In this paper we consider the problem of constructing confidence sets for the parameters of general linear models. Based on subsampling techniques and building on earlier exact finite sample results due to Hartigan, we compute the exact probability that the true parameters belong to certain regions in the parameter space. By intersecting these regions, a confidence set containing the true param...

SUMMARY We derive the joint distribution of the sequence of estimates of the parameter vector in a normal general linear model when data accumulate over a series of analyses. This sequence of estimates has a remarkably simple covariance structure, even when observations are correlated, allowing standard group sequential tests to be applied in very general settings. If observations' variances an...

High dimensional statistics deals with the challenge of extracting structured information from complex model settings. Compared with the growing number of frequentist methodologies, there are rather few theoretically optimal Bayes methods that can deal with very general high dimensional models. In contrast, Bayes methods have been extensively studied in various nonparametric settings and rate o...

The classical quadratic loss for the partially linear model (PLM) and the likelihood function for the generalized PLM are not resistant to outliers. This inspires us to propose a class of “robust-Bregman divergence (BD)” estimators of both the parametric and nonparametric components in the general partially linear model (GPLM), which allows the distribution of the response variable to be partia...

In previous work (Penny et al., [2005]: Neuroimage 24:350-362) we have developed a spatially regularised General Linear Model for the analysis of functional magnetic resonance imaging data that allows for the characterisation of regionally specific effects using Posterior Probability Maps (PPMs). In this paper we show how it also provides an approximation to the model evidence. This is importan...

The present paper considers a bias correction of Akaike’s information criterion (AIC) for selecting variables in the generalized linear model (GLM). When the sample size is not so large, the AIC has a non-negligible bias that will negatively affect variable selection. In the present study, we obtain a simple expression for a bias-corrected AIC (corrected AIC, or CAIC) in GLMs. A numerical study...

This paper presents the multivariate linear models for the evaluation of compressive, flexural and splitting tensile strengths, and toughness ratio of high-performance steel fiber reinforced concrete (HPSFRC). In this study, 44 series of concrete mixes with varying silica fume replacement and fiber dosage (Vf = 0.0, 0.5, 1.0 and 1.5%) were considered. Test results indicated that addition of fib...

This paper develops a methodology for approximating the posterior first two moments of the posterior distribution in Bayesian inference. Partially specified probability models, which are defined only by specifying means and variances, are constructed based upon second-order conditional independence, in order to facilitate posterior updating and prediction of required distributional quantities. ...

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We study estiuultion of regression parameters in heteroscedastic linear models when the ntunber of parameters is large. The results