Penalized likelihood smoothing in robust state space models

Efficient Likelihood Estimation in State Space Models

Motivated by studying asymptotic properties of the maximum likelihood estimator (MLE) in stochastic volatility (SV) models, in this paper we investigate likelihood estimation in state space models. We first prove, under some regularity conditions, there is a consistent sequence of roots of the likelihood equation that is asymptotically normal with the inverse of the Fisher information as its va...

Smoothing Algorithms for State-Space Models

A prevalent problem in statistical signal processing, applied statistics, and time series analysis is the calculation of the smoothed posterior distribution, which describes the uncertainty associated with a state, or a sequence of states, conditional on data from the past, the present, and the future. The aim of this paper is to provide a rigorous foundation for the calculation, or approximati...

Asymptotic Quasi-likelihood Based on Kernel Smoothing for Nonlinear and Non-Gaussian State-Space Models

This paper considers parameter estimation for nonlinear and non-Gaussian state-space models with correlation. We propose an asymptotic quasilikelihood (AQL) approach which utilises a nonparametric kernel estimator of the conditional variance covariances matrix Σt to replace the true Σt in the standard quasi-likelihood. The kernel estimation avoids the risk of potential miss-specification of Σt ...

Penalized Likelihood Estimation in Gaussian Mixture Models

Statistical models: Conventional, penalized and hierarchical likelihood

We give an overview of statistical models and likelihood, together with two of its variants: penalized and hierarchical likelihood. The Kullback-Leibler divergence is referred to repeatedly in the literature, for defining the misspecification risk of a model and for grounding the likelihood and the likelihood cross-validation, which can be used for choosing weights in penalized likelihood. Fami...