Showing papers on "Semiparametric model published in 1987"

Efficiency bounds for distribution-free estimators of the binary choice and the censored regression models

Abstract: We derive lower bounds on the asymptotic variances for regular distribution-free estimators of the parameters of the binary choice model and the censored regression (Tobit) model. A distribution-free (or semiparametric) estimator is one that does not require any assumption about the distribution of the stochastic error term in the model, apart from regularity conditions. For the binary choice model, we obtain an explicit lower bound for the asymptotic variance for the slope parameters, or more generally the parameters of a nonlinear regression function in the underlying latent variable model, but we find that there is no regular semiparametric estimator of the constant term (identified by requiring the error distribution to have zero median). Lower bounds are also obtained under the further assumption that the error distribution is symmetric, and in this case there is a finite lower bound for the constant term too. Comparison of the bounds with those for the classical parametric problem shows the loss of information due to lack of a priori knowledge of the functional form of the error distribution. We give the conditions for equality of the parametric and semiparametric lower bounds (in which case adaptive estimation may be possible), both with and without the assumption of a symmetric error distribution. In general, adaptive estimation is not possible, but one special case where these conditions hold is when the regression function is linear and the explanatory variables have a multivariate normal distribution. The Tobit model considered here is the censored nonlinear regression model, with a fixed censoring point. We again give an explicit lower bound for the asymptotic variance for the regression parameters, this time including a constant term (if the error term has zero median). Comparison with the corresponding lower bound for the parametric case shows that adaptive estimation is in general not possible for this model.

Semiparametric estimation of employment duration models

Abstract: There are a variety of economic areas, such as studies of employment duration and of the durability of capital goods, in which data on important variables typically are censored. The standard techinques for estimating a model from censored data require the distributions of unobservable random components of the model to be specified a priori up to a finite set of parameters, and misspecification of these distributions usually leads to inconsistent parameter estimates. However, economic theory rarely gives guidance about distributions and the standard estimation techniques do not provide convenient methods for identifying distributions from censored data. Recently, several distribution-free or semiparametric methods for estimating censored regression models have been developed. This paper presents the results of using two such methods to estimate a model of employment duration. The paper reports the operating characteristics of the semiparametric estimators and compares the semiparametric estimates with tho...

Penalized likelihood for general semiparametric regression models

Abstract: Summary This paper examines penalized likelihood estimation in the context of general regression problems, characterized as probability models with composite likelihood functions. The emphasis is on the common situation where a parametric model is considered satisfactory but for inhomogeneity with respect to a few extra variables. A finite-dimensional formulation is adopted, using a suitable set of basis functions. Appropriate definitions of deviance, degrees of freedom, and residual are provided, and the method of cross-validation for choice of the tuning constant is discussed. Quadratic approximations are derived for all the required statistics.

Semi parametric estimation of employment duration models

Abstract: Semi parametric methods provide estimates of finite parameter vectors without requiring that the complete data generation process be assumed in a finite-dimensional family. By avoiding bias from incorrect specification, such estimators gain robustness, although usually at the cost of decreased precision. The most familiar semi parametric method in econometrics is ordi¬nary least squares, which estimates the parameters of a linear regression model without requiring that the distribution of the disturbances be in a finite-parameter family. The recent literature in econometric theory has extended semi parametric methods to a variety of non-linear models, including models appropriate for analysis of censored duration data. Horowitz and Newman make perhaps the first empirical application of these methods, to data on employment duration. Their analysis provides insights into the practical problems of implementing these methods, and limited information on performance. Their data set, containing 226 male controls...

Semiparametric Estimation of Monotonic and Concave Utility Functions: The Discrete Choice Case

Abstract: This paper develops a semiparametric method for estimating the nonrandom part V(.) of a random utility function U(v, omega) - V(v) + e(omega) from data on discrete choice behavior. Here v and omega are, respectively, vectors of observable and unobservable attributes of an alternative, and e(omega) is the random part of the utility for that alternative. The method is semiparametric because it assumes that the distribution of the random parts is know up to a finite-dimensional parameter theta, while not requiring specification of a parametric form for V( ). The nonstochastic part V( ) of the utility function U( ) is assumed to be Lipschitzian and to possess a set of properties, typically assumed for utility functions. The estimator of the pair (V,theta) is shown to be strongly consistent.

Asymptotically efficient estimators of location and scale parameters in the two-sample semiparametric location-scale model

Abstract: We observe X1"",Xm and Y1, ... ,Yn where Xi's are Li.d. with density g and Yi'S are ..... ru independent of Xi's and Li.d. with density g« .-b..)jp). This paper presents an '0 asmptotically efficient estimator of (b..,p). The results of this paper are different from those of Park (1987) in two points. At first we consider unpaired two samples with different sample sizes, whereas Park (1987) dealt with paired sample cases. Secondly, we do not assume location-scale structure in Xi'S, while on the other hand he considered the case where Xi'S have that structure. It turns out that having location-scale structure in Xi's or not, does not make any significant difference in terms of efficient score function but one may prefer our consideration when one is not quite sure about the structure of the first sample. AMS 1980 Subject Classification: Primary 62G05, Secondary 62G20.