Showing papers on "Semiparametric model published in 1988"

Life Distributions Structure Of Nonparametric Semiparametric And Parametric Families

Abstract: Basics.- Preliminaries.- Ordering Distributions: Descriptive Statistics.- Mixtures.- Nonparametric Families.- Nonparametric Families: Densities and Hazard Rates.- Nonparametric Families: Origins in Reliability Theory.- Nonparametric Families: Inequalities for Moments and Survival Functions.- Semiparametric Families.- Semiparametric Families.- Parametric Families.- The Exponential Distribution.- Parametric Extensions of the Exponential Distribution.- Gompertz and Gompertz-Makeham Distributions.- The Pareto and F Distributions and Their Parametric Extensions.- Logarithmic Distributions.- The Inverse Gaussian Distribution.- Distributions with Bounded Support.- Additional Parametric Families.- Models Involving Several Variables.- Covariate Models.- Several Types of Failure: Competing Risks.- More About Semi-parametric Families.- Characterizations Through Coincidences of Semiparametric Families.- More About Semiparametric Families.- Complementary Topics.- Some Topics from Probability Theory.- Convexity and Total Positivity.- Some Functional Equations.- Gamma and Beta Functions.- Some Topics from Analysis.

Estimation and Testing in a Two-Sample Generalized Odds-Rate Model

Abstract: The generalized odds ratio for a survival variable T is defined as Λ T (t | c) = c -1[1 - Sc (t)]/Sc (t) for c > 0 and -log S(t) for c = 0, where S(t) = Pr(T > t). This ratio coincides with the integrated hazard for c = 0 and the odds ratio for c = 1. When the distribution of T depends on a covariate vector, we assume that conditionally on the covariates, log Λ T (t | c) is linear in the covariates. This model is a generalization of the proportional hazard model (PHM), which has an interpretation both as a PHM with random nuisance effects (Clayton and Cuzick 1986) and as a proportional odds-rate model with the odds rate defined from the response times of series systems. Harrington and Fleming (1982) and Bickel (1986a) considered rank tests for this semiparametric model, Clayton and Cuzick (1986) considered estimation. We use the odds-rate representation to define a class of estimates of the proportionality parameter in the two-sample case. We show that the estimates are consistent and asymptotica...

Semiparametric econometrics: A survey

Abstract: SUMMARY Semiparametric econometric models contain both parametric and nonparametric components, reflecting in some fashion what has been learned from economic theory and previous empirical experience, and what remains unknown. They raise such questions as how well the parametric component can be estimated, and how to construct rules of inference with good statistical properties. The paper attempts to survey the econometric and most relevant statistical literature on semiparametric inference, and includes a partial bibliography.

Goodness-of-fit Tests for Additive Hazards and Proportional Hazards Models

Abstract: Goodness-of-fit tests for Cox's proportional hazards model and Aalen's additive risk model, in which each model is compared on an equal footing with the best fitting fully nonparametric model, are developed. The goodness-of-fit statistics are based on differences each model, with a fully nonparametric estimator of d recently introduced by the authors. Here A( , z) denotes the conditional hazard function of the survival time of an individual with covariate vector z. Comparison of the results of the tests makes it possible to decide whether Cox's proportional hazards or Aalen's additive risk model gives a better fit to the data. In addition, a goodness-of-fit test for Cox's model within the family of all proportional hazards models A(t, z) = AO(t)r(z), where AO is a baseline hazard function and r is a general relative risk function, is developed. Additive hazards and proportional hazards regression models used in the analysis of censored survival data can give substantially different results. For instance, in connection with a study of cancer mortality among Japanese atomic bomb survivors, Muirhead & Darby (1987) have noted that the two models give substantially different estimates of the age-spe- cific probability that an individual will develop radiation induced cancer. Muirhead & Darby (see also Aranda-Ordaz, 1983) introduced a generalized parametric model which contains parametric additive hazards and proportional hazards models as special cases. The goodness- of-fit of each model is then obtained by comparing with the best fitting model within the generalized family, allowing the two special models to be treated on an equal footing. Beyond the parametric setting, much effort has been devoted to the development of goodness-of-fit tests for Cox's (1972) proportional hazards model

