EXACT INFERENCE IN FOUR-PARAMETER GENERALIZED GAMMA DISTRIBUTIONS

The paper considers Bayesian analysis of the generalized four-parameter gamma distribution. Estimation of parameters using classical techniques is associated with important technical problems while Bayesian methods are not currently available for such distributions. Posterior inference is performed using numerical methods organized around Gibbs sampling. Predictive distributions and reliability can be estimated routinely using the proposed methods.     

Random Accessibility as a Parallelism to Reliability Studies on Simple Graphs

ABSTRACT

Graphs are classified according to the numbers of vertices and edges they contain. For simple graphs a concept of accessibility is defined and its relation to the graph reliability problem is investigated. Exact results are derived for special subclasses of bipartite and tripartite graphs in relation to accessibility. Several conjectures on the relation of accessibility and all-terminal reliability are numerically illustrated without proof.     

The Detection of Influential Observations for Allocation,Separation, and the Determination of Probabilities in a Bayesian Framework

Normal theory separation and allocation problems are discussed from a predictive point of view. Influence statistics are defined and employed to ascertain the impact that particular observations will have on the inferential goals—allocation of future observations, separation between populations, and the determination of probabilities for future cases. Methods are illustrated on a collection of financial data taken from Johnson and Wichern (1982).     

The Effects of Detrending in Granger Causality Tests

Nonstationary time series are frequently detrended in empirical investigations by regressing the series on time or a function of time. The effects of the detrending on the tests for causal relationships in the sense of Granger are investigated using quarterly U.S. data. The causal relationships between nominal or real GNP and M1, inferred from the Granger–Sims tests, are shown to depend very much on, among other factors, whether or not series are detrended. Detrending tends to remove or weaken causal relationships, and conversely, failure to detrend tends to introduce or enhance causal relationships. The study suggests that we need a more robust test or a better definition of causality.     

Measuring the Influence of Unemployment Insurance on Unemployment Experiences

This article investigates the comprehensive effects of unemployment insurance (UI) policies on the amount of time and unemployment that individuals report between jobs. The econometric model jointly determines the effects of UI on the lengths of nonemployment spells, the classification of these spells as unemployment, and the likelihood of collecting program benefits. The model carefully attempts to isolate variation in UI benefits attributable to differences in generosity across programs to avoid biases in estimating policy effects induced by other contaminating sources of benefit variation. Using data on men from the National Longitudinal Survey of Youth, the empirical results find (a) UI recipients typically experience longer spells between jobs, at least up to the exhaustion of UI benefits, and report substantially larger fractions of these spells as unemployment; (b) weekly benefit amounts exert no significant influence on the likelihood of UI recipiency, on the length of spells between jobs, or on the fraction of these spells classified as unemployment; and (c) increases in weeks of UI eligibility raise the likelihood of UI collection and lengthen the number of weeks of unemployment between jobs by inducing long spells to become longer and not by altering short-duration behavior.     

Estimation and Welfare Analysis With Large Demand Systems

We develop an approach for estimating individual or household level preferences for a large set of quality-differentiated goods and for constructing Hicksian welfare measures within the demand system framework. Our approach uses a maximum simulated likelihood procedure to recover estimates of the structural parameters and a multistage, Monte Carlo Markov chain algorithm for constructing Hicksian consumer surplus estimates. We illustrate our approach with a recreation dataset consisting of day trips to 62 Mid-Atlantic beaches.     

The Increasingly Mixed Proportional Hazard Model: An Application to Socioeconomic Status,Health Shocks,and Mortality

We introduce a duration model that allows for unobserved cumulative individual-specific shocks, which are likely to be important in explaining variations in duration outcomes, such as length of life and time spent unemployed. The model is also a useful tool in situations where researchers observe a great deal of information about individuals when first interviewed in surveys but little thereafter. We call this model the “increasingly mixed proportional hazard” (IMPH) model. We compare and contrast this model with the mixed proportional hazard (MPH) model, which continues to be the workhorse of applied single-spell duration analysis in economics and the other social sciences. We apply the IMPH model to study the relationships among socioeconomic status, health shocks, and mortality, using 19 waves of data drawn from the German Socio-Economic Panel (SOEP). The IMPH model is found to fit the data statistically better than the MPH model, and unobserved health shocks and socioeconomic status are shown to play powerful roles in predicting longevity.     

Bayesian Approaches to Nonparametric Estimation of Densities on the Unit Interval

This paper investigates nonparametric estimation of density on [0, 1]. The kernel estimator of density on [0, 1] has been found to be sensitive to both bandwidth and kernel. This paper proposes a unified Bayesian framework for choosing both the bandwidth and kernel function. In a simulation study, the Bayesian bandwidth estimator performed better than others, and kernel estimators were sensitive to the choice of the kernel and the shapes of the population densities on [0, 1]. The simulation and empirical results demonstrate that the methods proposed in this paper can improve the way the probability densities on [0, 1] are presently estimated.     

Computational and statistical efficiency of semiparametric gls estimators

In this note, we report a dramatic improvement in the computational efficiency of semiparametric generalized least squares(SGLS) estimation. Computation of SGLS estimates no longer presents serious problems with data sets of moderate size. We also correct a numerical error in the standard errors of the SGLS estimates reported in our recent paper in this journal (Horowitz and Neumann, 1987). The corrected standard errors of SGLS are comparable to those we reported for quantile estimates.     

Interval estimation in discriminant analysis for large dimension

This paper is concerned with the interval estimation for the log odds of the posterior probability that the observation vector belongs to one of two homoscedastic multivariate normal distributions (Π₁ and Π₂). We give the limiting distribution of the unbiased estimator for the log odds as the sample sizes and the dimension jointly tend to infinity, and approximate the confidence interval based on the asymptotic distribution. Small-scale simulations are performed to check the precision of the approximation.