Search with small sets in presence of a liar

One unknown element of an n-element set is sought by asking if it is contained in given subsets. It is supposed that the question sets are of size at most k and all the questions are decided in advance, the choice of the next question cannot depend on previous answers. At most l of the answers can be incorrect. The minimum number of such questions is determined when the order of magnitude of k is n with <1. The problem can be formulated as determination of the maximum sized l-error-correcting code (of length n) in which the number of ones in a given position is at most k.     

Locking the Wiener Process to its Level-Crossing Time

We consider the specific transformation of a Wiener process {X(t), t ≥ 0} in the presence of an absorbing barrier a that results when this process is “time-locked” with respect to its first passage time T _a through a criterion level a, and the evolution of X(t) is considered backwards (retrospectively) from T _a . Formally, we study the random variables defined by Y(t) ≡ X(T _a  ? t) and derive explicit results for their density and mean, and also for their asymptotic forms. We discuss how our results can aid interpretations of time series “response-locked” to their times of crossing a criterion level.     

A unified approach to multilevel sample selection models

Abstract

We propose a unified approach for multilevel sample selection models using a generalized result on skew distributions arising from selection. If the underlying distributional assumption is normal, then the resulting density for the outcome is the continuous component of the sample selection density and has links with the closed skew-normal distribution (CSN). The CSN distribution provides a framework which simplifies the derivation of the conditional expectation of the observed data. This generalizes the Heckman’s two-step method to a multilevel sample selection model. Finite-sample performance of the maximum likelihood estimator of this model is studied through a Monte Carlo simulation.     

Unbiased F Tests for Factorial Experiments for Correlated Data

This paper finds a general form of the correlation matrix that may be used to provide unbiased F tests in a.k-way factorial experiment.     

Influential observations in the analysis of variance

The effect of influentia lob servations on t h e parameter estimates of ordinary l e a s t squares regression models has received considerable attentio n fn the last decade. However, very little attention has been given t o the problem of in fluent ia lobserva- tions in the analysis of variance . The purpose of t h i s paper is t o show by way of examples that influential observations can alter the conclusions of tests of hypotheses in the analysis of variance . Regression diagnostics for identif y in g both extreme points and outliers can be used to reveal potential data and design problems.     

On the coefficient of variation for residence time distributions of some stochastic compartmental models

The study of residence time distributions is motivated by the desire to develop new practical tools for the statistical analysis of compartmental systems. In particular, Gibaldi and Perrier (1982) describe three alternative models for a two-compartment system, which were noted to be "indistinguishable based solely on plasma or urinary excretion data," defining a residence time distribution. In this paper, properties of the coefficient of variation of the residence time distributions are developed for these three models. In addition to the standard Markovian model with exponential retention times, properties are also derived for a non-Markovian model with gamma retention times. A coefficient of variation may be estimated from commonly available elimination data, and may be used in principle to discriminate between these three models.     

Estimation of covariance matrices based on hierarchical inverse-Wishart priors

This paper focuses on Bayesian shrinkage methods for covariance matrix estimation. We examine posterior properties and frequentist risks of Bayesian estimators based on new hierarchical inverse-Wishart priors. More precisely, we give the conditions for the existence of the posterior distributions. Advantages in terms of numerical simulations of posteriors are shown. A simulation study illustrates the performance of the estimation procedures under three loss functions for relevant sample sizes and various covariance structures.     

Accent on Teaching Materials

Estimation of covariance components in the multivariate random-effect model with nested covariance structure is discussed. There are two covariance matrices to be estimated, namely, the between-group and the within-group covariance matrices. These two covariance matrices are most often estimated by forming a multivariate analysis of variance and equating mean square matrices to their expectations. Such a procedure involves taking the difference between the between-group mean square and the within-group mean square matrices, and often produces an estimated between-group covariance matrix that is not nonnegative definite. We present estimators of the two covariance matrices that are always proper covariance matrices. The estimators are the restricted maximum likelihood estimators if the random effects are normally distributed. The estimation procedure is extended to more complicated models, including the twofold nested and the mixed-effect models. A numerical example is presented to illustrate the use of the estimation procedure.     

Accent on Teaching Materials: Notices and Reviews of Important Teaching Materials

This article examines the probabilities of outcomes from rolling dice with the dimension 1 × 1 × r for various values of r. Experiments were conducted by school students and university students. The results of the experiments are given and the probabilities examined using a generalized linear model. Notes are also made about the value of the experiment in teaching the groups of students.