Objective Bayesian Analysis of an Exponential Regression Model with Constrained Parameters Applied to Animal Digestibility

In animal digestibility the proportion of degraded food along the time has usually been modeled as a normal random variable with mean a function of the time and the following three parameters: the proportion of degraded food almost instantaneously, remaining proportion of food to be degraded, and velocity of degradation. The estimation of these parameters has been carried out mainly from a frequentist viewpoint by using the asymptotic distribution of the maximum likelihood estimator. This may give inadmissible estimates, such as values outside of the range of the parameters. This drawback could not appear if a Bayesian approach were adopted. In this article an objective Bayesian analysis is developed and illustrated on real and simulated data.     

On the Nonparametric Mean Residual Life Estimator in Length-biased Sampling

In this article, we discuss nonparametric estimation of a mean residual life function from length-biased data. Precisely, we prove strong uniform consistency and weak converge of the nonparametric mean residual life estimator in length-biased setting.     

Obtaining a Trapezoidal Distribution

Given a most believed value for a quantity together with upper and lower possible deviations from that value, a rectangular distribution might be used to represent state-of-knowledge about the quantity. If the deviations are themselves known by probability distributions, and the value conditioned on the deviations is rectangular, then the marginal distribution of the value is determined by the distributions of the deviations. Here we show under quite general conditions that conversely, given the marginal distribution, the distributions of the deviations are uniquely determined. The case in which the marginal distribution is trapezoidal is studied in some detail.     

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.     

A generalization of mosteller's test

A generalization of Mosteller's test for slippage of the location parameter is proposed. The distribution of the test statistic under the null hypothesis is obtained and the power of the test is compared with that of Mosteller's test     

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).     

Infrence for non-negative autoregressive schemes

The object of this paper is the statistical analysis of Several Closely related models arising in water quality analysis. In particular, concern is with the autoregressive scheme X_r = ρX_r?1 + Y_r where 0 < ρ < 1 and Y's are i.i.d, and non-negative. The estimation and testing problem is considered for three parametric models - Gaussian, uniform and exponential - as well as for the nonparametric case where it is assumed that the Y's have a positive continuous distribution.