Maximum likelihood and the bootstrap for nonlinear dynamic models

Maximum Likelihood and the Bootstrap for Nonlinear Dynamic Models

The bootstrap is an increasingly popular method for performing statistical inference. This paper provides the theoretical foundation for using the bootstrap as a valid tool of inference for quasimaximum likelihood estimators (QMLE). We provide a unified framework for analyzing bootstrapped extremum estimators of nonlinear dynamic models for heterogeneous dependent stochastic processes. We apply...

Maximum likelihood and Bayesian estimation for nonlinear structural equation models

A comparison of algorithms for maximum likelihood estimation of Spatial GLM models

In spatial generalized linear mixed models, spatial correlation is assumed by adding normal latent variables to the model. In these models because of the non-Gaussian spatial response and the presence of latent variables the likelihood function cannot usually be given in a closed form, thus the maximum likelihood approach is very challenging. The main purpose of this paper is to introduce two n...

Better Nonlinear Models from Noisy Data: Attractors with Maximum Likelihood

A new approach to nonlinear modelling is presented which, by incorporating the global behaviour of the model, lifts shortcomings of both least squares and total least squares parameter estimates. Although ubiquitous in practice, a least squares approach is fundamentally flawed in that it assumes independent, normally distributed (IND) forecast errors: nonlinear models will not yield IND errors ...

Newton-based maximum likelihood estimation in nonlinear state space models ?

Maximum likelihood (ML) estimation using Newton’s method in nonlinear state space models (SSMs) is a challenging problem due to the analytical intractability of the loglikelihood and its gradient and Hessian. We estimate the gradient and Hessian using Fisher’s identity in combination with a smoothing algorithm. We explore two approximations of the log-likelihood and of the solution of the smoot...