On the Use of a Log-Rate Model for Survey-Weighted Categorical Data

For the analysis of survey-weighted categorical data, one recommended method of analysis is a log-rate model. For each cell in a contingency table, the survey weights are averaged across subjects and incorporated into an offset for a loglinear model. Supposedly, one can then proceed with the analysis of unweighted observed cell counts. We provide theoretical and simulation-based evidence to show that the log-rate analysis is not an effective statistical analysis method and should not be used in general. The root of the problem is in its failure to properly account for variability in the individual weights within cells of a contingency table. This results in goodness-of-fit tests that have higher-than-nominal error rates and confidence intervals for odds ratios that have lower-than-nominal coverage.     

Generalized Laplacian Distributions and Autoregressive Processes

Generalized Laplacian distribution is considered. A new distribution called geometric generalized Laplacian distribution is introduced and its properties are studied. First- and higher-order autoregressive processes with these stationary marginal distributions are developed and studied. Simulation studies are conducted and trajectories of the process are obtained for selected values of the parameters. Various areas of application of these models are discussed.     

Analyzing Binomial Data in a Split-Plot Design: Classical Approach or Modern Techniques?

Modeling data that are non-normally distributed with random effects is the major challenge in analyzing binomial data in split-plot designs. Seven methods for analyzing such data using mixed, generalized linear, or generalized linear mixed models are compared for the size and power of the tests. This study shows that analyzing random effects properly is more important than adjusting the analysis for non-normality. Methods based on mixed and generalized linear mixed models hold Type I error rates better than generalized linear models. Mixed model methods tend to have higher power than generalized linear mixed models when the sample size is small.     

Robust estimation methods for exponential data: a monte-carlo comparison

We compare the performance of seven robust estimators for the parameter of an exponential distribution. These include the debiased median and two optimally-weighted one-sided trimmed means. We also introduce four new estimators: the Transform, Bayes, Scaled and Bicube estimators. We make the Monte Carlo comparisons for three sample sizes and six situations. We evaluate the comparisons in terms of a new performance measure, Mean Absolute Differential Error (MADE), and a premium/protection interpretation of MADE. We organize the comparisons to enhance statistical power by making maximal use of common random deviates. The Transform estimator provides the best performance as judged by MADE. The singly-trimmed mean and Transform method define the efficient frontier of premium/protection.     

Notes on likelihood intervals and profiling

In many applications, decisions are made on the basis of function of parameters g(θ). When the value of g(theta;) is calculated using estimated values for te parameters, its is important to have a measure of the uncertainty associated with that value of g(theta;). Likelihood ratio approaches to finding likelihood intervals for functions of parameters have been shown to be more reliable, in terms of coverage probability, than the linearization approach. Two approaches to the generalization of the profiling algorithm have been proposed in the literature to enable construction of likelihood intervals for a function of parameters (Chen and Jennrich, 1996; Bates and Watts, 1988). In this paper we show the equivalence of these two methods. We also provide and analysis of cases in which neither profiling algorithm is appropriate. For one of these cases an alternate approach is suggested Whereas generalized profiling is based on maximizing the likelihood function given a constraint on the value of g(θ), the alternative algorithm is based on optimizing g(θ) given a constraint on the value of the likelihood function.     

Multicollinearity and the value of a priori information

A measure of multicollinearity is defined which is useful in evaluating maintained hypotheses and aiding estimator selection as it suggests when a non-traditional estimator proposed by Bock (1975) is minimax and dominates ordinary least squares. An example is used to illustrate the presented methodology.     

Smooth goodness of fit tests for the weibull distribution with singly censored data

The smooth goodness of fit tests are generalized to singly censored data and applied to the problem of testing Weibull (or extreme value) fit. Smooth tests, Pearson-type tests, and the spacings tests proposed by Mann, Schemer, and Fertig (1973) are compared on the basis of local asymptotic relative efficiency with respect to the asymptotic best test against generalized gamma alternatives, The smooth test of order one Is found to be most efficient for the generalized gamma alternatives.     

Nonparametric estimation of the survival distribution in censored data

Two nonparametric estimators o f the survival distributionare discussed. The estimators were proposed by Kaplan and Meier (1958) and Breslow (1972) and are applicable when dealing with censored data. It is known that they are asymptotically unbiased and uniformly strongly consistent, and when properly normalized that they converge weakly to the same Gaussian process. In this paper, the properties of the estimators are carefully inspected in small or moderate samples. The Breslow estimator, a shrinkage version of the Kaplan-Meier, nearly always has the smaller mean square error (MSE) whenever the truesurvival probabilityis at least 0.20, but has considerably larger MSE than the Kaplan-Meier estimator when the survivalprobability is near zero.     

Recurrence relations for moments of different orders of extremes from gamma distribution

Certain recurrence relations for the moments of different orders of the largest order statistic from a gamma distribution with shape parameter p are obtained. By using this it is shown that for obtaining the moment of any order of each order statistic of a sample of size n from the gamma distribution, one has to evaluate at most n-2 single integrals.     

Predicting Insurance Losses Under Cross-Classification: A Comparison of Alternative Approaches

Various mathematical and statistical models for estimation of automobile insurance pricing are reviewed. The methods are compared on their predictive ability based on two sets of automobile insurance data for two different states collected over two different periods. The issue of model complexity versus data availability is resolved through a comparison of the accuracy of prediction. The models reviewed range from the use of simple cell means to various multiplicative-additive schemes to the empirical-Bayes approach. The empirical-Bayes approach, with prediction based on both model-based and individual cell estimates, seems to yield the best forecast.