A flexible nonparametric regression model is considered in which the response depends linearly on some covariates, with regression coefficients as additive functions of other covariates. Polynomial spline estimators are proposed for the unknown coefficient functions, with optimal univariate mean square convergence rate under geometric mixing condition. Consistent model selection method is also ...

We consider the nonparametric functional estimation of the drift of a Gaussian process via minimax and Bayes estimators. In this context, we construct superefficient estimators of Stein type for such drifts using the Malliavin integration by parts formula and superharmonic functionals on Gaussian space. Our results are illustrated by numerical simulations and extend the construction of James–St...

In this paper, the two-parameter Pham(Loglog) model is considered to analyze the software reliability data. The Markov Chain Monte Carlo (MCMC) method is used to compute the Bayes estimates of the model parameters. It has been assumed that the parameters have gamma priors and they are independently distributed. Under the above priors, Gibbs algorithm in OpenBUGS has been applied to generate MCM...

This paper describes the Bayesian inference and prediction of the inverse Weibull distribution for Type-II censored data. First we consider the Bayesian inference of the unknown parameter under a squared error loss function. Although we have discussed mainly the squared error loss function, any other loss function can easily be considered. Gibbs sampling procedure is used to draw Markov Chain M...

The paper deals with construction of exact confidence intervals for the variance component σ 1 and ratio θ of variance components σ 1 and σ in mixed linear models for the family of normal distributions Nt (0, σ 2 1 W + σ2It). This problem essentially depends on algebraic structure of the covariance matrix W (see Gnot and Michalski, 1994, Michalski and Zmyślony, 1996). In the paper we give two c...

In this paper we study inference for a conditional model with a jump in the conditional density, where the location and size of the jump are described by regression lines. This interesting structure is shared by several structural econometric models. Two prominent examples are the standard auction model where density jumps from zero to a positive value, and the equilibrium job search model, whe...

In this paper, we propose a class of Bayes estimators for the covariance matrix of graphical Gaussian models Markov with respect to a decomposable graph G. Working with the WPG family defined by Letac and Massam [Ann. Statist. 35 (2007) 1278–1323] we derive closed-form expressions for Bayes estimators under the entropy and squared-error losses. The WPG family includes the classical inverse of t...

In this paper, we propose a class of Bayes estimators for the covariance matrix of graphical Gaussian models Markov with respect to a decomposable graph G. Working with the WPG family defined by Letac and Massam [Ann. Statist. 35 (2007) 1278–1323] we derive closed-form expressions for Bayes estimators under the entropy and squared-error losses. The WPG family includes the classical inverse of t...

to estimate the value taken by a probability density at a point in the state space. When the normalisation of the prior density is known, this value may be used to estimate a Bayes factor. It is shown that the multi-block Metropolis-Hastings estimators of Chib and Jeliazkov (2001) are bridge sampling estimators. This identification leads to estimators for the quantity of interest which may be s...