Nonparametric estimation of a change point in positive shift models

Six nonparametric estimators of the change point are compared via Monte Carlo simulation in positive shift models of widely different taillengths. It is found that the best estimator in terms of smallest mean-squared error depends on the taillength of the underlying distribution. Overall, an estimator of Lombard (1987) based on a Wilcoxon scores rank statistic is recommended.     

MSE-matrix superiority of the mixed over the least squares estimator in the presence of outliers

In his recent paper, Ali (1991) has shown that the mixed regression estimator, when data contain mean-shift or variance inflation outliers, is uniformly superior to the ordinary least squares estimator in terms of scalar-valued mean square error. However, when using the matrix-valued mean square error criterion, this dominance fails to hold in general. The subsequent investigation gives a complete characterization of the situation where the mixed estimator is superior to the LS-estimator when the comparison is made with respect to this stronger MSE-property. Vice versa, the LS-estimator never dominates the mixed estimator relative to this criterion.     

Inference for quantile measures of kurtosis,peakedness, and tail weight

Insight into measures of peakedness, heavy-tailedness, and kurtosis can be gained by studying Ruppert’s ratios of interquantile ranges. They are not only monotone in Horn’s measure of peakedness when applied to the central portion of the population, but also monotone in the practical tail-index of Morgenthaler and Tukey, when applied to the tails. Non-parametric confidence intervals are found for Ruppert’s ratios, and sample sizes required to obtain such intervals for a pre-specified relative width and level are provided. In addition, the empirical power of distribution-free tests for peakedness and bimodality are found for some symmetric distributions.     

Point Estimates of Test Sensitivity and Specificity from Sample Means and Variances

In a wide variety of biomedical and clinical research studies, sample statistics from diagnostic marker measurements are presented as a means of distinguishing between two populations, such as with and without disease. Intuitively, a larger difference between the mean values of a marker for the two populations, and a smaller spread of values within each population, should lead to more reliable classification rules based on this marker. We formalize this intuitive notion by deriving practical, new, closed-form expressions for the sensitivity and specificity of three different discriminant tests defined in terms of the sample means and standard deviations of diagnostic marker measurements. The three discriminant tests evaluated are based, respectively, on the Euclidean distance and the Mahalanobis distance between means, and a likelihood ratio analysis. Expressions for the effects of measurement error are also presented. Our final expressions assume that the diagnostic markers follow independent normal distributions for the two populations, although it will be clear that other known distributions may be similarly analyzed. We then discuss applications drawn from the medical literature, although the formalism is clearly not restricted to that application.     

Bayesian adjustment for unidirectional misclassification in ordinal covariates

In this paper, we study the identification of Bayesian regression models, when an ordinal covariate is subject to unidirectional misclassification. Xia and Gustafson [Bayesian regression models adjusting for unidirectional covariate misclassification. Can J Stat. 2016;44(2):198–218] obtained model identifiability for non-binary regression models, when there is a binary covariate subject to unidirectional misclassification. In the current paper, we establish the moment identifiability of regression models for misclassified ordinal covariates with more than two categories, based on forms of observable moments. Computational studies are conducted that confirm the theoretical results. We apply the method to two datasets, one from the Medical Expenditure Panel Survey (MEPS), and the other from Translational Research Investigating Underlying Disparities in Acute Myocardial infarction Patients Health Status (TRIUMPH).     

The generalized odd half-Cauchy family of distributions: Properties and applications

We introduce and study general mathematical properties of a new generator of continuous distributions with one extra parameter called the generalized odd half-Cauchy family. We present some special models and investigate the asymptotics and shapes. The new density function can be expressed as a linear mixture of exponentiated densities based on the same baseline distribution. We derive a power series for the quantile function. We discuss the estimation of the model parameters by maximum likelihood and prove empirically the flexibility of the new family by means of two real data sets.     

Matrix mean square error comparisons based on a certain covariance structure

For two given estimators of a parameter vector the covariance structure of their difference is used to compare them in terms of their mean square error matrices. The results obtained are applied to the covariance adjustment technique and regression     

Asymptotic tests and monte carlo studies associated with the multiplicative interaction model

Several authors have proposed approximations to percentage points required for testing certain hypotheses associated with the multiplicative interaction model. Alternative approximations based on the asymptotic joint distribution of the characteristic roots of a noncentral Wishart matrix are proposed in this paper. The type I error rates of the resulting tests and the existing procedures are then compared using Monte Carlo methods.     

Empirical Likelihood Inference for the Rao‐Hartley‐Cochran Sampling Design

The Hartley‐Rao‐Cochran sampling design is an unequal probability sampling design which can be used to select samples from finite populations. We propose to adjust the empirical likelihood approach for the Hartley‐Rao‐Cochran sampling design. The approach proposed intrinsically incorporates sampling weights, auxiliary information and allows for large sampling fractions. It can be used to construct confidence intervals. In a simulation study, we show that the coverage may be better for the empirical likelihood confidence interval than for standard confidence intervals based on variance estimates. The approach proposed is simple to implement and less computer intensive than bootstrap. The confidence interval proposed does not rely on re‐sampling, linearization, variance estimation, design‐effects or joint inclusion probabilities.     

The size-density hypothesis in Great Britain: Analysis of a deviant case

Recent studies have found size of territorial units to vary inversely with population density, the only exception to this regularity being Great Britain, where size and density were found to be unrelated. The present research accounts for this anomaly by demonstrating Britain's historical conformity to the size-density relation. The size-density hypothesis is further supported by direct test, made possible by a recent reorganization of british counties. Results show that reorganization has restored the expected inverse relation between size and density and has restructured the size and density of counties in a manner precisely specified by underlying theory.