A monotone estimate of the conditional variance function in a heteroscedastic, nonpara- metric regression model is …

'i, X'j )' ; using the sampled data we seek to construct a nonparametric estimate of the mean regression function g … regression function at (i) a point and (ii) under the infinity norm. Second, we calculate (i) pointwise and (ii) uniform … convergence rates for the dyadic analog of the familiar Nadaraya-Watson (NW) kernel regression estimator. We show that the NW …

able to impose monotonicity of the estimated function. The use of such a shape restriction may signi cantly improve the … constrained estimator that imposes the monotonicity, on the other hand, signi cantly reduces variance by removing oscillations of …

In this paper we are concerned with shape restricted estimation in inverse regression problems with convolution …) unconstrained estimate of the unknown regression function. An advantage of our approach is that it is not necessary that prior shape … information is known to be valid on the complete domain of the regression function. Instead, it is sufficient if it holds on some …