Seminar Notice
                           Statistical Laboratory
                            Iowa State University

Date and Time:  Monday, January 26, 1998, 4:10 p.m.

Place:          319 Snedecor

Speaker:        Yuhong Yang
                Iowa State University

Title:          Effects of Long-Range Dependence on Nonparametric Regression


                                   ABSTRACT

        In this talk, we study nonparametric regression with dependent
errors. We examine how dependence of errors affects capability of
estimating the regression function. Previous work (e.g., Hall and
Hart (1990)) show that with fixed equally spaced design, long-range
dependence always damages rate of convergence for smooth
nonparametric function classes. It is rather surprising that unlike
i.i.d. error case, under long-range dependence, the story changes
dramatically when the fixed design is replaced by a random design.
Indeed, we show that long-range dependence has an effect (in terms of rate of 
convergence) not beyond the estimation of the mean value of the
regression function. Under very mild conditions, the minimax square
L_2 risk for a general nonparametric function class is shown to be
at the rate of maximum of two quantities: the minimax risk of the
same class but under i.i.d. errors, and the square risk for
estimating the mean of the regression function. Note that the
minimax rates we identified under a random design are always faster
than those under the fixed design. This finding suggests an
advantage of a random design over the equally spaced fixed design in
presence of long-range dependent errors.



Coffee:  3:45 p.m., 104 Snedecor

Seminar schedules and abstracts are available via WWW:

    http://www.stat.iastate.edu