We study holonomic gradient decent for maximum likelihood estimation of exponentialpolynomial distribution, whose density is the exponential function of a polynomial in the random variable. We first consider the case that the support of the distribution is the set of positive reals. We show that the maximum likelihood estimate (MLE) can be easily computed by the holonomic gradient descent, even...

Finite mixtures of simpler component models such as mixtures of normals and mixtures of generalized linear models (GLM) have proven useful for modelling data arising from a heterogeneous population, typically under an independence assumption. Mixed-effects models are often used to handle correlation as arises in longitudinal or other clustered data. In Chapter 3 of this dissertation, we present...

This document contains supplementary material to the paper “Fast smoothing parameter separation in multidimensional generalized P-splines: the SAP algorithm”. A description on how to obtain the derivatives of the approximate restricted maximum likelihood (REML) with respect to the variance components is given, as well as the closed-form expressions for maximum likelihood (ML) estimates of the v...

In this paper, an algorithm providing Maximum Likelihood estimates and their asymptotic covariance matrix for the parameters in correlation models and association models is proposed. It is based on a Fisher's scoring type algorithm using the asymptotic covariance matrix of Maximum Likelihood estimates whose expression is also given. The convergence of the proposed algorithm is generally quickly...

Gamma processes and their variants are natural choices for degradation modeling of many products. Motivated by practical needs, this paper investigates semiparametric inference of the simple gamma process model and the random effect variant. Maximum likelihood estimates (MLEs) are obtained through the EM algorithm, while the confidence intervals are constructed via the bootstrap method. The sim...

This paper surveys the theoretical and computational development of the restricted maximum likelihood (REML) approach for the estimation of covariance matrices in linear stochastic models. A new derivation of this approach is given, valid under very weak conditions on the noise. Then the calculation of the gradient of restricted loglikelihood functions is discussed , with special emphasis on th...