We derive analytic expressions for the biases, to O(n), of the maximum likelihood estimators of the parameters of the generalized Pareto distribution. Using these expressions to bias-correct the estimators in a selective manner is found to be extremely effective in terms of bias reduction, and can also result in a small reduction in relative mean squared error. In terms of remaining relative bi...

The inflated beta regression model aims to enable the modeling of responses in the intervals (0,1], [0,1) or [0,1]. In this model, hypothesis testing is often performed based on the likelihood ratio statistic. The critical values are obtained from asymptotic approximations, which may lead to distortions of size in small samples. In this sense, this paper proposes the bootstrap Bartlett correcti...

Pietra ratio (Pietra index), also known as Robin Hood index, Schutz coefficient (RicciSchutz index) or half the relative mean deviation, is a good measure of statistical heterogeneity in the context of positive-valued data sets. In this thesis, two novel methods namely “adjusted jackknife empirical likelihood” and “extended jackknife empirical likelihood” are developed from the jackknife empiri...

For 1 dimension reduction in l1, the method of Cauchy random projections multiplies the original data matrix A ∈ R with a random matrix R ∈ R (k ≪ min(n,D)) whose entries are i.i.d. samples of the standard Cauchy C(0, 1). Because of the impossibility results, one can not hope to recover the pairwise l1 distances in A from B = AR ∈ R, using linear estimators without incurring large errors. Howev...

Parameter constraints in generalized linear latent variable models are discussed. Both linear equality and inequality constraints are considered. Maximum likelihood estimators for the parameters of the constrained model and corrected standard errors are derived. A significant reduction in the dimension of the optimization problem is achieved with the proposed methodology for fitting models subj...

We consider state-aggregation schemes for Markov chains from an information-theoretic perspective. Specifically, we aggregating the states of a chain such that mutual information aggregated separated by $T$ time steps is maximized. show $T=1$ this recovers maximum-likelihood estimator degree-corrected stochastic block model as particular case, which enables us to explain certain features likeli...

We introduce, for the first time, a class of Birnbaum–Saunders nonlinear regression models. The new class of models generalizes the regression model described by Rieck and Nedelman [1991, A log-linear model for the Birnbaum–Saunders distribution, Technometrics, 33, 51–60]. We discuss maximum likelihood estimation for the parameters of the model, and derive closed-form expressions for the second...

In this paper we provide a new methodology to analyze the (Gaussian) profile quasi likelihood function for panel regression models with interactive fixed effects, also called factor models. The number of factors is assumed to be known. Employing the perturbation theory of linear operators, we derive a power series expansion of the likelihood function in the regression parameters. Using this exp...

A common study design to map quantitative trait loci (QTL) is to compare the phenotypes and marker genotypes of two or more siblings in a sample of unrelated sib groups, and to test for linkage between chromosome location and quantitative trait values. The simplest case is sib pairs only, in particular dizygotic twin pairs, and a simple and elegant regression method was proposed by Haseman & El...