We study a semi-varying coefficient model where the regressors are generated by the multivariate unit root I(1) processes. The influence of the explanatory vectors on the response variable satisfies the semiparametric partially linear structure with the nonlinear component being functional coefficients. A semiparametric estimation methodology with the first-stage local polynomial smoothing is applied to estimate both the constant coefficients in the linear component and the functional coefficients in the nonlinear component. The asymptotic distribution theory for the proposed semiparametric estimators is established under some mild conditions, from which both the parametric and nonparametric estimators are shown to enjoy the well-known superconsistency property. Furthermore, a simulation study is conducted to investigate the finite sample performance of the developed methodology and results.
This paper considers methods of estimating a static correlated random coefficient model with panel data. We mainly focus on comparing two approaches of estimating unconditional mean of the coefficients for the correlated random coefficients models, the group mean estimator and the generalized least squares estimator. For the group mean estimator, we show that it achieves Chamberlain (1992) semi-parametric efficiency bound asymptotically. For the generalized least squares estimator, we show that when T is large, a generalized least squares estimator that ignores the correlation between the individual coefficients and regressors is asymptotically equivalent to the group mean estimator. In addition, we give conditions where the standard within estimator of the mean of the coefficients is consistent. Moreover, with additional assumptions on the known correlation pattern, we derive the asymptotic properties of panel least squares estimators. Simulations are used to examine the finite sample performances of different estimators.
In this paper we consider the problem of estimating an unknown multivariate cumulative distribution function which is defined over mixed discrete and continuous variables. A consistent nonparametric kernel estimator is proposed with bandwidth parameters obtained from the cross-validated minimization of the estimator's integrated squared error. We provide theoretical underpinnings including rate of convergence and uniqueness of the optimal smoothing parameter vector.
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