Goodness-of-Fit Tests in Nonparametric Regression

AMS classifications: 62G08, 62G10, 62G20, 62G30; 60F17.Bootstrap;empirical process;goodness-of-fit;location-scale regression;model diagnostics;nonparametric regression;test for independence;weak convergence

Goodness-of-fit Tests in Nonparametric Regression

AMS classifications: 62G08, 62G10, 62G20, 62G30; 60F17.Goodness-of-fit;nonparametric regression;test for independence;weak convergence

Goodness-of-fit Tests in Nonparametric Regression

AMS classifications: 62G08, 62G10, 62G20, 62G30; 60F17.

Goodness-of-Fit Tests in Nonparametric Regression

AMS classifications: 62G08, 62G10, 62G20, 62G30; 60F17.

Inference on the bivariate L1 median with censored data

Consider two random variables subject to random right censoring, like the time to two different diseases for individuals under study or the survival times of twins. Of interest is the bivariate median of these two random variables. There are various ways that the univariate median has been extended to higher dimensions for completely observed data. We concentrate on the so-called bivariate L1 median and extend this estimator to the censored data situation. The estimator is based on van der Laan (1996)'s estimator of the bivariate distribution of two random variables that are subject to censoring. Asymptotic results for the proposed estimator are established. The obtained results include the asymptotic normality of the estimator, its local power and the construction of a confidence region for the true median. Finally, we consider a data set on kidney dialysis patients and estimate the median time to two different infections for these individuals

Inference on the bivariate L1 median with censored data

Consider two random variables subject to random right censoring, like the time to two different diseases for individuals under study or the survival times of twins. Of interest is the bivariate median of these two random variables. There are various ways that the univariate median has been extended to higher dimensions for completely observed data. We concentrate on the so-called bivariate L1 median and extend this estimator to the censored data situation. The estimator is based on van der Laan (1996)'s estimator of the bivariate distribution of two random variables that are subject to censoring. Asymptotic results for the proposed estimator are established. The obtained results include the asymptotic normality of the estimator, its local power and the construction of a confidence region for the true median. Finally, we consider a data set on kidney dialysis patients and estimate the median time to two different infections for these individuals

The least squares method in heteroscedastic censored regression models

Consider the heteroscedastic polynomial regression model $Y = \beta_0 + \beta_1X + ... + \beta_pX^p + \sqrt{Var(Y|X)}\epsilon$, where \epsilon is independent of X, and Y is subject to random censoring. Provided that the censoring on Y is 'light' in some region of X, we construct a least squares estimator for the regression parameters whose asymptotic bias is shown to be as small as desired. The least squares estimator is defined as a functional of the Van Keilegom and Akritas (1999) estimator of the bivariate distribution $P(X \leq x, Y \leq y)$, and its asymptotic normality is obtained

Tests for Independence in Nonparametric Regression

Consider the nonparametric regression model Y = m(X)+e, where the function m is smooth, but unknown.We construct tests for the independence of e and X, based on n independent copies of (X; Y ).The testing procedures are based on differences of neighboring Y 's.We establish asymptotic results for the proposed tests statistics, investigate their finite sample properties through a simulation study and present an econometric application to household data.The proofs are based on delicate empirical process theory.