An approximation for analyzing a broad class of implicitly and explicitly defined estimators

An approximation is presented that can be used to gain insight into the characteristics – such as outlier sensitivity, bias, and variability – of a wide class of estimators, including maximum likelihood and least squares. The approximation relies on a convenient form for an arbitrary order Taylor expansion in a multivariate setting. The implicit function theorem can be used to construct the expansion when the estimator is not defined in closed form. We present several finite-sample and asymptotic properties of such Taylor expansions, which are useful in characterizing the difference between the estimator and the expansion.     

Strong laws of large numbers for dependent heterogeneous processes: a synthesis of recent and new results

This paper surveys recent developments in the strong law of large numbers for dependent heterogeneous processes. We prove a generalised version of a recent strong law for Lz-mixingales, and also a new strong law for Lpmixingales. These results greatly relax the dependence and heterogeneity conditions relative to those currently cited, and introduce explicit trade-offs between dependence and heterogeneity. The results are applied to proving strong laws for near-epoch dependent functions of mixing processes. We contrast several methods for obtaining these results, including mapping directly to the mixingale properties, and applying a truncation argument.     

Rank-based analysis of repeated measures block designs

A rank-based inference is developed for repeated measures balanced incomplete block and randomized complete block designs using a suitable dispersion function. Asymptotic distributions of rank estimators are developed after establishing approximate linearity of the gradient vector of the dispersion function. Unlike available nonparametric procedures for those designs, estimation and testing are tied together. Three different test statistics are developed for testing the linear hypotheses. Friedman's (1937) statistic and Durbin's (1951) statistic are particular cases of one of the three proposed statistics. An estimate of a scale parameter which appears in the ARE expression as well as as in the variences and covariances of the rank estimators is discussed.     

Approximating discrete multivariate distributions prom known moments

To approximate the joint distribution of the two-colony stepping-stone model, a finite mixture approach is proposed for constructing discrete multi-variate distributions. This approach generahzes the classic method of linear combinations of independent variables. The stepping-stone model is approximated through matching known moments. Numerical examples from entomology are given. Comparisons are made with the work by Wehrly et al (1993).     

Sample design for observing classes of objects

We consider optimal sample designs for observing classes of objects. Suppose we will take a simple random sample of equal-sized sectors from a study population and observe the classes existing on these sectors. The classes might be many different things, for example, herbaceous plant species (in sampling quadrats), microinvertebrate species (in sampling cores), and side effects from a drug (in conducting medical trials). Under a nonparametric mixture model and data from a previous related study, we first estimate the optimal number of sample sectors of a given size. Then for negative binomial dispersions of individuals with a common aggregation parameter k, we consider the optimal size as well as number of sample sectors. A simple test exists to check our common k assumption and our optimal size method requires far less data than would be required by a grid method or other method which utilizes data from sample sectors of several different sizes.     

P-value adjustment for multiple binary endpoints

The p-value-based adjustment of individual endpoints and the global test for an overall inference are the two general approaches for the analysis of multiple endpoints. Statistical procedures developed for testing multivariate outcomes often assume that the multivariate endpoints are either independent or normally distributed. This paper presents a general approach for the analysis of multivariate binary data under the framework of generalized linear models. The generalized estimating equations (GEE) approach is applied to estimate the correlation matrix of the test statistics using the identity and exchangeable working correlation matrices with the model-based as well as robust estimators. The objectives of the approaches are the adjustment of p-values of individual endpoints to identify the affected endpoints as well as the global test of an overall effect. A Monte Carlo simulation was conducted to evaluate the overall family wise error (FWE) rates of the single-step down p-value adjustment approach from two adjustment methods to three global test statistics. The p-value adjustment approach seems to control the FWE better than the global approach Applications of the proposed methods are illustrated by analyzing a carcinogenicity experiment designed to study the dose response trend for 10 tumor sites, and a developmental toxicity experiment with three malformation types: external, visceral, and skeletal.     

The Relative Size of Windfall Income and the Permanent Income Hypothesis

A reconciliation is offered for the diverse test results on Friedman's permanent income hypothesis. A large data sample of those receiving windfall income in the Bureau of Labor Statistics' 1972–1973 Consumer Expenditure Survey is divided according to the size of the windfall relative to estimated permanent income. A pattern of a declining marginal propensity to consume windfall income as the relative size of the windfall increases is apparent. These results support the permanent income hypothesis for relatively large windfalls.     

The True Cost-of-Living Index With Changing Preferences

This article investigates the theoretical and empirical properties of a true cost-of-living index under conditions of changing preferences. A family of true indexes is defined based on the notion of the current utility function. A particular index, based on the previous period's utility level, is then defined. Given this definition, a true cost-of-living index is computed based on a quadratic expenditure system estimated with quarterly data from 1960–1981. For empirical purposes, changes in preferences are represented by the linear habit formation hypothesis. This index is then compared with Paasche and Laspeyres indexes. The true cost-of-living index grows somewhat faster than either the Paasche or Laspeyres index. It also displays considerably more variability.