DeepAI
Log In Sign Up

Nonparametric Asymptotic Distributions of Pianka's and MacArthur-Levins Measures

11/24/2020
by   Tareq Alodat, et al.
0

This article studies the asymptotic behaviors of nonparametric estimators of two overlapping measures, namely Pianka's and MacArthur-Levins measures. The plug-in principle and the method of kernel density estimation are used to estimate such measures. The limiting theory of the functional of stochastic processes is used to study limiting behaviors of these estimators. It is shown that both limiting distributions are normal under suitable assumptions. The results are obtained in more general conditions on density functions and their kernel estimators. These conditions are suitable to deal with various applications. A small simulation study is also conducted to support the theoretical findings. Finally, a real data set has been analyzed for illustrative purposes.

READ FULL TEXT

page 1

page 2

page 3

page 4

05/12/2022

Estimation of Matusita Overlapping Coefficient for Pair Normal Distributions

The Matusita overlapping coefficient is defined as agreement or similari...
12/31/2020

On Gaussian Approximation for M-Estimator

This study develops a non-asymptotic Gaussian approximation theory for d...
04/23/2021

Nonparametric estimation of marginal distributions for unordered pairs

In this article, we consider the estimation of the marginal distribution...
10/15/2018

About kernel-based estimation of conditional Kendall's tau: finite-distance bounds and asymptotic behavior

We study nonparametric estimators of conditional Kendall's tau, a measur...
08/19/2022

Approximating Symmetrized Estimators of Scatter via Balanced Incomplete U-Statistics

We derive limiting distributions of symmetrized estimators of scatter, w...
04/23/2018

Positive data kernel density estimation via the logKDE package for R

Kernel density estimators (KDEs) are ubiquitous tools for nonparametric ...
04/23/2018

Log-transformed kernel density estimation for positive data

Kernel density estimators (KDEs) are ubiquitous tools for nonpara- metri...