Showing papers on "Semiparametric model published in 1989"

Spline Smoothing and Nonparametric Regression

Abstract: A wheeled toy vehicle including a drive assembly which comprises a monofilament line having one extremity connected to a manually operable control means and the opposite end connected to the running gear of the vehicle. The dimensions and configuration of the monofilament line is such as to transmit rotation of the line about its own longitudinal axis, caused by activation of the control means, directly to the running gear which may comprise a drive axle and/or one or more drive wheels. Connecting means may attach the one extremity of the line to a predetermined outer portion of an axle or wheel by means of forming a socket therein correspondingly shaped to at least partially enclose a finger attached to the extremity of the line means cooperating therewith. Alternately, a finger can be connected to the extremity of the drive axle and be disposed so as to be enclosed within a socket formed within a sleeve which is connected to the extremity of the line and comprises another embodiment of the connecting means.

Non- and semi-parametric maximum likelihood estimators and the von Mises method. II

Abstract: Having shown in Part I of this paper that some well-known NPMLE's are compactly differentiable functions of the empirical data, and moreover solve a compactly differentiable generalized likelihood equation, we prove an efficiency theorem which shows that such an estimator asymptotically achieves the information bound in the generalized Hajek-Le Cam convolution and asymptotic local minimax theorems.

A Semiparametric Model for Randomly Truncated Data

Abstract: For randomly censored data, it is known that the maximum likelihood estimate (MLE) of the survival curve is not affected by parametric assumption on the censoring variable. The Kaplan-Meier (1958) estimate is the MLE for both nonparametric and semiparametric models. For randomly truncated data, the truncation product-limit estimate is the MLE for nonparametric models. This is not the case if the truncation mechanism is parameterized, however. Specifically, let X be a generic random variable and T be the truncation variable. If the distribution of T is parameterized and the distribution of X is left unspecified, it can be shown that the truncation product-limit estimate is not the MLE for this semiparametric model, even though it is for the fully nonparametric model. In this article the MLE is characterized for the semiparametric model, and the large-sample properties of the estimate are established. The results show that, unlike censoring, the parametric information from the truncation mechanism ...

Hypothesis Testing in Semiparametric and Nonparametric Models for Econometric Time Series

Abstract: A restriction on a semiparametric or nonparametric econometric time series model determines the value of a finite-dimensional functional τ of an infinite-dimensional nuisance function. The estimate of τ and its estimated covariance matrix use nonparametric probability and spectral density estimation. A consequent test of the restriction is given approximate large sample justification under absolute regularity on the time series and other conditions. The methodology relates closely to recent proposals of Powell, Stock, Stoker and Robinson in cross-sectional applications, but serial dependence generally affects the test statistic's form, as well as statistical theory.

Specification testing in censored regression models: Parametric and semiparametric methods

Abstract: We define a hierarchy of parametric and semiparametric specifications for censored regression models that is ordered according to the strength of the assumptions that are made. We review the estimation techniques and specification tests that are available at each level of the hierarchy. The estimation and testing procedures are illustrated by applying them to a model of strike duration. Several tests (some graphical) are able to detect errors in standard parametric specifications even in the presence of fairly heavy censoring, but two distinct semiparametric specifications leading to different substantive inferences cannot be rejected. In addition, the conditional mean as a prediction of the dependent variable is highly sensitive to specification errors, whereas the conditional median is not.

Asymptotics for Semiparametric Econometric Models: I. Estimation

Abstract: This paper provides a general framework for proving the square root of T consistency and asymptotic normality of a wide variety of semiparametric estimators The results apply in time series and cross-sectional modeling contexts The class of estimators considered consists of estimators that can be defined as the solution to a minimization problem based on a criterion function that may depend on a preliminary infinite dimensional nuisance parameter estimator The criterion function need not be differentiable The method of proof exploits results concerning the stochastic equicontinuity or weak convergence of normalized sums of stochastic processes This paper also considers tests of nonlinear parametric restrictions in seimparametric econometric models To date, only Wald tests of such restrictions have been considered in the literature Here, Wald, Lagrange multiplier, and likelihood ratio-like tests statistics are considered A general framework is provided for proving that these test statistics have asymptotic chi-square distributions under the null hypothesis and local alternatives The results hold for a wide variety of underlying estimation techniques and in a wide variety of model scenarios

Rank estimates in a class of semiparametric two-sample models

Abstract: We consider a two-sample semiparametric model involving a real parameter θ and a nuisance parameter F which is a distribution function. This model includes the proportional hazard, proportional odds, linear transformation and Harrington-Fleming models (1982, Biometrika, 69, 533–546). We propose two types of estimates based on ranks. The first is a rank approximation to Huber's M-estimates (1981, Robust Statistics, Wiley) and the second is a Hodges-Lehmann type rank inversion estimate (1963, Ann. Math. Statist., 34, 598–611). We obtain asymptotic normality and efficiency results. The estimates are consistent and asymptotically normal generally but fully efficient only for special cases.

