Pairwise Likelihood Inference for General State Space Models

Abstract

This article concerns parameter estimation for general state space models, following a frequentist likelihood-based approach. Since exact methods for computing and maximizing the likelihood function are usually not feasible, approximate solutions, based on Monte Carlo or numerical methods, have to be considered. Here, we concentrate on a different approach based on a simple pseudolikelihood, called “pairwise likelihood.” Its merit is to reduce the computational burden so that it is possible to fit highly structured statistical models, even when the use of standard likelihood methods is not possible. We discuss pairwise likelihood inference for state space models, and we present some touchstone examples concerning autoregressive models with additive observation noise and switching regimes, the local level model and a non-Makovian generalization of the dynamic Tobit model

A spatial generalized ordered response model to examine highway crash injury severity

“…However, previous studies (Varin and Vidoni, 2009, Varin and Czado, 2010 have shown that spatial dependency drops quickly with interobservation distance. Therefore, there is no need to retain all observation pairs because the pairs formed from the closest crashes provide much more information than pairs from crashes that occur far from one another.…”

Estimating Space and Space-Time Covariance Functions for Large Data Sets: A Weighted Composite Likelihood Approach

“…For instance Heagerty and Lele (1998) recommended to consider only significant lags but only to save computations. Varin and Vidoni (2007) There exist other ways to construct CL in a space-time setting. For instance the approximating likelihoods on selected blocks introduced by Caragea and Smith (2005) are special cases of the CL.…”

A latent variable representation of count data models to accommodate spatial and temporal dependence: Application to predicting crash frequency at intersections

“…Almost all earlier research efforts employing the CML technique have used the pairwise approach in which the observed events e A correspond to a pair of observations from the (QT×1) vector m. These earlier studies include Apanasovich et al, (2008), Varin and Vidoni (2009), Engle et al (2007), Bhat et al (2010a), and Bhat and Sener (2009). Alternatively, the analyst can also consider larger subsets of observations, such as triplets or quadruplets or even higher dimensional subsets (see Engler et al, 2006 andCaragea and.…”

“…Procedures similar to those available with the maximum likelihood approach are also available for model selection with the CML approach (see Varin and Vidoni, 2009, Pace et al, 2011and Bhat, 2011. The statistical test for a single parameter may be pursued using the usual t-statistic.…”