The method of sieves and its application in REML estimation

JIMING JIANG

Statistics, Case Western Reserve University

Statistical inference typically uses an object function, e.g., the likelihood. In many cases, however, optimizing of the object function over the entire parameter space is undesirable. For example, the maximum likelihood estimate may be inconsistent when the parameter space is too large. For these reasons, the maximization is often carried out over a subspace which approximates the whole space. In the language of Grenander (1981), such a sequence of approximating spaces is called a sieve. In this talk, some examples of the application of the method of sieves will be given. These include: the sieve likelihood for the proportional odds model and general regression; the analysis of Case 2 interval sensored data; identification of the orders of an autoregressive moving average model; hypothesis testing using sieves in nonparametric regression. Some theoretical aspects of the method of sieves such as consistency and rates of convergence will be briefly overviewed. Finally, the application of the method of sieves in REML -- restricted (or residual) maximum likelihood estimation will be discussed. The latter is a method of estimating dispersion parameters associated with linear models.

Refreshments: 3:30 - 4:00 p.m. Friday, at 327 Yost
Talk: 4:00 - 5:00 p.m. Friday, at 327 Yost.

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Questions? jiayang@sun.cwru.edu
Wed Aug 13 13:54:29 EDT 1997