Bandwidth plays an important role in determining the performance of nonparametric estimators, such as the local constant estimator. In this paper, we propose a Bayesian approach to bandwidth estimation for local constant estimators of time–varying coefficients in time series models. We establish a large sample theory for the proposed bandwidth estimator and Bayesian estimators of the unknown pa...

In this paper we propose an efficient Markov chain Monte Carlo (MCMC) method for estimation of discrete distributions by solving an appropriate system of linear equations. We call the estimator the equation-solving estimator. Our numerical results show that the new estimator makes significant improvements over the conventional frequencyMCMCestimator in terms of accuracy of the estimates. The ne...

The two standard methods of obtaining a least-squares optimal estimator are (1) Bayesian estimation, in which one assumes a prior distribution on the true values and combines this with a model of the measurement process to obtain an optimal estimator, and (2) supervised regression, in which one optimizes a parametric estimator over a training set containing pairs of corrupted measurements and t...

In estimation of the large precision matrix, this paper suggests a new shrinkage estimator, called the linear ridge estimator. This estimator is motivated from a Bayesian aspect for a spike and slab prior distribution of the precision matrix, and has a form of convex combination of the ridge estimator and the identity matrix multiplied by scalar. The optimal parameters in the linear ridge estim...

This note is concerned with Bayesian estimation of the transition probabilities of a binary Markov chain observed from heterogeneous individuals. The model is founded on Jeffreys’ prior which allows for transition probabilities to be correlated. The Bayesian estimator is approximated by means of Monte Carlo Markov chain (MCMC) techniques. The performance of the Bayesian estimates is illustrated...

In this paper, by conditioning on the matrix variate normal distribution (MVND) the construction of the matrix t-type family is considered, thus providing a new perspective of this family. Some important statistical characteristics are given. The presented t-type family is an extension to the work of Dickey [8]. A Bayes estimator for the column covariance matrix &Sigma of MVND is derived under ...