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Data sharpening for kernel regression and density estimation was intro- duced by the late Peter Hall. We review briey his enormous contribution to the literature in this area and then propose a data sharpening procedure arising from imposition of a soft global functional constraint in local regression analysis. Instead of enforcing the constraint everywhere, the procedure guides the data in directions which enable satisfaction or near-satisfaction of the given property globally through the use of a penalty. It results in a modified local regression estimator which pos- sesses a closed functional form and which includes a conventional local regression estimator as a special case. The approach can accommodate various constraints, most of which in practice are motivated by expert prior knowledge. We demonstrate theoretically and numerically that the proposed estimator is an improved variant of the corresponding local regression estimator. It achieves a reduction in variance while maintaining the bias at the same level. Although the focus in the paper is on local polynomial regression, the technique can be applied, in principle, to any linear nonparametric estimator, including regression splines, smoothing and penal- ized splines and other recently proposed kernel estimators. We exhibit usefulness of the proposed approach with an analysis of a collection of temperatures at the airport of Vancouver. The analysis reveals a possible monotonic trend underlying the conventional supposition of a periodic (seasonal) temporal structure. [ABSTRACT FROM AUTHOR]

Conditional expectation imputation and local-likelihood methods are contrasted with a midpoint imputation method for bivariate regression involving interval-censored responses. Although the methods can be extended in principle to higher order polynomials, our focus is on the local constant case. Comparisons are based on simulations of data scattered about three target functions with normally distributed errors. Two censoring mechanisms are considered: the first is analogous to current-status data in which monitoring times occur according to a homogeneous Poisson process; the second is analogous to a coarsening mechanism such as would arise when the response values are binned. We find that, according to a pointwise MSE criterion, no method dominates any other when interval sizes are fixed, but when the intervals have a variable width, the local-likelihood method often performs better than the other methods, and midpoint imputation performs the worst. Several illustrative examples are presented. [ABSTRACT FROM PUBLISHER]

The article discusses a study which proposed kernel spline regression, a method of combining spline regression and kernel smoothing by replacing the polynomial estimation for local polynomial kernel regression with the spline basis. The bias and variance of the kernel linear spline estimator are computed and compared with local linear regression. The study showed that kernel spline regression performs better than ordinary spline regression and local polynomial regression.

Proposes a new method for selecting the bandwidth parameter in nonparametric regression. Bandwidth selection; Kernel methods; Autocorrelation; Goodness-of-fit statistic.