A generalization of Jeffreys' rule for non regular models

ABSTRACT

We propose a generalization of the one-dimensional Jeffreys' rule in order to obtain non informative prior distributions for non regular models, taking into account the comments made by Jeffreys in his article of 1946. These non informatives are parameterization invariant and the Bayesian intervals have good behavior in frequentist inference. In some important cases, we can generate non informative distributions for multi-parameter models with non regular parameters. In non regular models, the Bayesian method offers a satisfactory solution to the inference problem and also avoids the problem that the maximum likelihood estimator has with these models. Finally, we obtain non informative distributions in job-search and deterministic frontier production homogenous models.     

Empirical bayes interval estimates involving uniform distributions

Bayesian and empirical Bayesian decision rules are exhibited for the interval estimation of the parameter 0 of a Uniform (0,θ) distribution. The estimate ?,δ>resulting in the interval [?,?+δ]suffers loss given by L(?,δ>,θ)=1-[?≦e≦?+δ]+c₁((?-θ)²+(?+δ?θ)²))+c₂δ. The solution is presented for prior distributions G which have bounded support, no point masses,∫θ^?mdG(θ)<∞ and for some integer m. An example is presented involving a particular parametric form for G and rates of risk convergence in the empirical Bayes problem for this example are calculated.     

On the choice of co-ordinates in simultaneous estimation of normal means under misspecification of normal priors

The problem of choice of coordinates in Stein-type estimators,when simultaneously estimating normal means, is considered. The question of deciding whether to use all coordinates in one combined shrinkage estimators or to separate into groups and use separate shrinkage estimators on each group is considered in the situation in which part of the prior information may be " misspecified". It is observed that the amount of misspecification determines whether to use the combined shrinkage estimator the separate shrinkage estimator.     

Locally most powerful rank tests

It is the purpose of this present paper to introduce a new concept of locally most powerful rank tests. In the sequel we obtain finite sample results undervery mild regularity conditions. The approach is more v general than the related treatment of Hájek and ?idák (1967). In contrast to those authors, we need no assumptions concerning the derivatives of the underlying denstities. For instance, in the case of a regression problem in location, the density of the location family must be only square integrable. Thus the results also apply to discontinuous densities. We treat hypotheses H. of the following kind against parametric alternatives; H₀, H₁(secttest of symmetry) and H(test of independence).     

Reliability Characteristics of the Maxwell Distribution: A Bayes Estimation Study

ABSTRACT

This article presents maximum likelihood, Bayes, and empirical Bayes estimators of the truncated first moment and hazard function of the Maxwell distribution. A comparison of the relative efficiency of these three estimators is performed via a Monte Carlo simulation study.     

A Bayesian Model for Markov Chains via Jeffrey's Prior

Abstract

This work deals with the problem of Bayesian estimation of the transition probabilities associated with multistate Markov chain. The model is based on the Jeffreys' noninformative prior. The Bayesian estimator is approximated by means of MCMC techniques. A numerical study by simulation is done in order to compare the Bayesian estimator with the maximum likelihood estimator.     

Estimation of covariance matrices based on hierarchical inverse-Wishart priors

This paper focuses on Bayesian shrinkage methods for covariance matrix estimation. We examine posterior properties and frequentist risks of Bayesian estimators based on new hierarchical inverse-Wishart priors. More precisely, we give the conditions for the existence of the posterior distributions. Advantages in terms of numerical simulations of posteriors are shown. A simulation study illustrates the performance of the estimation procedures under three loss functions for relevant sample sizes and various covariance structures.     

Using Bayesian Techniques for Data Pooling in Regional Payroll Forecasting

This article adapts to the regional level a multicountry technique recently used by Garcia-Ferrer, Highfield, Palm, and Zellner (1987) and extended by Zellner and Hong (1987) to forecast the growth rates in gross national product across nine countries. This forecasting methodology is applied to the regional level by modeling payroll formation in seven Ohio metropolitan areas. We compare the forecasting performance of these procedures with that of a ridge estimator and find that the ridge estimator produces forecasts equal to or better than those from the newly proposed estimators. We conclude that the ridge estimator, which does not reference the pooled data information introduced by the newly proposed techniques, may serve as a benchmark against which to judge the relative importance of this kind of information in improving forecasts.     

The portfolio choice problem: comparison of certainty equivalence and optimal Bayes portfolios

For the portfolio problem with unknown parameter values, we compare the conventional certainty equivalence portfolio choice with the optimal Bayes portfolio. In the important single risky asset case a diffuse Bayes rule leads to portfolios that differ significantly from those suggested by a certainty equivalence rule which we show are inadmissible relative to a quadratic utility function for the range of parameters we consider. These results are invariant to arbitrary changes in the utility function parameters. We illustrate the results using a simple mutual fund example.