Abstract. In a pioneer work, Révész (1973) introduces the stochastic approximation method to build up a recursive kernel estimator of the regression function x 7→ E(Y |X = x). However, according to Révész (1977), his estimator has two main drawbacks: on the one hand, its convergence rate is smaller than that of the nonrecursive Nadaraya-Watson’s kernel regression estimator, and, on the other ha...

A neural network architecture for clustering and classification is described. The Adaptive Kernel Neural Network (AKNN) is a density estimation technique closely related to kernel estimation. The accompanying learning scheme adjusts the connection weights, activation functions, and the number of nodes in the network. The network, as described here, is made up of three layers of nodes: the input...

The kernel density estimator (KDE) based on a radial positive-semidefinite kernel may be viewed as a sample mean in a reproducing kernel Hilbert space. This mean can be viewed as the solution of a least squares problem in that space. Replacing the squared loss with a robust loss yields a robust kernel density estimator (RKDE). Previous work has shown that RKDEs are weighted kernel density estim...

In a partially linear regression model with a high dimensional unknown component we find an estimator of the parameter of the linear part based on projection pursuit methods to be considerably more efficient than the standard density weighted kernel estimator.

Stuetzle and Mittal for ordinary nonparametric kernel regression and Kauermann and Tutz for nonparametric generalized linear model kernel regression constructed estimators with lower order bias than the usual estimators without the need for devices such as second derivative estimation and multiple bandwidths of di erent order We derive a similar estimator in the context of local multivariate es...

We use the sinc kernel to construct an estimator for the integrated squared regression function. Asymptotic normality of the estimator at different rates is established, depending on whether the regression function vanishes or not.

Stuetzle and Mittal (1979) for ordinary nonparametric kernel regression and Kauermann and Tutz (1996) for nonparametric generalized linear model kernel regression constructed estimators with lower order bias than the usual estimators, without the need for devices such as second derivative estimation and multiple bandwidths of diierent order. We derive a similar estimator in the context of local...

We propose a nonparametric variance estimator when ranked set sampling (RSS) and judgment post stratification (JPS) are applied by measuring a concomitant variable. Our proposed estimator is obtained by conditioning on observed concomitant values and using nonparametric kernel regression.

Standard fixed symmetric kernel type density estimators are known to encounter problems for positive random variables with a large probability mass close to zero. We show that in such settings, alternatives of asymmetric gamma kernel estimators are superior but also differ in asymptotic and finite sample performance conditional on the shape of the density near zero and the exact form of the cho...

Abstract: Density weighted average is a nonparametric quantity expressed by expectation of a function of random variables with density weight. It is associated with parametric components of some semiparametric models, and we are concerned with an estimator of this quantity. Asymptotic properties of semiparametric estimators have been studied in econometrics since the end of 1980’s and it is now...