Bayesian estimation of the difference between two proportions

This paper is concerned with the problem of allocating a fixed number of trials between two independent binomial populations with unknown success probabilities θ₁ and θ₂, in order to estimate θ₁ - θ₂ with squared error loss. Introducing independent beta priors on θ₁ and θ₂, a heuristic allocation procedure is introduced and compared both with the optimal and with the best fixed allocation procedure. Numerical and asymptotic results of these comparisons are given and seem to indicate that there are situations when the best fixed allocation procedure performs almost as well as the optimal procedure.     

Interval estimates for variance components

The fiducial approach to the two components of variance random effects model developed by Venables and James (1978) is related to the Bayesian approach of Box and Tiao (1973). The operating characteristics, under repeated sampling, of the resulting interval estimators for the “within classes” variance component are investigated, and the behaviour of the two sets of intervals is found to be very similar, the coverage frequency of 95% probability intervals being approximately 91% when the “between classes” variance component is zero but rising rapidly to 95% as the between component increases. The probability intervals are shown to be shorter on average than a comparable confidence interval based upon the within classes sum of squares, and to be robust against nonnormality in the class means.     

Cognitive Components of Risk Ratings

This study examined what lay people mean when they judge the "risk" of activities that involve the potential for accidental fatalities (e.g., hang gliding, living near a nuclear reactor). A sample of German and American students rated the "overall risk" of 14 such activities and provided 3 fatality estimates: the number of fatalities in an "average year," the individual yearly fatality probability (or odds), and the number of fatalities in a "disastrous accident." Subjects' fatality estimates were reasonably accurate and only moderately influenced by attitudes towards nuclear energy. Individual fatality probability correlated most highly with intuitive risk ratings. Disaster estimates correlated positively with risk ratings for those activities that had a low fatality probability and a relatively high disaster potential. Annual average fatality rates did not correlate with risk ratings at all. These findings were interpreted in terms of a two-dimensional cognitive structure. Subjective notions of risk were determined primarily by the personal chance of death; for some activities, "disaster potential" played a secondary role in shaping risk perception.     

Sampling properties of estimators of a Weibull distribution of use in the lumber industry

We consider maximum-likelihood estimators of the three parameters in the Weibull distribution. Motivated by an application regarding the determination of a lower percentile of the strength of dimension lumber, we investigate the sampling properties of these estimators. Consistency is established when the shape parameter is greater than one, including some nonregular cases encountered in fitting lumber data. The joint distribution of the estimators is studied by a Monte Carlo approach. The maximum-likelihood estimator of the 5th percentile is compared with the sample 5th percentile. For the cases considered it was generally found that with sample size 70 the usual asymptotic normality does not hold.     

Estimation of frequencies of sinusoids in the presence of noise

A method is proposed and developed for estimating the frequencies of K sinusoids given the sum of these sinusoids in Gaussian noise. Attention is focused on the properties of these estimators when the observation time is short, the separation between frequencies is small, and the signal-to-noise ratio is high. The estimators are shown to be approximately unbiased and approximately normally distributed. The covariance matrix is also calculated. Relatively simple bounds on the variance of the estimators are found.     

Estimation of poisson means under weighted squared error loss

In estimating the means of several independent Poisson distributions, we show that the maximum likelihood estimator is inadmissible when general weighted squared error loss is the criterion. Using this result, we extend the known results on estimation of several Poisson means (Peng 1975, Hudson 1978) to the case where possibly more than one observation is taken from each Poisson distribution and the samples are not necessarily of the same size.     

Bias in Population Estimates of Long-Term Exposure from Short-Term Measurements of Individual Exposure

A population's long-term exposure distribution for a specified compound is typically estimated from short-term measurements of a sample of individuals from the population of interest. In this situation, estimates of a population's long-term exposure parameters contain two sources of sampling error: the typical sampling error associated with taking a sample from the population and the sampling error from estimating individual long-term exposure. These components are not separable in the data collected, i.e. , the value observed is due partly to the individual sampled and partly to the time at which the individual was sampled. Hence, the distribution of the data collected is not the same as the population exposure distribution. Monte Carlo simulations are used to compare the distribution of the observed data with the population exposure distribution for a simple additive model. A simple adjustment to standard estimates of percentiles and quantils is shown to be effective in reducing bias particularly for the upper percentiles and quantils of the population distribution.     

Asymptotic properties of randomly indexed sequences of random variables

Conditions are given for a randomly indexed sequence of random variables to converge weakly. The key concept employed is the so-called generalized Anscombe condition. The results give a method of determining sequential stopping rules, which have the required accuracy of estimation of an unknown parameter in the case when the observations are not necessarily independent and identically distributed.     

Smooth Conditional Distribution Function and Quantiles under Random Censorship

We consider a nonparametric random design regression model in which the response variable is possibly right censored. The aim of this paper is to estimate the conditional distribution function and the conditional -quantile of the response variable. We restrict attention to the case where the response variable as well as the explanatory variable are unidimensional and continuous. We propose and discuss two classes of estimators which are smooth with respect to the response variable as well as to the covariate. Some simulations demonstrate that the new methods have better mean square error performances than the generalized Kaplan-Meier estimator introduced by Beran (1981) and considered in the literature by Dabrowska (1989, 1992) and Gonzalez-Manteiga and Cadarso-Suarez (1994).     

Estimation and Inference in Large Heterogeneous Panels with a Multifactor Error Structure

This paper presents a new approach to estimation and inference in panel data models with a general multifactor error structure. The unobserved factors and the individual‐specific errors are allowed to follow arbitrary stationary processes, and the number of unobserved factors need not be estimated. The basic idea is to filter the individual‐specific regressors by means of cross‐section averages such that asymptotically as the cross‐section dimension (N) tends to infinity, the differential effects of unobserved common factors are eliminated. The estimation procedure has the advantage that it can be computed by least squares applied to auxiliary regressions where the observed regressors are augmented with cross‐sectional averages of the dependent variable and the individual‐specific regressors. A number of estimators (referred to as common correlated effects (CCE) estimators) are proposed and their asymptotic distributions are derived. The small sample properties of mean group and pooled CCE estimators are investigated by Monte Carlo experiments, showing that the CCE estimators have satisfactory small sample properties even under a substantial degree of heterogeneity and dynamics, and for relatively small values of N and T.