Philip L. H. Yu

Regression Estimator in Ranked Set Sampling

Ranked set sampling (RSS) utilizes inexpensive auxiliary information about the ranking of the units in a sample to provide a more precise estimator of the population mean of the variable of interest Y, which is either difficult or expensive to measure. However, the ranking may not be perfect in most situations. In this paper, we assume that the ranking is done on the basis of a concomitant variable X. Regression-type RSS estimators of the population mean of Y will be proposed by utilizing this concomitant variable X in both the ranking process of the units and the estimation process when the population mean of X is known. When X has unknown mean, double sampling will be used to obtain an estimate for the population mean of X. It is found that when X and Y jointly follow a bivariate normal distribution, our proposed RSS regression estimator is more efficient than RSS and simple random sampling (SRS) naive estimators unless the correlation between X and Y is low (/rho/ < 0.4). Moreover, it is always superior to the regression estimator under SRS for all rho. When normality does not hold, this approach could still perform reasonably well as long as the shape of the distribution of the concomitant variable X is only slightly departed from symmetry. For heavily skewed distributions, a remedial measure will be suggested. An example of estimating the mean plutonium concentration in surface soil on the Nevada Test Site, Nevada, U.S.A., will be considered.

A Comparative Study of Chinese, American and Japanese Nurses’ Perceptions of Ethical Role Responsibilities

This article reports a survey of nurses in different cultural settings to reveal their perceptions of ethical role responsibilities relevant to nursing practice. Drawing on the Confucian theory of ethics, the first section attempts to understand nursing ethics in the context of multiple role relationships. The second section reports the administration of the Role Responsibilities Questionnaire (RRQ) to a sample of nurses in China (n = 413), the USA (n = 163), and Japan (n = 667). Multidimensional preference analysis revealed the patterns of rankings given by the nurses to the statements they considered as important ethical responsibilities. The Chinese nurses were more virtue based in their perception of ethical responsibilities, the American nurses were more principle based, and the Japanese nurses were more care based. The findings indicate that the RRQ is a sensitive instrument for outlining the embedded sociocultural factors that influence nurses’ perceptions of ethical responsibilities in the realities of nursing practice. This study could be important in the fostering of partnerships in international nursing ethics.

Statistical Methods for Ranking Data

This book introduces advanced undergraduate, graduate students and practitioners to statistical methods for ranking data. An important aspect of nonparametric statistics is oriented towards the use of ranking data. Rank correlation is defined through the notion of distance functions and the notion of compatibility is introduced to deal with incomplete data. Ranking data are also modeled using a variety of modern tools such as CART, MCMC, EM algorithm and factor analysis. This book deals with statistical methods used for analyzing such data and provides a novel and unifying approach for hypotheses testing. The techniques described in the book are illustrated with examples and the statistical software is provided on the authors website.

Distance-based tree models for ranking data

Ranking data has applications in different fields of studies, like marketing, psychology and politics. Over the years, many models for ranking data have been developed. Among them, distance-based ranking models, which originate from the classical rank correlations, postulate that the probability of observing a ranking of items depends on the distance between the observed ranking and a modal ranking. The closer to the modal ranking, the higher the ranking probability is. However, such a model basically assumes a homogeneous population and does not incorporate the presence of covariates. To overcome these limitations, we combine the strength of a tree model and the existing distance-based models to build a model that can handle more complexity and improve prediction accuracy. We will introduce a recursive partitioning algorithm for building a tree model with a distance-based ranking model fitted at each leaf. We will also consider new weighted distance measures which allow different weights for different ranks in formulating more flexible distance-based tree models. Finally, we will apply the proposed methodology to analyze a ranking dataset of Ingleharts items collected in the 1999 European Values Studies.

On exact confidence intervals for the common mean of several normal populations

In this paper we consider the problem of constructing exact confidence intervals for the common mean of several normal populations with unknown and possibly unequal variances. Several procedures based on pivots and P-values are discussed and compared.

On the residual autocorrelation of the autoregressive conditional duration model

Abstract The asymptotic distribution of residual autocorrelations in the autoregressive conditional duration model is derived. This results in a portmanteau goodness-of-fit statistic for this kind of model. Our result extends the model diagnostic checking methodology of Box–Jenkins to the autoregressive conditional duration models.

Fast ML Estimation for the Mixture of Factor Analyzers via an ECM Algorithm

In this brief, we propose a fast expectation conditional maximization (ECM) algorithm for maximum-likelihood (ML) estimation of mixtures of factor analyzers (MFA). Unlike the existing expectation-maximization (EM) algorithms such as the EM in Ghahramani and Hinton, 1996, and the alternating ECM (AECM) in McLachlan and Peel, 2003, where the missing data contains component-indicator vectors as well as latent factors, the missing data in our ECM consists of component-indicator vectors only. The novelty of our algorithm is that closed-form expressions in all conditional maximization (CM) steps are obtained explicitly, instead of resorting to numerical optimization methods. As revealed by experiments, the convergence of our ECM is substantially faster than EM and AECM regardless of whether assessed by central processing unit (CPU) time or number of iterations.

Predicting potential drop‐out and future commitment for first‐time donors based on first 1·5‐year donation patterns: the case in Hong Kong Chinese donors

Background and Objectives  Adequate blood supply is crucial to the health‐care system. To maintain a stable donor pool, donation‐promotion strategies should not only be targeted in recruitment but also focus on retaining donors to give blood regularly. A study using statistical modelling is conducted to understand the first 4‐year donation patterns for drop‐out and committed first‐time blood donors and to build model for the donor‐type identification based on their first 1·5‐year donation patterns.

Estimation of Normal Variance Based on Balanced and Unbalanced Ranked Set Samples

In this paper we address the problem of estimation of the variance of a normal population based on a balanced as well as an unbalanced ranked set sample (RSS), which is a modification of the original RSS of McIntyre (1952).We have proposed several methods of estimation of variance by combining different unbiased between and within estimators, and compared their performances

Bayesian analysis of order-statistics models for ranking data

In this paper, a class of probability models for ranking data, the order-statistics models, is investigated. We extend the usual normal order-statistics model into one where the underlying random variables follow a multivariate normal distribution. Bayesian approach and the Gibbs sampling technique are used for parameter estimation. In addition, methods to assess the adequacy of model fit are introduced. Robustness of the model is studied by considering a multivariate-t distribution. The proposed method is applied to analyze the presidential election data of the American Psychological Association (APA).