A0576
Title: Quasi-maximum likelihood estimation and penalized estimation under non-standard conditions
Authors: Junichiro Yoshida - University of Tokyo, Graduate School of Mathematical Sciences (Japan) [presenting]
Nakahiro Yoshida - University of Tokyo (Japan)
Abstract: A general parametric estimation theory is suggested that allows the derivation of the limit distribution of estimators under the following two non-standard conditions: (i) The true parameter value may lie on the boundary of the parameter space, and (ii) even identifiability fails. For Singularity (i), the local form of the parameter space is sought around the true value lying on the boundary in the framework of the local asymptotic theory established by Ibragimov and Khasminskii. This approach can handle some complex examples that previous studies cannot under quasi-maximum likelihood estimation (in the ergodic or non-ergodic statistics, and with or without penalization). An example is penalized maximum likelihood estimation of variance components of random effects in linear mixed models. For Singularity (ii), penalized estimation is used to stabilize the asymptotic behavior of the estimator by forcing it to converge to the most parsimonious of all the true values. This estimator can show the oracle property even in singular models where other estimation methods for model selection, such as likelihood ratio tests, seem complicated. An example is a superposition of parametric proportional hazard models.