Semiparametric M-Estimation of Censored Linear Regression Models

Abstract: Quantile and semiparametric M estimation are methods for estimating a censored linear regression model without assuming that the distribution of the random component of the model belongs to a known parametric family. Both methods require estimating derivatives of the unknown cumulative distribution function of the random component. The derivatives can be estimated consistently using kernel estimators in the case of quantile estimation and finite difference quotients in the case of semiparametric M estimation. However, the resulting estimates of derivatives, as well as parameter estimates and inferences that depend on the derivatives, can be highly sensitive to the choice of the kernel and finite difference bandwidths. This paper discusses the theory of asymptotically optimal bandwidths for kernel and difference quotient estimation of the derivatives required for quantile and semiparametric M estimation, respectively. We do not present a fully automatic method for bandwidth selection.

Estimating a Real Parameter in a Class of Semiparametric Models

Abstract: We study semiparametric models where for a fixed value of the finite-dimensional parameter there exists a sufficient statistic for the nuisance parameter. An asymptotically normal sequence of estimators for the parametric component is constructed, which is efficient under the assumption that projecting on the set of nuisance scores is equivalent to taking conditional expectations given the sufficient statistic. The latter property is checked for a number of examples, in particular for mixture models. We discuss the relation of our approach to conditional maximum likelihood estimation.

Minimax Estimates in a Semiparametric Model

Abstract: The statistical analysis of multidimensional data has been greatly influenced by the widespread use of computer-intensive smoothing techniques. These techniques allow one to look at the dependency of a response on several covariates without actually specifying the exact form of that dependency. Nevertheless, when the response's dependency on some subset of the covariates can be assumed to be, say, linear, common sense dictates incorporating this assumption into the estimation technique. In the semiparametric model with covariates X and t, the response, Y, is modeled as the sum of three components: g(t) with g (unknown) lying in an infinite-dimensional space, a linear component Xβ, and random error. If β were the parameter of interest, with the function g treated as a nuisance parameter, the conservative statistician would be led to a minimax approach, with the estimate of β minimizing the worst that could happen over a specified class of functions. Of course, the class of functions should be one ...

Semiparametric and nonparametric econometrics

Abstract: The Asymptotic Efficiency of Semiparametric Estimators for Censored Linear Regression Models.- Nonparametric Kernel Estimation Applied to Forecasting: An Evaluation Based on the Bootstrap.- Calibrating Histograms with Application to Economic Data.- The Role of Fiscal Policy in the St. Louis Model: Nonparametric Estimates for a Small Open Economy.- Automatic Smoothing Parameter Selection: A Survey.- Bayes Prediction Density and Regression Estimation - A Semiparametric Approach.- Nonparametric Estimation and Hypothesis Testing in Econometric Models.- Some Simulation Studies of Nonparametric Estimators.- Estimating a Hedonic Earnings Function with a Nonparametric Method.

Rates of convergence of some estimators for a semiparametric model

Abstract: In this paper, we analyze the rates of convergence of the mean square error of a partial spline estimator and a Denby/Speckman - type estimator for the parametric component of a semiparametric model under a wide range of conditions. It is found that the Denby/Speckman - type estimator has a faster rate of convergence than the partial spline estimator for some cases. It is shown that the optimal rate of decrease for the smoothing parameter X under the criterion of minimizing MSE for the parametric component is not necessarily the same as the optimal rate for minimization of the predictive mean square error in the function estimate. Thus data based estimates for X optimal for predictive mean square error in the function, such as GCV, may not be optimal for mean square error in the parametric component, leaving open the question of a data based estimate for X in this context.

Algorithms for multidimensional semiparametric glm's

Abstract: Purpose and Description Purpose These Fortran-77 subroutines provide tools for penalized likelihood estimation and model checking for generalized linear models (GLMs) in which the model has a semi-parametric form. The routines build on GCVPACK (Bates et al., 1987) and are designed to use the generalized cross-validation criteria (Craven and Wahba. 1979) to determine the degree of data smoothing. 'Ihese problems include smoothed GLMs (O'Sullivan, YandeU and Raynor, 1986). iteratively reweighted least squares (Green, 1984), and general nonlinear problems. We present some of the problems PGLMPACK is designed for and describe the structure of the routines. General Problem: A variety of penalized nonlinear problems can be solved by an iterative scheme in which the inner step involves a linear model approximation.