New Developments in Statistical Computing: New Bias Evaluation Features of EXPLOR—A Program for Assessing Experimental Design Properties

Longitudinal investigations play an increasingly prominent role in biomedical research. Much of the literature on specifying and fitting linear models for serial measurements uses methods based on the standard multivariate linear model. This article proposes a more flexible approach that permits specification of the expected response as an arbitrary linear function of fixed and time-varying covariates so that mean-value functions can be derived from subject matter considerations rather than methodological constraints. Three families of models for the covariance function are discussed: multivariate, autoregressive, and random effects. Illustrations demonstrate the flexibility and utility of the proposed approach to longitudinal analysis.     

A Recursive Formula for the Probability of Occurrence of at Least m out of N Events

A recursive same-sign relation is derived that reduces the probability of occurrence of at least m out of N independent events to the probability of occurrence of at least m out of N ? 1 of these N events.     

Book Reviews

Statistics for Engineering Problem Solving.: Stephen B. Vardeman. Boston, MA: PWS Publishing, 1994. 840 pp. $59.95. Reviewed by Soren Bisgaard

A Data-Based Approach to Statistics.: Ronald L. Iman. Belmont, CA: Wadsworth Publishing, 1994. xiv + 898 pp. $51.95. Reviewed by Katherine Halvorsen

Concepts in Probability and Stochastic Modeling.: James J. Higgins and Sallie Keller-McNulty. Belmont, CA: Duxbury Press, 1995. xi + 420 pp. $67.43. Reviewed by David M. Nickerson

Statistics (6th ed.).: James T. McClave and Frank H. Dietrich II. New York: Dellen/Macmillan College Publishing, 1994. xix + 967 pp. $66.00. Reviewed by Katherine Halvorsen

Data Analysis for Monitoring Human Rights.: Herbert Spirer and Louise Spirer. Washington, DC: American Association for the Advancement of Science, 1994. xiv + 126 pp. $15.00. Reviewed by Diane G. Saphire     

Estimation for the bivariate normal correlation coefficient using asymptotic expansions

Harley (1954) gave asymptotic expansions for the distributio function and for percentiles of the distribution of the bivariate normal sample correlation coefficient. To the stated order of approximation these expansions were incomplete in that contributions from some higher cumulants were not taken into account. In this article the completed expansions are given together with an asymptotic expansion yielding approximate confidence limits for the population correlation coefficient. Numerical comparisons indicate that asymptotic expansions are superior to other suggested approximate methods     

A fortran implementation of univariate fourier series density estimation

A set of Fortran-77 subroutines is described which compute a nonparametric density estimator expressed as a Fourier series. In addition, a subroutine is given for the estimation of a cumulative distribution. Performance measures are given based on samples from a Weibull distribution. Due to small size and modest space demands, these subroutines are easily implemented on most small computers.     

Some aspects of statistical inference on the lagrange (generalized) poisson distribution

A generalization of the Poisson distribution was defined by Consul and Jain (Ann. Math. Statist., 41, (1970)) and was obtained as a particular family of Lagrange distributions by Consul and Shenton (SIAM. J. Appl. Math., 23, (1972)). The distribution is subsequently named the generalized Poisson distribution (GPD). This GPD reduces to the Poisson distribution for ? = 0. When the data have a one-way layout structure, the asymptotically locally optimal Neyman's C(d) test is constructed and compared with the conditional test on the hypothesis H_o? = 0. Within the framework of the generalized linear models an appropriate link function is given, and the asymptotic distributions of the estimated parameters are derived.     

Modified ridge analyses under nonstandard

A well-known procedure for the optimization of a second-degree response function over a spherical region of interest is that of ridge analysis. Khuri and Myers (1979) introduced a modification of this procedure by incorporating a certain constraint on the prediction variance. Both procedures, however, assume that the response variable has a constant variance throughtout the experimental region. In the present article, we consider two extensions to Khuri and Myers modifioed ridge analysis. The first extension relaxes the constant variance assumption. In the second extension. generalised linear models are used instead of the trasitional linear model. which are commenly used in responce variables that are not necessaily continusly distribution, including these have discreate distributions, Two examples are presented to illustrate the implementation of the proposed extensions.     

An Investigation of Quantile Function Estimators Relative to Quantile Confidence Interval Coverage

In this article, we investigate the limitations of traditional quantile function estimators and introduce a new class of quantile function estimators, namely, the semi-parametric tail-extrapolated quantile estimators, which has excellent performance for estimating the extreme tails with finite sample sizes. The smoothed bootstrap and direct density estimation via the characteristic function methods are developed for the estimation of confidence intervals. Through a comprehensive simulation study to compare the confidence interval estimations of various quantile estimators, we discuss the preferred quantile estimator in conjunction with the confidence interval estimation method to use under different circumstances. Data examples are given to illustrate the superiority of the semi-parametric tail-extrapolated quantile estimators. The new class of quantile estimators is obtained by slight modification of traditional quantile estimators, and therefore, should be specifically appealing to researchers in estimating the extreme tails.     

Survival Estimation with Missing Censoring Times for the Generalized Koziol–Green Model

ABSTRACT

When analyzing time-to-event data, there are various situations in which right censoring times for unfailed units are missing. In that context, by taking a supplementary sample of a convenient percentage of unfailed units, we propose a semi-parametric method for estimating a survival function under the natural extension of the Koziol–Green model to double random censoring. Some large sample properties of this estimator are derived. We prove uniform strong consistency and asymptotic weak convergence to a Gaussian process. A simulation study is also presented in order to analyze the behavior of the proposed estimator.