Forthcoming

Data Analytic and Distribution Function Estimation via Mean Absolute Deviation: Nonparametric Approach

Accepted - January 2023

Authors

Keywords:

empirical distribution function, nonparametric estimation, numerical differentiation, Richardson extrapolation, skewness, uniform consistency

Abstract

Mean absolute deviation function is used to explore the pattern and the distribution of the data graphically to enable analysts gaining greater understanding of raw data and to foster quick and a deep understanding of the data as an important fundament for successful data analytic. Furthermore, new nonparametric approaches for estimating the cumulative distribution function based on the mean absolute deviation function are proposed. These new approaches are meant to be a general nonparametric class that includes the empirical distribution function as a special case. Simulation study reveals that the Richardson extrapolation approach has a major improvement in terms of average squared errors over the classical empirical estimators and has comparable results with smooth approaches such as cubic spline and constrained linear spline for practically small samples. The properties of the proposed estimators are studied. Moreover, the Richardson approach applied for real data application and used to estimate the hazardous concentration five percent.

Published

2023-01-25

How to Cite

H. Elamir, E. A. (2023). Data Analytic and Distribution Function Estimation via Mean Absolute Deviation: Nonparametric Approach: Accepted - January 2023. REVSTAT-Statistical Journal. Retrieved from https://revstat.ine.pt/index.php/REVSTAT/article/view/438

Issue

Section

Forthcoming Paper