Asymptotics for Semiparametric Econometric Models: II. Stochastic Equicontinuity and Nonparametric Kernel Estimation

Abstract: This paper presents several stochastic equicontinuity results that are useful for establishing the asymptotic properties of estimators and tests in parametric, semiparametric, and nonparametric econometric models In particular, they can be applied straightforwardly in the estimation and testing results of Andrews (1989b) The paper takes various stochastic equicontinuity results from the probability literature, which rely on entropy conditions of one sort or another, and provides primitive conditions under which the entropy conditions hold This yields stochastic equicontinuity results that are readily applicable in a variety of contexts This paper also presents a number of consistency results for nonparametric kernel estimators of density and regression functions and their derivatives These results are particularly useful in semiparametric estimation and testing problems that rely on preliminary nonparametric estimators, as in Andrews (1989b) The results allow for near epoch dependent non-identically distributed random variables, data-dependent bandwidth sequences, preliminary estimation of parameters (eg, regression based on residuals), and nonparametric regression on index functions Some of the results make use of the stochastic equicontinuity results of the paper

Asymptotics for Semiparametric Econometric Models: III. Testing and Examples

Abstract: This paper considers tests of nonlinear parametric restrictions in semiparametric econometric models. To date, only Wald tests of such restrictions have been considered in the literature. Here, Wald, Lagrange multiplier, and likelihood ratio-like test statistics are considered and are shown to have asymptotic chi-square distributions under the null and local alternatives. The results hold for a wide variety of underlying estimation techniques and in a wide variety of model scenarios. A number of examples are given to illustrate the testing results of this paper and the estimation and stochastic equicontinuity results of the antecedents to this paper, viz. Andrews (1989b, c).

Heteroskedasticity in the Tobit model

Abstract: The paper deals with parameter estimation and the testing of individual parameters in heteroskedastic Tobit models. The statistical properties of semiparametric and maximum likelihood estimators ar ...

Optimal estimation for weighted distributions: semi-parametric models

Abstract: Utilizing the theory of estimating functions (Godambe, 1960, 1985), Godambe & Thompson (1989) obtained optimal estimation for generalized linear models or semi-parametric models. Their results are extended to cover response dependent sampling (Scott & Wild, 1986), including weighted distributions (Rao, 1965).

A unifying perspective on statistical modeling

Abstract: This paper presents a streamlined perspective on the various approaches to statistical modeling. This perspective can bethought of as a way to unify the Bayes, empirical-Bayes, Bayes–empirical-Bayes, parametric, nonparametric, and semiparametric models used to describe uncertainty. It is emphasized here that this paper concentrates on modeling, not on the approaches to inference that can also be categorized under the above labels, but that are quite different in their philosophical orientation.

Estimating Long Run Economic Equilibria

Abstract: Our subject is econometric estimation and inference concerning long-run economic equilibria in models with stochastic trends. Our interest is focused on single equation specifications such as those employed in the Error Correction Model (ECM) methodology of David Hendry (1987, 1989 inter alia) and the semiparametric modified least squares method of Phillips and Hansen (1989). We start by reviewing the prescriptions for empirical time series research that are presently available. We argue that the diversity of choices is confusing to practitioners and obscures the fact that statistical theory is clear about optimal inference procedures. Part of the difficulty arises from the many alternative time series representations of cointegrated systems. We present a detailed analysis of these various representations, the links between them, and the estimator choices to which they lead. An asymptotic theory is provided for a wide menu of econometric estimators and system specifications, accommodating different levels of prior information about the presence of unit roots and the nature of short-run dynamic adjustments. The single equation ECM approach is studied in detail and our results lead to certain recommendations. Weak exogeneity and data coherence are generally insufficient for valid conditioning on the regressors in this approach. Strong exogeneity and data coherency are sufficient to validate conditioning. But the requirement of strong exogeneity rules out most cases of interest because long-run economic equilibrium typically relates interdependent variables for which there is substantial time series feedback. One antidote for this problem in practice is the inclusion of leads as well as lags in the differences of the regressors. The simulations that we report, as well as the asymptotic theory support the use of this procedure in practice. Our results also support the use of dynamic specifications that involve lagged long-run equilibrium relations rather than lagged differences in the dependent variable. Finally, our simulations point to problems of overfitting in single equation ECM's. These appear to have important implications for empirical research in terms of size distortions that are produced in significance tests that utilize nominal critical values delivered by conventional asymptotic theory. In sum, our results indicate that the single equation ECM methodology has good potential for further development and improvement. But in comparison with the semi parametric modified least squares method of Phillips and Hansen (1989) the latter method seems superior for inferential purposes in most cases.

Het gebruik van een parametrische en een semi-parametrische schattingsmethode voor het binaire keuzemodel: Probit Maximum Likelihood versus Maximum Score [The use of a parametric and a semi-parametric estimation method for the binary choice model: Probit Maximum Likelihood versus Maximum Score]

Abstract: This Master thesis investigates the semi-parametric estimation method Maximum Score of Manski (1988) that can be used to estimate binary choice models. This method only asumes that the median of the disturbances of the econometric model takes the value zero. We compare Maximum Score with the semi parametric estimation method of Maximum Likelihood, that is based on the explicit assumption of normality of the the distribution of the disturbances. We proceed in three steps. First, the two estimation methods are compared theoretically. Second, the use of bootstrap methods is explained for the calculation of standard errors and confidence intervals for the Maximum Score estimators. Third, empirical applications are estimated and the results of both estimation methods are compared. One main conclusion of this research is that Maximum Score should be used in case of uncertainty about the disturbances' distribution and in case of large samples. A drawback of Maximum Score is that the estimators converge rather slowly. Moreover, one of the explanatory variables in the binary choice model must be continuous.