Some Papers

(The following papers can be viewed or downloaded in Acrobat format.)

Miscellaneous NonParametric Stuff

• "Nonparametric Censored and Truncated Regression" (with A. Lewbel) We investigate a nonparametric censored regression model, with a fixed, known censoring point (normalized to zero), is $y=\max [0,m(x)+e]$, where both the regression function $m(x)$ and the distribution of the error $e$ are unknown. This paper provides consistent estimators of $m(x)$ and its derivatives. The convergence rate is the same as for an uncensored nonparametric regression and its derivatives. We also provide root n estimates of weighted average derivatives of $m(x)$, which equal the coefficients in linear or partly linear specifications for $m(x).$ An extension permits estimation in the presence of a general form of heteroscedasticity. We also extend the estimator to the nonparametric truncated regression model, in which only uncensored data points are observed. The estimators are based on the relationship $\partial E(y^{k}|x)/\partial m(x)=kE[y^{k-1}I(y>0)|x]$, which we show holds for positive integers $k$.
  Forthcoming in Econometrica
  
  
• "Local Nonlinear Least Squares: Using Parametric Information in Nonparametric Regression" (with P. Gozalo) We introduce a new nonparametric regression estimator that uses prior information on regression shape in the form of a parametric model. In effect, we nonparametrically encompass the parametric model. We obtain estimates of the regression function and its derivatives along with local parameter estimates that can be interpreted from within the parametric model. We establish the uniform consistency and derive the asymptotic distribution of the local parameter estimates and of the corresponding regression and derivative estimates. For estimating the regression function our method has superior performance to the usual kernel estimators at or near the parametric model. It is particularly well motivated for binary data using the probit or logit parametric model as a base. We include an application to the Horowitz (1993) transport choice dataset.
  The Journal of Econometrics, 2000
  
  
• "Testing Conditional Independence Restrictions" (with P. Gozalo)
  
  
• "Nonparametric Estimation with Aggregated Data" (with Y. Whang) We introduce a kernel-based estimator of the density function and regression function for data that have been grouped into family totals. We allow for a common intra-family component but require that observations from different families be independent. We establish consistency and asymptotic normality for our procedures. As usual, the rates of convergence can be very slow depending on the behaviour of the characteristic function at infinity. We investigate the practical performance of our method in a simple Monte Carlo experiment.
  Forthcoming in Econometric Theory
  
  
• "A Nonparametric Prewhitened Covariance Estimator" (with Z. Xiao) This paper proposes a new nonparametric spectral density estimator for time series models with general autocorrelation. We show that the best implementation of our estimator has mean squared error of order $n^{-8/9},$ provided there is sufficient smoothness present in the spectral density, improving upon the performance of the conventional nonparametric estimator whose best mean squared error decreases at rate $n^{-4/5}$. This is of course achieved by bias reduction; however, unlike most other bias reduction methods our procedure ensures a positive definite estimate. Our method is a generalization of the well known prewhitening method of spectral estimation; we argue that this can best be interpreted as multiplicative bias reduction. Higher order expansions for the proposed estimator are derived, providing an improved bandwidth choice that minimizes the mean squared error to the second order. A simulation study shows that the recommended prewhitened kernel estimator reduces bias and mean squared error in spectral density estimation. .
  Forthcoming in the Journal of Time Series Analysis.
  
  
• "Nonparametric Factor Analysis of Residual Time Series" (with J.M. Rodriguez-Poo) We introduce a nonparametric smoothing procedure for nonparametric factor analysis of multivariate time series. Our main objective is to develop an adaptive method for estimating a time-varying covariance matrix. The asymptotic properties of the proposed procedures are derived. We present an application based on the residuals from the Fair macromodel of the U.S. economy. We find substantial evidence of time varying second moments and breaks in the contemporaneous correlation structure during the mid 1970's to the early 1980's. .
  Forthcoming in TEST.