Variance estimation from integrated likelihoods (VEIL)

Consistent estimation using approximate likelihoods

Conditionally Gaussian Random Sequences for Robust Integrated Variance Estimation

Conditionally Gaussian random sequences generalize State Space models along two relevant directions: (a) the parameters of the model depend in an arbitrary way from past observations, but once this dependence is realized, the randomness can be expressed in terms of Gaussian random variables, (b) correlation is introduced between the transition and measurement equations, through the presence of ...

Integrated likelihoods in models with stratum nuisance parameters

Inference about a parameter of interest in presence of a nuisance parameter can be based on an integrated likelihood function. We analyze the behaviour of inferential quantities based on such a pseudolikelihood in a two-index asymptotics framework, in which both sample size and dimension of the nuisance parameter may diverge to infinity. We show that the integrated likelihood, if chosen wisely,...

REML Variance-Component Estimation

In the numerous forms of analysis of variance (ANOVA) discussed in previous chapters, variance components were estimated by equating observed mean squares to expressions describing their expected values, these being functions of the variance components. ANOVA has the nice feature that the estimators for the variance components are unbiased regardless of whether the data are normally distributed...

Sparse Estimation Using General Likelihoods and Non-Factorial Priors

Finding maximally sparse representations from overcomplete feature dictionaries frequently involves minimizing a cost function composed of a likelihood (or data fit) term and a prior (or penalty function) that favors sparsity. While typically the prior is factorial, here we examine non-factorial alternatives that have a number of desirable properties relevant to sparse estimation and are easily...