Using locally polynomial regression, we develop nonparametric estimators for the conditional density function and its square root, and their partial derivatives. Two measures of sensitivity to initial conditions in nonlinear stochastic dynamic systems are proposed, one of which relates Fisher information with initial-value sensitivity in dynamical systems. We propose estimators for these, and show asymptotic normality for one of them. We further propose a simple method for choosing the bandwidth. The methods are illustrated by simulation of two well-known models in dynamical systems.

Estimation of conditional densities and sensitivity measures in nonlinear dynamical systems

Publication bias is a serious problem in meta-analysis. Various methods have been developed to detect the presence of publication bias in meta-analysis. These methods have been assessed and compared in many dichotomous studies utilizing the log-odds ratio as the measure of effect. This paper evaluates and compares the performance of three popular methods, namely the Egger’s linear regression method, the Begg and Mazumdar’s rank correlation method and the Duvall and Tweedie’s trim and fill method, on meta-analysis of continuous data. The data comprised simulated meta-analyses with different levels of primary studies in the absence and presence of induced publication bias. The performance of these methods were measured through the power and type 1 error rate for the tests. The results suggest the trim and fill method to be superior in terms of its ability to detect publication bias when it exists, even in presence of only 5% unpublished studies. However this method is not recommended for large meta-analysis as it produces high rate of false-positive results. Both linear regression and rank correlation method performed relatively well in moderate bias but should be avoided in small meta-analysis as their power is very low in this data.

A Comparison of Methods to Detect Publication Bias for Meta-analysis of Continuous Data

Multivariate nonnegative orthant data are real vectors bounded to the left by the null vector, and they can be continuous, discrete or mixed. We first review the recent relative variability indexes for multivariate nonnegative continuous and count distributions. As a prelude, the classification of two comparable distributions having the same mean vector is done through under-, equi- and over-variability with respect to the reference distribution. Multivariate associated kernel estimators are then reviewed with new proposals that can accommodate any nonnegative orthant dataset. We focus on bandwidth matrix selections by adaptive and local Bayesian methods for semicontinuous and counting supports, respectively. We finally introduce a flexible semiparametric approach for estimating all these distributions on nonnegative supports. The corresponding estimator is directed by a given parametric part, and a nonparametric part which is a weight function to be estimated through multivariate associated kernels. A diagnostic model is also discussed to make an appropriate choice between the parametric, semiparametric and nonparametric approaches. The retention of pure nonparametric means the inconvenience of parametric part used in the modelization. Multivariate real data examples in semicontinuous setup as reliability are gradually considered to illustrate the proposed approach. Concluding remarks are made for extension to other multiple functions.

Bayesian Bandwidths in Semiparametric Modelling for Nonnegative Orthant Data with Diagnostics

Asymptotic properties of Dirichlet kernel density estimators

Given a stationary multidimensional spatial process $$\left\{ Z_{\mathbf{i}}=\left( X_{\mathbf{i}},\ Y_{\mathbf{i}}\right) \in \mathbb R ^d\right. \left. \times \mathbb R ,\mathbf{i}\in \mathbb Z ^{N}\right\} $$
 , we investigate a kernel estimate of the spatial conditional mode function of the response variable $$Y_{\mathbf{i}}$$
 given the explicative variable $$X_{\mathbf{i}}$$
 . Consistency in $$L^p$$
 norm and strong convergence of the kernel estimate are obtained when the sample considered is a $$\alpha $$
 -mixing sequence. An application to real data is given in order to illustrate the behavior of our methodology.

Consistency of a nonparametric conditional mode estimator for random fields

In this paper, we define the Weibull kernel and use it to nonparametric estimation of the probability density function (pdf) and the hazard rate function for independent and identically distributed (iid) data. The bias, variance and the optimal bandwidth of the proposed estimator are investigated. Moreover, the asymptotic normality of the proposed estimator is investigated. The performance of the proposed estimator is tested using simulation study and real data.

/pdf/hazard-rate-function-estimation-using-weibull-kernel-enkegkap1m.pdf

Hazard Rate Function Estimation Using Weibull Kernel

In this paper, the estimation of the regression mean using the Reweighted Nadaraya-Watson (RNW) estimator has been considered. The RNW is a modification of the Nadaraya-Watson (NW) estimator in order to obtain some more refinement estimator. We have considered some conditions under which the asymptotic normality of the proposed estimator has been derived. Then we generalized this result to the multivariate case by considering the estimation of the regression mean at distinct points.

/pdf/reweighted-nadaraya-watson-estimator-of-the-regression-mean-18y2lswfwt.pdf

Reweighted Nadaraya-Watson Estimator of the Regression Mean

On the Kernel Estimation of the Conditional Mode

In this paper, we define the Erlang kernel and use it to nonparametically estimation of the probability density function (pdf) and the hazard rate function for independent and identically distributed (iid) data.The bias, variance and the optimal bandwidth of the proposed estimator are investigated. Moreover, the asymptotic normality of the proposed estimator is investigated. The performance of the proposed estimator is tested using simulation study and real data.

/pdf/hazard-rate-function-estimation-using-erlang-kernel-1pweixhfqi.pdf

Hazard rate function estimation using Erlang kernel

In this paper, we define the adaptive Weighted Nadaraya–Watson estimation (AWNW) of the conditional distribution function (cdf) for independent and identically distributed (iid) data using varying ...

Hazem I. El Shekh Ahmed

Papers

Hazard Rate Function Estimation Using Weibull Kernel

Reweighted Nadaraya-Watson Estimator of the Regression Mean

On the Kernel Estimation of the Conditional Mode

Hazard rate function estimation using Erlang kernel

Adaptive weighted Nadaraya–Watson estimation of the conditional quantiles by varying bandwidth