Using simulation methods for bayesian econometric models: inference,development and communication: some comments

We extend the average derivatives estimator to the case of functionally dependent regressors. We show that the proposed estimator is consistent and has a limiting normal distribution. A consistent covariance matrix estimator for the proposed estimator is provided.     

Tests of association between survival time and a continuous covariate

Proportional hazards model(Cox, 1972) is reviewed for the case of grouped data with one continuously measured covariate. This leads to a logit-rank procedure for tied data which is reduced to the test proposed by O’Brien(1978) and studied by O’Quigley and Prentice(1991) in the absence of ties. The proposed test is then applied to a special ranking method in order to study non-monotonic associations.     

Bayes prediction of number of failures in weibull samples

This work is concerned with the Bayesian prediction problem of the number of components which will fail in a future time interval, when the failure times are Weibull distributed. Both the 1-sample and the 2-sample prediction problems are dealed with, and some choices of the prior densities on the distribution parameters are discussed which are relatively easy to work with and allow different degrees of knowledge on the failure mechanism to be incorporated in the predictive procedure. Useful relations between the predictive distribution on the number of future failures and the predictive distribution on the future failure times are derived. Numerical examples are also given.     

A new goodness of fit test for the equality of multinomial cell probabilities versus trend alternatives

In this paper, a new test statistic is presented for testing the null hypothesis of equal multinomial cell probabilities versus various trend alternatives. Exact asymptotic critical values are obtained, The power of the test is compared with several other statistics considered by Choulakian et al (1995), The test is shown to have better power for certain trend alternatives.     

A note on second order slope rotatable designs over all directions

Hader and Park (1978) introduced second order slope rotatability in axial directions. Park (1987) introduced second order slope rotatabilty over all directions. It is shown that these designs have the additional properly that the sum of the variances of estimates of slopes in all directions at any point is a function of the distance of the point from the design origin.     

GNR,MGR, and exact misspeclfication testing

The Gauss-Newton regression (GNR) is widely used to compute Lagrange multiplier statistics. A regression described by Milliken and Graybill yields an exact F test in a certain class of nonlinear models which are linear under the null. This paper shows that the Milliken-Graybill regression is a GNR. Hence one interpretation of Milliken-Graybill is that they identified a class of nonlinear models for which the GNR yields an exact test.     

The non-null distributions in anoya

Under the traditional assumptions, any entry in ANOVA interpreted to include all Linear model analyses] is equivalent in disiributien to a quadratic form Q=[μ₁+σ₁Z₁]²+…+ [μ_ν+σ_νZ_ν]²]wherein Z₁..Z_ν are independent standard normal variables. Test statisics in ANOVE are distributed as ratio R of two depenbent such quadretic forms. The non-null distribution of R is a mixture of null distributions; the mixing variable is an easy generalitatlon of the Poisson variable. Fast algorithms yield the power function in both fixed and random effects models in AVOVA to user-specified accuracy.     

Optimal spacing of quantiles for the estimation of the mixing parameters in a mixture of two exponential distributions

Methods for estimating the mixing parameters in a mixture of two exponential distributions are proposed. The estimators proposed are consistent and BAN(best asymptotically normal). The optimal spacings for estimating these mixture parameters are calculated.     

Conditional interval estimation of the mean following rejection of a two sided test

The effect of rejecting a two-sided preliminary test of significance for the mean of a normal distribution upon subsequent interval estimation of the mean is examined. For the case where the variance is known, conditional confidence intervals may be shorter than unconditional intervals, in contrast to the one-sided preliminary test case examined by Meeks and D’Agostino (1983, The American Statistician, 7, 134-136) . For the case where the variance is unknown and must be estimated by the sample variance, it is shown that customary intervals do not offer uniformly greater or lesser coverage than the nominal level.