Local polynomial regression for circular predictors

We consider local smoothing of datasets where the design space is the d-dimensional (d >= 1) torus and the response variable is real-valued. Our purpose is to extend least squares local polynomial fitting to this situation. We give both theoretical and empirical results

A power comparison between nonparametric regression tests

In this paper, we consider three major types of nonparametric regression tests that are based on kernel and local polynomial smoothing techniques. Their asymptotic power comparisons are established systematically under the fixed and contiguous alternatives, and are also illustrated through non-asymptotic investigations and finite-sample simulation studies. --Goodness-of-fit,Local alternative,Local polynomial regression,Power,Smoothing parameter

Local Polynomial Regression for Binary Response

24 pages, 1 article*Local Polynomial Regression for Binary Response* (Aragaki, Aaron; Altman, Naomi) 24 page

Central limit theorems for the integrated squared error of derivative estimators

A central limit theorem for the weighted integrated squared error of kernel type estimators of the first two derivatives of a nonparametric regression function is proved by using results for martingale differences and U-statistics. The results focus on the setting of the Nadaraya-Watson estimator but can also be transfered to local polynomial estimates. --central limit theorem,integrated squared error,kernel estimates,local polynomial estimate,Nadaraya-Watson estimate,nonparametric regression

Local polynomial regression with truncated or censored response

Truncation or censoring of the response variable in a regression model is a problem in many applications, e.g. when the response is insurance claims or the durations of unemployment spells. We introduce a local polynomial re­gression estimator which can deal with such truncated or censored responses. For this purpose, we use local versions of the STLS and SCLS estimators of Powell (1986) and the QME estimator of Lee (1993) and Laitila (2001). The asymptotic properties of our estimators, and the conditions under which they are valid, are given. In addition, a simulation study is presented to investigate the finite sample properties of our proposals.Non-parametric regression; truncation; censoring; asymptotic properties

Local polynomial regression estimation with correlated errors

In this paper, we study the nonparametric estimation of the regression function and its derivatives using weighted local polynomial fitting. Consider the fixed regression model and suppose that the random observation error is coming from a strictly stationary stochastic process. Expressions for the bias and the variance array of the estimators of the regression function and its derivatives are obtained and joint asymptotic normality is established. The influence of the dependence of the data is observed in the expression of the variance. We also propose a variable bandwidth selection procedure. A simulation study and an analysis with real economic data illustrate the proposed selection method.Xunta de Galicia; XUGA10501B97Xunta de Galicia; PB98-0182-c02-0