Date of Award
7-7-2020
Publication Type
Master Thesis
Degree Name
M.Sc.
Department
Mathematics and Statistics
Keywords
Nonparametric estimation
Supervisor
Mohamed Belalia
Rights
info:eu-repo/semantics/openAccess
Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.
Abstract
In this thesis, we propose a new nonparametric approach based on Bernstein polynomials to estimate the conditional density function. The proposed estimators have desired properties at the boundaries and can outperform the kernel and local linear estimators in terms of Integrated Mean Square Error for an appropriate choice of the polynomials' order. The idea is to construct a two-stage conditional probability density function estimator based on Bernstein polynomials. Specifically, the Nadaraya-Watson (NW) and local linear (LL) conditional distribution function estimators were smoothed using Bernstein polynomials in the first stage. Secondly, the proposed estimators are obtained by differentiating the smoothed Bernstein NW and LL estimators.
Recommended Citation
Lyu, Guanjie, "Two-Stage Conditional Density Estimation Based on Bernstein Polynomials" (2020). Electronic Theses and Dissertations. 8380.
https://scholar.uwindsor.ca/etd/8380