ABSTRACT

First, we proceed in line with Robinson (1995). Let (X;, Y1), 1 =I, ... ,n, represent independent observations on an R"+ 1-valued variate (X', Y). Let K: R" ___.. R1 be a differentiable kernel function satisfying JR" K(u) du = I, and having column vector of partial derivatives K'(u) = (8/8u)K(u). For h > 0, consider the statistic

( 6.1)

We assume that X has the probability density function .f( · ), and set down g(X) = £( YIX), e(X) =.f(X)g(X), 11-t = YJ'( Yt)- e'(Xt), J.L = -E{g'(X).f'(X)}

and