Quantile plots for mean effects in the presence of variance effects for 2k-p designs

In robust parameter design, variance effects and mean effects in a factorial experiment are modelled simultaneously. If variance effects are present in a model, correlations are induced among the naive estimators of the mean effects. A simple normal quantile plot of the mean effects may be misleading because the mean effects are no longer iid under the null hypothesis that they are zero. Adjusted quantiles are computed for the case when one variance effect is significant and examples of 8-run and 16-run fractional factorial designs are examined in detail. We find that the usual normal quantiles are similar to adjusted quantiles for all but the largest and smallest ordered effects for which they are conservative. Graphically, the qualitative difference between the two sets of quantiles is negligible (even in the presence of large variance effects) and we conclude that normal probability plots are robust in the presence of variance effects.     

Confidence Intervals for the Youden Index and Corresponding Optimal Cut-Point

A global measure of biomarker effectiveness is the Youden index, the maximum difference between sensitivity, the probability of correctly classifying diseased individuals, and 1-specificity, the probability of incorrectly classifying healthy individuals. The cut-point leading to the index is the optimal cut-point when equal weight is given to sensitivity and specificity. Using the delta method, we present approaches for estimating confidence intervals for the Youden index and corresponding optimal cut-point for normally distributed biomarkers and also those following gamma distributions. We also provide confidence intervals using various bootstrapping methods. A comparison of interval width and coverage probability is conducted through simulation over a variety of parametric situations. Confidence intervals via delta method are shown to have both closer to nominal coverage and shorter interval widths than confidence intervals from the bootstrapping methods.     

Confidence Intervals for the Hyperparameters in Structural Models

This article deals with the bootstrap as an alternative method to construct confidence intervals for the hyperparameters of structural models. The bootstrap procedure considered is the classical nonparametric bootstrap in the residuals of the fitted model using a well-known approach. The performance of this procedure is empirically obtained through Monte Carlo simulations implemented in Ox. Asymptotic and percentile bootstrap confidence intervals for the hyperparameters are built and compared by means of the coverage percentages. The results are similar but the bootstrap procedure is better for small sample sizes. The methods are applied to a real time series and confidence intervals are built for the hyperparameters.     

A Copula‐Based Non‐parametric Measure of Regression Dependence

Abstract. This article presents a framework for comparing bivariate distributions according to their degree of regression dependence. We introduce the general concept of a regression dependence order (RDO). In addition, we define a new non‐parametric measure of regression dependence and study its properties. Besides being monotone in the new RDOs, the measure takes on its extreme values precisely at independence and almost sure functional dependence, respectively. A consistent non‐parametric estimator of the new measure is constructed and its asymptotic properties are investigated. Finally, the finite sample properties of the estimate are studied by means of a small simulation study.     

An Interesting Property of the Sample Mean under a First-Order Autoregressive Model

The unweighted sample mean is examined as an estimator of the population mean in a first-order autoregressive model. It is demonstrated that the precision of this estimator deteriorates as the number of equally spaced observations taken within a fixed time interval increases.     

Delta Method,Moment Convergence,and Inference

Statistics, as functions of the observations, are usually given by well-behaved functions. This fact is used to obtain limit distributions for statistics whose components are given by asymptotically linear functions. These results are then extended to the moments of distributions, covariance matrices and confidence regions for parameters of interest. These regions may be used to test, through duality, hypothesis on these parameters. A theoretical application is presented.     

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.