Reduced-rank Vector Generalized Linear Models

The VGAM Package for Categorical Data Analysis

Classical categorical regression models such as the multinomial logit and proportional odds models are shown to be readily handled by the vector generalized linear and additive model (VGLM/VGAM) framework. Additionally, there are natural extensions, such as reduced-rank VGLMs for dimension reduction, and allowing covariates that have values specific to each linear/additive predictor, e.g., for ...

Minimum-variance Pseudo-unbiased Reduced-rank Estimator (mv-pure) and Its Applications to Ill-conditioned Inverse Problems

This paper presents mathematically novel estimator for the linear regression model named Minimum-Variance Pseudo-Unbiased Reduced-Rank Estimator (MV-PURE), designed specially for applications where the model matrix under consideration is ill-conditioned, and auxiliary knowledge on the unknown deterministic parameter vector is available in the form of linear constraints. We demonstrate closed al...

The Negative Binomial Distribution Efficiency in Finite Mixture of Semi-parametric Generalized Linear Models

Introduction Selection the appropriate statistical model for the response variable is one of the most important problem in the finite mixture of generalized linear models. One of the distributions which it has a problem in a finite mixture of semi-parametric generalized statistical models, is the Poisson distribution. In this paper, to overcome over dispersion and computational burden, finite ...

Practical Problems with Reduced Rank ML Estimators for Cointegration Parameters and a Simple Alternative

Johansen’s reduced rank maximum likelihood (ML) estimator for cointegration parameters in vector error correction models is known to produce occasional extreme outliers. Using a small monetary system and German data we illustrate the practical importance of this problem. We also consider an alternative generalized least squares (GLS) system estimator which has better properties in this respect....

On Solving Linear Diophantine Systems Using Generalized Rosser's Algorithm