Summary It is common to want regress a scalar response on random function. This paper presents results that advocate local linear regression based projection as nonparametric approach this problem. Our asymptotic demonstrate functional outperforms its constant counterpart. Beyond the estimation of operator itself, also useful tool for predicting derivative operator, promising mathematical objec...

In this paper we propose an estimator of the entropy of a continuous random variable. The estimator is obtained by modifying the estimator proposed by Vasicek (1976). Consistency of estimator is proved, and comparisons are made with Vasicek’s estimator (1976), van Es’s estimator (1992), Ebrahimi et al.’s estimator (1994) and Correa’s estimator (1995). The results indicate that the proposed esti...

Estimation of density ridges has been gathering a great deal of attention since it enables us to reveal lower-dimensional structures hidden in data. Recently, subspace constrained mean shift (SCMS) was proposed as a practical algorithm for density ridge estimation. A key technical ingredient in SCMS is to accurately estimate the ratios of the density derivatives to the density. SCMS takes a thr...

Compared to the REINFORCE gradient estimator, the reparameterization trick usually gives lower-variance estimators. We propose a simple variant of the standard reparameterized gradient estimator for the evidence lower bound that has even lower variance under certain circumstances. Specifically, we decompose the derivative with respect to the variational parameters into two parts: a path derivat...

In the article, we propose a new estimator of the hazard rate function in the framework of the multiplicative point process intensity model. The technique combines the reflection method and the method of transformation. The new method eliminates the boundary effect for suitably selected transformations reducing the bias at the boundary and keeping the asymptotics of the variance. The transforma...

Asymptotically minimax nonparametric estimation of a regression function observed in white Gaussian noise over a bounded interval is considered, with respect to a L 2-loss function. The unknown function f is assumed to be m times diierentiable except for an unknown, though nite, number of jumps, with piecewise mth derivative bounded in L 2-norm. An estimator is constructed, attaining the same o...

SUMMARY This is the rst in a series of two papers in which the patch recovery technique proposed by Zienkiewicz and Zhu is analyzed. In this work, it is proved that the recovered derivative by the least squares tting is superconvergent for the two point boundary value problems. Further the a posteriori error estimator based on the recovery technique is show to be asymptotically exact. This conn...

A new perturbation estimator, using radial basis function (RBF) neural networks (RBFNN) to modify the sliding observer (SPO), is proposed with fast fractional-order terminal mode control (FFOTSMC). It aims a seven-degree-of-freedom (7-DOF) robot manipulator. The estimator applies data-driven method RBFNN compensate for estimation error in conventional SPO first time. modified estimates perturba...

In this paper, we propose a new ridge-type estimator called the new mixed ridge estimator (NMRE) by unifying the sample and prior information in linear measurement error model with additional stochastic linear restrictions. The new estimator is a generalization of the mixed estimator (ME) and ridge estimator (RE). The performances of this new estimator and mixed ridge estimator (MRE) against th...

When analyzing the productivity of rms one may want to compare how the rms transform a set of inputs x typically labor energy or capital into an output y typically a quantity of goods produced The economic e ciency of a rm is then de ned in terms of its ability of operating close to or on the production frontier which is the boundary of the production set The frontier function gives the maximal...