Date of Award
Doctor of Philosophy
Kenneth J. Koehler
The thesis consists of two papers. The first develops an estimation technique termed Adjusted Quasi Maximum Likelihood Estimation (AQMLE), while the second applies it to a particular situation of practical interest and compares its performance to several other methods of estimation in a simulation study. The AQMLE is a two-step procedure. It starts with a quasi maximum likelihood estimate (QMLE), obtained by maximization of an incorrect likelihood (quasilikelihood). The quasilikelihood is often a simplified approximation to the correct likelihood, used to avoid excessive numerical computations required to maximize the true likelihood. On the second step, the QMLE is adjusted to remove asymptotic bias. The adjustment is defined implicitly through the expectation of the quasiscore under the correct model, hence the amount of computations involved does not depend on sample size (n). When the QMLE is easy to obtain, the AQMLE has an advantage of rather stable computational requirements even for large n, suggesting it might be a practical alternative to the MLE, when evaluation of the correct likelihood is complicated. The AQMLE is consistent. We present a consistent estimator for the covariance matrix in its limiting normal distribution. Finite sample behavior of the AQMLE is compared with two computational variants of the MLE and a popular QMLE in the estimation of the lognormal parameters in a censored lognormal-normal convolution. This model is used to describe measurement of a random quantity that is subject to independent, additive error. Left censoring is introduced through the use of a detection limit, a situation frequently encountered in measuring the concentration of a chemical substance in a particular material. The AQMLE offers a practically feasible alternative to both the MLE (which is difficult to evaluate because it requires separate numerical integration for each observation) and the QMLE (which suffers from asymptotic bias). In simulations for lower censoring levels, the AQMLE generally compares favorably with the QMLE, reducing its bias without excessively increasing variance. We generalize the AQMLE approach to a pseudo-AQMLE (PAQMLE) in order to handle nuisssance parameters and certain semiparametric extensions. The adjustment approach can also be extended to estimators obtained from other types of estimating functions.
Digital Repository @ Iowa State University, http://lib.dr.iastate.edu/
Brabec, Marek, "Consistent estimation using approximate likelihoods " (1997). Retrospective Theses and Dissertations. 12275.