Some Papers

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

Additive Nonparametric Models and their Estimation

  • "The existence and asymptotic properties of a backfitting algorithm under weak conditions" (with E. Mammen and J. Nielsen) This paper proposes a new class of estimators for additive nonparametric regression based on the idea of empirical projection. It is a clever modification of the original backfitting idea of Breiman and Freedman, with the advantage that the distribution theory can be worked out under weak conditions.
    The Annals of Statistics, October 1999.

  • "Estimating Additive Nonparametric Models by Partial L_q Medianning: The Curse of Fractionality" This paper shows that replacing median by mean averaging can worsen the rate of convergence of integration estimators.
    Forthcoming in Econometric Theory

  • "Estimating Multiplicative and Additive Marker Dependent Hazard Functions by Backfitting with the Assistance of Marginal Integration" (with J. Nielsen and S. van de Geer) Revised 17/12/01 "Estimating Multiplicative and Additive Marker Dependent Hazard Functions by Kernel Methods" Revised 04/02 We propose new procedures for estimating the univariate quantities of interest in both additive and multiplicative nonparametric marker dependent hazard models. We work with a full counting process framework that allows for left truncation and right censoring. Our procedures are based on kernels and on the idea of marginal integration. We provide a central limit theorem for our estimator.
    Forthcoming in The Annals of Statistics

  • "Testing Additivity in Generalized Nonparametric Regression Models with Estimated Parameters" (with P. Gozalo) We develop several kernel-based consistent tests of an hypothesis of additivity in nonparametric regression. We allow for discrete covariates and parameters estimated from a semiparametric GMM criterion function. The additivity hypothesis is of interest because it delivers interpretability and reasonably fast convergence rates for nonparametric estimators. The asymptotic distribution of the parameter estimators are found. We also derive the asymptotic distribution of the additivity test statistics under a sequence of local alternatives. We give a ranking of the different tests based on local asymptotic power. The practical performance is investigated through simulations based on the dataset used in Linton and H\"{a}rdle (1996).
    Forthcoming in Journal of Econometrics [9/01/01]

  • "An Analysis of Transformations for Additive Nonparametric Regression" with R. Chen, N. Wang, and W. H\"{a}rdle. We consider a nonparametric regression model with a parametric family of dependent variable transformations one of which induces additive covariate effects. We estimate the additive regression effects using the integration method; the transformation parameter is estimated from a profiled instrumental variable and pseudo-likelihood criterion. The asymptotic distributions of the parameter and regression estimates are given. The practical performance is investigated via an application.
    Journal of the American Statistical Association, 1997

  • "Efficient estimation of generalized additive nonparametric regression models" We define new procedures for estimating generalized additive nonparametric regression models that are more efficient than the Linton and\ H\"{a}rdle (1996) integration-based method and achieve certain oracle bounds. We consider criterion functions based on the Linear Exponential Family, which includes many important special cases. We also consider the extension to multiple parameter models like the Gamma distribution and to models for conditional heteroskedasticity.
    Econometric Theory, 2000