Two-Stage Conditional Density Estimation Based on Bernstein Polynomials

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\u27 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