Showing papers on "Semiparametric model published in 1990"

Semiparametric efficiency bounds

Abstract: Semiparametric models are those where the functional form of some components is unknown. Efficiency bounds are of fundamental importance for such models. They provide a guide to estimation methods and give an asymptotic efficiency standard. The purpose of this paper is to provide an introduction to research methods and problems for semiparametric efficiency bounds. The nature of the bounds is discussed, as well as ways of calculating them. Their uses in solving estimation problems are outlined, including construction of semiparametric estimators and calculation of their limiting distribution. The paper includes new results as well as survey material.

Semiparametric Estimation of Selection Models: Some Empirical Results

Abstract: Among the central theoretical developments in the econometric analysis of nonexperimental microeconomic data has been the analysis of selectivity bias. Following the work of James Heckman (1974), statistical techniques were developed in the 1970s to consistently estimate the parameters of these models. One potential drawback to the application of these techniques is their sensitivity to the assumed parametric distribution of the unobservable error terms in the model. In recent years, a number of estimation methods for selection models have been developed which do not impose parametric forms on error distributions; these methods are termed "semiparametric," since only part of the model of interest (the regression function) is parametrically specified. While the statistical theory of these semiparametric estimators has received much attention, practical applications of the methods are lacking (an exception being the paper by Joel Horowitz and George Neumann, 1987). In this paper, we use semiparametric methods to reanalyze data on the labor supply of married women first studied by Thomas Mroz (1987) using parametric methods. The object of this reanalysis is to determine whether Mroz's results are sensitive to his parametric assumptions.

Semiparametric Comparison of Regression Curves

Abstract: The comparison of nonparametric regression curves is considered. It is assumed that there are parametric (possibly nonlinear) transformations of the axes which map one curve into the other. Estimation and testing of the parameters in the transformations are studied. The rate of convergence is $n^{-1/2}$ although the nonparametric components of the model typically have a rate slower than that. A statistic is provided for testing the validity of a given completely parametric model.

Achieving Information Bounds in Non and Semiparametric Models

Abstract: We consider in this paper two widely studied examples of nonparametric and semiparametric models in which the standard information bounds are totally misleading. In fact, no estimators converge at the $n^{-\alpha}$ rate for any $\alpha > 0$, although the information is strictly positive "promising" that $n^{-1/2}$ is achievable. The examples are the estimation of $\int p^2$ and the slope in the model of Engle et al. A class of models in which the parameter of interest can be estimated efficiently is discussed.

Bayesian semiparametric estimation of proportional hazards models

Abstract: This paper proposes a semiparametric analysis of proportional hazards models. This approach consists in specifying the relation between a duration and explanatory variables, without specifying the data distribution. The parameters involved in this relation are then considered as parameters of interest, and the data distribution is treated as a nuisance parameter. We propose a Bayesian estimation method, the principle of which is to specify a prior distribution on the nuisance parameter. We then obtain semiparametric estimators for the parameters of interest, by computing their posterior distribution, conditional on the data and integrated with respect to the nuisance parameter.

Bandwidth Selection in Semiparametric 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.

Cross-Validation in Semiparametric Models: Some Monte Carlo Results

Abstract: We present some Monte Carlo results on three semi parametric models, namely, partly linear, error-in-variables, and generalised least squares models. The results favour the use of computational expensive cross-validation criterion for bandwidth selection only when the relative sample size is large.

A new method for robust nonparametric regression

Abstract: Consider the problem of estimating the mean function underlying a set of noisy data. Least squares is appropriate if the error distribution of the noise is Gaussian, and if there is good reason to believe that the underlying function has some particular form. But what if the previous two assumptions fail to hold? In this regression setting, a mbust method is one that is resistant against outliers, while a nonparametric method is one that allows the data to dictate the shape of the curve (rather than choosing the best parameters for a fit from a particular family). Although it is easy to find estimators that are either robust or nonpara.metric, the literature reveals very few that are both. In this thesis, a new method is proposed that uses the fact that the L 1 norm naturally leads to a robust estimator. In spite of the L1 norm's reputation for being computationally intractable, it turns out that solving the least absolute deviations problem leads to a linear program with special structure. By utilizing this property, but over local neighborhoods, a method that is also non parametric is obtained. Additionally, the new method generalizes naturally to higher dimensions; to date, the problem of smoothing in higher dimensions has met with little success. A proof of consistency is presented, and the results from simulated da.ta are shown.