Statistical Inference Based on an Integrated Likelihood Function

Project: Research project

Project Details

Description

1. Intellectual Merit
Integrated likelihood methods provide a promising approach to likelihood inference
in which any nuisance parameters in the model are eliminated by averaging the likelihood
with respect to a weight function for the nuisance parameter. Such an integrated
likelihood offers a number of advantages over other approaches to likelihood inference:
it is always available; it is based on averaging rather than maximization, an approach
that is often more reliable; it has a certain type of finite-sample optimality; by appropriate
selection of the weight function it has many of the same properties of marginal and
conditional likelihood functions, when either of those is available. Integrated likelihood
methods combine ideas from both Bayesian and non-Bayesian inference and, hence, provide
a hybrid method with many of the benefits of both approaches. One drawback of
integrated likelihood methods is that they are computationally intensive; however, recent
advances in computational methods has made the integrated likelihood approach attractive
even in very complex models. These methods represent a new way of thinking about
likelihood inference in models with nuisance parameters in which the traditional approach
of eliminating nuisance parameters through maximization is replaced by averaging.
The goal of the proposed research is to further develop the integrated likelihood
methodology and to apply those ideas to new areas of application. The research will
focus on three broad areas: a study of the asymptotic properties of point estimators and
the associated standard errors of maximum integrated likelihood estimators; the use of
integrated likelihood methods for estimation in models with an unknown function, and
the application of integrated likelihood theory and methodology to models with random
effects. In each of the areas, models with a high-dimensional nuisance parameter will
be of particular interest. This work will lead to better understanding of the properties
of likelihood-based methods of inference as well as the development of new statistical
methodology based on those results.
StatusFinished
Effective start/end date7/1/136/30/16

Funding

  • National Science Foundation (DMS-1308009)

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