We consider estimation of the linear component of a partial linear model when errors and regressors have long-range dependence. Assuming that errors and the stochastic component of regressors are linear processes with i.i.d. innovations, we closely examine the asymptotic properties of the OLS...

In this paper a new test for the parametric form of the variance function in the common nonparametric regression model is proposed which is applicable under very weak assumptions. The new test is based on an empirical process formed from pseudo residuals, for which weak convergence to a Gaussian...

In this paper a new test for the parametric form of the variance function in the common nonparametric regression model is proposed which is applicable under very weak smoothness assumptions. The new test is based on an empirical process formed from pseudo residuals, for which weak convergence to...

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...

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

In this paper a new test for the parametric form of the variance function in the common nonparametric regression model is proposed which is applicable under very weak smoothness assumptions. The new test is based on an empirical process formed from pseudo residuals, for which weak convergence to...

In this paper a new test for the parametric form of the variance function in the common nonparametric regression model is proposed which is applicable under very weak assumptions. The new test is based on an empirical process formed from pseudo residuals, for which weak convergence to a Gaussian...

This paper derives the asymptotic distribution of a smoothing-based estimator of the Lyapunov exponent for a stochastic time series under two general scenarios. In the first case, we are able to establish root-T consistency and asymptotic normality, while in the second case, which is more...