Negative Binomial Quasi-Likelihood Inference for General Integer-Valued Time Series Models

On Some Negative Integer Moments of Quasi-Negative-Binomial Distribution

Quasi-likelihood models and optimal inference

Consider an ergodic Markov chain on the real line, with parametric models for the conditional mean and variance of the transition distribution. Such a setting is an instance of a quasi-likelihood model. The customary estimator for the parameter is the maximum quasi-likelihood estimator. It is not eecient, but as good as the best estimator that ignores the parametric model for the conditional va...

Fully Bayesian inference for neural models with negative-binomial spiking

Characterizing the information carried by neural populations in the brain requires accurate statistical models of neural spike responses. The negative-binomial distribution provides a convenient model for over-dispersed spike counts, that is, responses with greater-than-Poisson variability. Here we describe a powerful data-augmentation framework for fully Bayesian inference in neural models wit...

A negative binomial model for time series of counts

We study generalized linear models for time series of counts, where serial dependence is introduced through a dependent latent process in the link function. Conditional on the covariates and the latent process, the observation is modelled by a negative binomial distribution. To estimate the regression coefficients, we maximize the pseudolikelihood that is based on a generalized linear model wit...

The Combined Poisson Inma(2) Models for Integer-valued Time Series

In this paper, we introduce a new combined integer-valued moving average model of order 2 with poisson innovation, denoted by PCINMA(2). We consider some properties of this process, such as expectation, variance, autocovariance function. Stationary and ergodicity are obtained. We estimate the unknown parameters by using Yule-Walker estimation, and use simulation to assess the performance of Yul...