Some Papers

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

Higher Order Approximations

• "Second order approximations for adaptive regression estimators" (with Z. Xiao) We derive asymptotic expansions for semiparametric adaptive regression estimators. In particular, we derive the asymptotic distribution of the second order effect of an adaptive estimator in a linear regression whose error density is of unknown functional form. We then show how the choice of smoothing parameters influences the estimator through higher order terms. A method of bandwidth selection is defined by minimizing the second order mean squared error. We examine both i.i.d. and time series regressors; we also extend our results to a t-statistic. Monte Carlo simulations confirm the second order theory and the usefulness of the bandwidth selection method.
  Forthcoming in Econometric Theory
  
  
• "Edgeworth approximation for semiparametric instrumental variable estimators and test statistics" We establish the validity of higher order asymptotic expansions to the distribution of a version of the nonlinear semiparametric instrumental variable estimator considered in Newey (1990) as well as to the distribution of a Wald statistic derived from it. We employ local polynomial smoothing with variable bandwidth, which includes local linear, kernel, and [a version of] nearest neighbor estimates as special cases. Our expansions are valid to order $n^{-2\epsilon }$ for some $0<\epsilon <1/2,$ where $\epsilon $ depends on the smoothness and dimensionality of the data distribution and on the order of the polynomial chosen by the practitioner. We use the expansions to define optimal bandwidth selection methods for both estimation and testing problems and apply our methods to simulated data.
  Forthcoming in Journal of Econometrics
  
  
• "Some higher order theory for a consistent nonparametric model specification test" (with Y. Fan)
  Forthcoming in JSPI
  
  
• "Second order approximation in the partially linear regression model" We examine the second order properties of various quantities of interest in the partially linear regression model. We obtain a stochastic expansion with remainder $o_P(n^{-2\mu }),$ where $\mu <1/2,$ for the standardised semiparametric least squares estimator, a standard error estimator, and a studentised statistic. We use the second order expansions to correct the standard error estimates for second order effects, and to define a method of bandwidth choice. A monte carlo experiment provides favourable evidence on our method of bandwidth choice.
  Econometrica, 1995.