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.     

Small-Sample Methods for Cluster-Robust Variance Estimation and Hypothesis Testing in Fixed Effects Models

ABSTRACT

In panel data models and other regressions with unobserved effects, fixed effects estimation is often paired with cluster-robust variance estimation (CRVE) to account for heteroscedasticity and un-modeled dependence among the errors. Although asymptotically consistent, CRVE can be biased downward when the number of clusters is small, leading to hypothesis tests with rejection rates that are too high. More accurate tests can be constructed using bias-reduced linearization (BRL), which corrects the CRVE based on a working model, in conjunction with a Satterthwaite approximation for t-tests. We propose a generalization of BRL that can be applied in models with arbitrary sets of fixed effects, where the original BRL method is undefined, and describe how to apply the method when the regression is estimated after absorbing the fixed effects. We also propose a small-sample test for multiple-parameter hypotheses, which generalizes the Satterthwaite approximation for t-tests. In simulations covering a wide range of scenarios, we find that the conventional cluster-robust Wald test can severely over-reject while the proposed small-sample test maintains Type I error close to nominal levels. The proposed methods are implemented in an R package called clubSandwich. This article has online supplementary materials.     

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.     

Differential equation models for statistical functions

Differential equations have been used in statistics to define functions such as probability densities. But the idea of using differential equation formulations of stochastic models has a much wider scope. The author gives several examples, including simultaneous estimation of a regression model and residual density, monotone smoothing, specification of a link function, differential equation models of data, and smoothing over complicated multidimensional domains. This paper aims to stimulate interest in this approach to functional estimation problems, rather than provide carefully worked out methods.     

Data skeletons: simultaneous estimation of multiple quantiles for massive streaming datasets with applications to density estimation

We consider the problem of density estimation when the data is in the form of a continuous stream with no fixed length. In this setting, implementations of the usual methods of density estimation such as kernel density estimation are problematic. We propose a method of density estimation for massive datasets that is based upon taking the derivative of a smooth curve that has been fit through a set of quantile estimates. To achieve this, a low-storage, single-pass, sequential method is proposed for simultaneous estimation of multiple quantiles for massive datasets that form the basis of this method of density estimation. For comparison, we also consider a sequential kernel density estimator. The proposed methods are shown through simulation study to perform well and to have several distinct advantages over existing methods.