Related papers: The distribution of Pearson residuals in generaliz…
This paper considers estimation of the predictive density for a normal linear model with unknown variance under alpha-divergence loss for -1 <= alpha <= 1. We first give a general canonical form for the problem, and then give general…
We present improved methods for calculating confidence intervals and $p$-values in situations where standard asymptotic approaches fail due to small sample sizes. We apply these techniques to a specific class of statistical model that can…
The purpose of this paper is to provide a discussion, with illustrating examples, on Bayesian forecasting for dynamic generalized linear models (DGLMs). Adopting approximate Bayesian analysis, based on conjugate forms and on Bayes linear…
Generalized likelihoods are commonly used to obtain consistent estimators with attractive computational and robustness properties. Formally, any generalized likelihood can be used to define a generalized posterior distribution, but an…
The likelihood for the parameters of a generalized linear mixed model involves an integral which may be of very high dimension. Because of this intractability, many approximations to the likelihood have been proposed, but all can fail when…
Generalized linear models are flexible tools for the analysis of diverse datasets, but the classical formulation requires that the parametric component is correctly specified and the data contain no atypical observations. To address these…
This paper presents a general framework for the estimation of regression models with circular covariates, where the conditional distribution of the response given the covariate can be specified through a parametric model. The estimation of…
Denoising diffusion models have become ubiquitous for generative modeling. The core idea is to transport the data distribution to a Gaussian by using a diffusion. Approximate samples from the data distribution are then obtained by…
This paper extends earlier work on the distribution in the complex plane of the roots of random polynomials. In this paper, the random polynomials are generalized to random finite sums of given "basis" functions. The basis functions are…
In this paper we address the complexity of solving linear programming problems with a set of differential equations that converge to a fixed point that represents the optimal solution. Assuming a probabilistic model, where the inputs are…
We study full Bayesian procedures for high-dimensional linear regression under sparsity constraints. The prior is a mixture of point masses at zero and continuous distributions. Under compatibility conditions on the design matrix, the…
The linear regression models are widely used statistical techniques in numerous practical applications. The standard regression model requires several assumptions about the regres- sors and the error term. The regression parameters are…
Statistical inferences for high-dimensional regression models have been extensively studied for their wide applications ranging from genomics, neuroscience, to economics. However, in practice, there are often potential unmeasured…
The binomial, the negative binomial, the Poisson, the compound Poisson and the Erlang distribution do all admit integral representations with respect to its (continuous) parameter. We use the Margulis-Russo type formulas for Bernoulli and…
Consider the family of power divergence statistics based on $n$ trials, each leading to one of $r$ possible outcomes. This includes the log-likelihood ratio and Pearson's statistic as important special cases. It is known that in certain…
Stochastic models share many characteristics with generic parametric models. In some ways they can be regarded as a special case. But for stochastic models there is a notion of weak distribution or generalised random variable, and the same…
Products between phase-type distributed random variables and any independent, positive and continuous random variable are studied. Their asymptotic properties are established, and an expectation-maximization algorithm for their effective…
This paper is concerned with general nonlinear regression models where the predictor variables are subject to Berkson-type measurement errors. The measurement errors are assumed to have a general parametric distribution, which is not…
Uncovering genuine relationships between a response variable of interest and a large collection of covariates is a fundamental and practically important problem. In the context of Gaussian linear models, both the Bayesian and non-Bayesian…
A formalism is presented for analytically obtaining the probability density function, (P_{n}(s)), for the random distance (s) between two random points in an (n)-dimensional spherical object of radius (R). Our formalism allows (P_{n}(s)) to…