has an unknown prior to be estimated from data. The predictive recursion (PR) algorithm provides fast nonparametric estimation of mixing distributions and is ideally suited for empirical Bayes applications. This article presents a general notion of empirical Bayes asymptotic optimality, and it is shown that PR-based procedures satisfy this property under certain conditions. As an application, the problem of in-season prediction of baseball batting averages is considered. There the PR-based empirical Bayes rule performs well in terms of prediction error and ability to capture the distribution of the latent features.     

Testing of Suspected Observations in an Exponential Sample With Unknown Origin

The problem of multiple upper outliers in two-parameter exponential sample is considered. A test statistic is proposed to identify the outliers at the upper end of the sample. The null distribution of the test statistic is obtained and the critical values are found. The performance of the test is also compared with the earlier work.     

On selecting the best population

This paper deals with the problem of selecting the “best” population from a given number of populations in a decision theoretic framework. The class of selection rules considered is based on a suitable partition of the sample space. A selection rule is given which is shown to have certain optimum properties among the selection rules in the given class for a mal rules are known.     

A multivariate solution of the multivariate ranking and selection problem

The problem of selection of the best multivariate population is given a new formulation which does not involve reducing the populations to univariate quantities. This formulation's solution is developed for known, and (using the Heteroscedastic Method) also for unknown, variance-covariance matrices. Preference reversals and arbitrary nonlinear preference functions are explicitly allowed in this new theory     

On the asymptotic distribution of cramer-von mises one-sample test statistics under an alternative

The asymptotic normality of the Cramer-von Mises one-sample test statistic and one of its variants under an alternative cdf is demonstrated. The derivation herein is unique in that it does not require knowledge of the theory of weak convergence of probability measures defined on metrized function spaces, and thus is accessible to a broader class of students and practitioners.     

Nonparametric prediction analysis for binary data

A nonparametric inference algorithm developed by Davis and Geman (1983) is extended problem. The algorithm and applied to a medical prediction employs an estimation procedure for acquiring pairwise statistics among variables of a binary data set, allows for the data-driven creation of interaction terms among the variables, and employs a decision rule which asymptotically gives the minimum expected error. The inference procedure was designed for large data sets but has been extended via the method of cross-validation to encompass smaller data sets.     

More flexible sequential and non-sequential designs in long-term clinical trial

In this paper, we describe decision making procedures as they exist in most clinical trials,review some recently suggested approaches to monitoring and clarify how these methods allow greater flexibility in monitoring and explicit specification of data monitoring methods in the protocol.     

Rank test statistics for umbrella alternatives

This paper proposes an optimal rank test procedure for testing an umbrella alternative when the peak of the umbrella is known. It is referred to as maximin efficient linear rank test. Also when the peak of the umbrella is unknown, a test procedure is proposed and its performance is discussed.