Showing papers on "Semiparametric model published in 1966"

Chapter III: Nonparametric Statistics

Abstract: In their statistical review six years ago, Michael and Hunka (1960) gave four pages to nonparametric considerations and stated their belief that there had been \"somewhat less attention\" to the field from 1957 to 1960 than during the preceding three-year period. They did, however, cite a number of papers in what was then a controversy about the appropriate use of nonparametrics, about its relationship to measurement scales, and similar concerns. Three years later the same reviewer (Michael, 1963) gave still less explicit attention to nonparametrics, noting that the period from 1960 to 1963 was marked by efforts to furnish \"a partial rapprochement\" between parametric and nonparametric methods (p. 486) . This developing view of unity, together with emerging Bayesian strategies (in the parametric case), seemed to dominate the world of statistical change affecting educational research. From the present perspective, Michael's judgments appear very sound. During the past three years, much work has been spent in nonparametrics. There have been some impressive developments, and nonparametric tools have achieved a stable position with the statistical arsenal (justifying this brief chapter). Yet the field does not appear involved in many exciting new research thrusts, and the special charisma of expectation about nonpara­ metrics seems to have become faded in the last decade.

Statistical Inference of a Bivariate Proportional Hazard Model with Grouped Data

Abstract: This paper studies the estimation of a semiparametric bivariate proportional hazard model from grouped event time data. As a direct generalization of the bivariate exponential distribution of Marshall and Olkin, the model, on the one hand, controls for the effects of observed covariates, and on the other, achieves great exibility through nonparametrically specified baseline hazards. The model is most relevant in analyzing the joint distribution of two event times arising from "systems of two components". Examples include the two infection times of the left and the right kidneys of patients and the two retirement times of married couples. To estimate this semiparametric model from grouped data, we propose a maximum likelihood estimator and a minimum chi-square estimator. Both estimation methods exploit the fact that the most flexible model structure that can be identified with grouped data is finite-dimensional. Compared with the maximum likelihood estimation, the minimum chi-square procedure is computationally more attractive but applies only to "many observations per cell" cases where the covariates are either categorical or amendable to sensible grouping. Specification tests for different model assumptions are also discussed.