Noriah M. Al-Kandari

VARIABLE SELECTION AND INTERPRETATION OF COVARIANCE PRINCIPAL COMPONENTS

In practice, when a principal component analysis is applied on a large number of variables the resultant principal components may not be easy to interpret, as each principal component is a linear combination of all the original variables. Selection of a subset of variables that contains, in some sense, as much information as possible and enhances the interpretations of the first few covariance principal components is one possible approach to tackle this problem. This paper describes several variable selection criteria and investigates which criteria are best for this purpose. Although some criteria are shown to be better than others, the main message of this study is that it is unwise to rely on only one or two criteria. It is also clear that the interdependence between variables and the choice of how to measure closeness between the original components and those using subsets of variables are both important in determining the best criteria to use.

AQAK: A Library Anxiety Scale for Undergraduate Students

The library environment has drastically changed since 1992 when Bostick’s Library Anxiety Scale was developed. This project aimed to develop a scale specifically for undergraduate students. A three-stage study was conducted, using students of Kuwait University. A variety of statistical measures, including factor analysis, were used to process the data. A test re-test was undertaken to estimate the reliability of the scale. The resulting scale, named AQAK, consists of 40 statements clustered into five factors which are: (1) Library resources, (2) Library staff, (3) User knowledge, (4) Library environment, and (5) User education. This new scale with a Cronbach’s alpha value of 0.904 is 90 percent reliable. The gender of the participants, the type of high school attended, and the college where they are studying have no relationship with library anxiety.

Nonparametric inference strategies for the quantile functions under left truncation and right censoring

This paper addresses the problem of estimating the quantile function in a multiple-sample set up when the data are left-truncated and right-censored (LTRC). Assuming an uncertain prior non-sample information on the value of the quantile, we propose improved estimators based on Stein-type shrinkage estimators. A test statistic is also proposed to define improved estimators for the quantile function. The asymptotic bias and risk of the estimators are derived and compared with the benchmark estimator analytically. For several choices of parameters, a Monte Carlo simulation experiment is conducted to appraise the risk reduction of the proposed estimators at different levels of censoring and truncation. We demonstrate that the proposed estimators have superior performance in terms of risk reduction over the benchmark estimator.

Estimating and testing effect size from an arbitrary population

In this article, we develop inference tools for an effect size parameter in a paired experiment. A class of estimators is defined that includes natural, shrinkage and shrinkage preliminary test estimators. The shrinkage and preliminary test methods incorporate uncertain prior information on the parameter. This information may be available in the form of a realistic guess on the basis of the experimenter’s knowledge and experience, which can be incorporated into the estimation process to increase the efficiency of the estimator. Asymptotic properties of the proposed estimators are investigated both analytically and computationally. A simulation study is also conducted to assess the performance of the estimators for moderate and large samples. For illustration purposes, the method is applied to a data set.

Estimation of cumulative incidence functions when the lifetime distributions are uniformly stochastically ordered.

In the competing risks problem an important role is played by the cumulative incidence function (CIF), whose value at time t is the probability of failure by time t from a particular type of risk in the presence of other risks. Assume that the lifetime distributions of two populations are uniformly stochastically ordered. Since this ordering may not hold for the empiricals due to sampling variability, it is natural to estimate these distributions under this constraint. This will in turn affect the estimation of the CIFs. This article considers this estimation problem. We do not assume that the risk sets in the two populations are related, give consistent estimators of all the CIFs and study the weak convergence of the resulting processes. We also report the results of a simulation study that show that our restricted estimators outperform the unrestricted ones in terms of mean square error. A real life example is used to illustrate our theoretical results.

Continuity and Analysis of Sequences of Principal Components

Double arrays of n rows and p columns can be regarded as n drawings from some p-dimensional population. A sequence of such arrays is considered. Principal component analysis for each array forms sequences of sample principal components and eigenvalues. The continuity of these sequences, in the sense of convergence with probability one and convergence in probability, is investigated, that appears to be informative for pattern study and prediction of principal components. Various features of paths of sequences of population principal components are highlighted through an example.

Testing and Merging Information for Effect Size Estimation

Abstract A large-sample test for testing the equality of two effect sizes is presented. The null and non-null distributions of the proposed test statistic are derived. Further, the problem of estimating the effect size is considered when it is a priori suspected that two effect sizes may be close to each other. The combined data from all the samples leads to more efficient estimator of the effect size. We propose a basis for optimally combining estimation problems when there is uncertainty concerning the appropriate statistical model-estimator to use in representing the sampling process. The objective here is to produce natural adaptive estimators with some good statistical properties. In the context of two bivariate statistical models, the expressions for the asymptotic mean squared error of the proposed estimators are derived and compared with the parallel expressions for the benchmark estimators. We demonstrate that the suggested preliminary test estimator has superior asymptotic mean squared error performance relative to the benchmark and pooled estimators. A simulation study and application of the methodology to real data are presented.