Empirical Bayes Regression Analysis with Many Regressors but Fewer Observations

Regression Analysis under Inverse Gaussian Model: Repeated Observation Case

 Traditional regression analyses assume normality of observations and independence of mean and variance. However, there are many examples in science and Technology where the observations come from a skewed distribution and moreover there is a functional dependence between variance and mean. In this article, we propose a method for regression analysis under Inverse Gaussian model when th...

Supplement to Empirical Bayes Regression with Many Regressors

EMPIRICAL BAYES ANALYSIS OF TWO-FACTOR EXPERIMENTS UNDER INVERSE GAUSSIAN MODEL

A two-factor experiment with interaction between factors wherein observations follow an Inverse Gaussian model is considered. Analysis of the experiment is approached via an empirical Bayes procedure. The conjugate family of prior distributions is considered. Bayes and empirical Bayes estimators are derived. Application of the procedure is illustrated on a data set, which has previously been an...

Empirical Bayes Forecasts of One Time Series Using Many Predictors

We consider both frequentist and empirical Bayes forecasts of a single time series using a linear model with T observations and K orthonormal predictors. The frequentist formulation considers estimators that are equivariant under permutations (reorderings) of the regressors. The empirical Bayes formulation (both parametric and nonparametric) treats the coefficients as i.i.d. and estimates their...

Adaptive Monte Carlo for Binary Regression with Many Regressors

This article describes a method for efficient posterior simulation for Bayesian variable selection in probit regression models with many regressors but few observations. A proposal on model space is described which contains a tuneable parameter. An adaptive approach to choosing this tuning parameter is described which allows automatic, efficient computation in these models. The methods is appli...