Recursive distribution estimator defined by stochastic approximation method using Bernstein polynomials

Optimal bandwidth selection for recursive Gumbel kernel density estimators

“…We plan also to consider Bernstein polynomials rather than kernels and to propose an adaptation of the estimators developed in [15] and [36] with application to heavy tailed data. Moreover, we plan to make an extensions of our proposed plug-in method in future with application on extreme value and to consider the case of the averaged Révész's regression estimators (see [22] and [31,32]) and the semi-recursive kernel regression estimators proposed by [34] and the case of time series as in [13] in recursive way (see [14]).…”

Wild bootstrap bandwidth selection of recursive nonparametric relative regression for independent functional data

“…We plan to extend this work by considering Bernstein polynomials rather than kernels and to propose an adaptation of the estimators developed in Jmaei et al [30] and Slaoui and Jmaei [48] in the case of functional data. We plan also to compare these estimators to the kernel nearest-neighbor approach developed in Kara et al [32], the semi-parametric functional projection pursuit regression [11], the single index model [25], the partial linear models [4,35] and the sparse modeling approach [5].…”

hermiter: R package for Sequential Nonparametric Estimation

“…See also Slaoui and Jmaei (2019) for recursive estimators based on Bernstein polynomials. In the case of CDFs, existing algorithms include those based on the empirical distribution function estimator, the smooth kernel distribution function estimator, Slaoui (2014), and Bernstein polynomials, Jmaei, Slaoui, and Dellagi (2017). These PDF and CDF estimators furnish sequential estimates of the probability density and cumulative probability at predefined values of the support of the probability density function.…”