NONPARAMETRIC REGRESSION WITH LONG-RANGE DEPENDENCE Academic Article uri icon

abstract

  • The effect of dependent errors in fixed-design, nonparametric regression is investigated. It is shown that convergence rates for a regression mean estimator under the assumption of independent errors are maintained in the presence of stationary dependent errors, if and only if r(j) < , where r is the covariance function. Convergence rates when r(j) = are also investigated. In particular, when the sample is of size n, when the mean function has k derivatives and r(j) C|j|-, the rate is n-k/(2k+) for 0 < < 1 and (n-1 log n)k/(2k+1) for = 1. These results refer to optimal convergence rates. It is shown that the optimal rates are achieved by kernel estimators. 1990.

published proceedings

  • STOCHASTIC PROCESSES AND THEIR APPLICATIONS

author list (cited authors)

  • HALL, P., & HART, J. D.

citation count

  • 117

complete list of authors

  • HALL, P||HART, JD

publication date

  • January 1990