This article proposes a novel non-stationary BINMA time series model by extending two INMA processes where their innovation series follow the bivariate Poisson under time-varying moment assumptions. This article also demonstrates, through simulation studies, the use and superiority of the generalized quasi-likelihood (GQL) approach to estimate the regression effects, which is computationally less complicated as compared to conditional maximum likelihood estimation (CMLE) and the feasible generalized least squares (FGLS). The serial and bivariate dependence correlations are estimated by a robust method of moments.

This article addresses the modelling of day and night larceny incidents in two regions of Mauritius through a bivariate integer-valued autoregressive of order 1 (BINAR(1)) model with a flexible Conway–Maxwell Poisson (CMP) innovations under time-varying moments. The outcome of the study demonstrates scientifically the contributory effects and helps to understand the main influential factors which could guide policy makers for remedial measures. A small simulation study is also incorporated to assess the performance of the generalized quasi-likelihood (GQL) estimation method. The proposed model is compared with other relevant competing bivariate models in the application part.

The problem of multicollinearity among predictor variables is a frequent issue in longitudinal data analysis. In this context, this paper proposes a mixed ridge regression model via shrinkage methods to analyze such data. Furthermore, in view of obtaining more efficient estimators, we propose preliminary and Stein-type estimators using prior information for fixed-effects parameters. The model parameters are estimated via the EM algorithm. A simulation study is also presented to assess the performance of the estimators under different estimation methods. An application to the HIV data is also illustrated.