Plug‐in bandwidth selector for recursive kernel regression estimators defined by stochastic approximation method

2016

JJSS

Self Cite

: In this paper we consider the kernel estimators of a distribution function defined by the stochastic approximation algorithm when the observation are contamined by measurement errors. It is well known that this estimators depends heavily on the choice of a smoothing parameter called the bandwidth. We propose a specific second generation plug-in method of the deconvolution kernel distribution estimators defined by the stochastic approximation algorithm. We show that, using the proposed bandwidth selection and the stepsize which minimize the M ISE (Mean Integrated Squared Error), the proposed estimator will be better than the classical one for small sample setting when the error variance is controlled by the noise to signal ratio. We corroborate these theoretical results through simulations and a real dataset.

Section: Assumptions and Main Resultsmentioning

confidence: 95%

Section: Assumptions and Main Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

See 1 more Smart Citation

Bandwidth Selection in Deconvolution Kernel Distribution Estimators Defined by Stochastic Approximation Method with Laplace Errors

2016

JJSS

Self Cite

“…Then, we present a data-driven bandwidth selection algorithm for the proposed estimators. Data-driven bandwidth selection procedure was proposed by Slaoui (2014a) in the framework of the recursive kernel density estimators, then, Slaoui (2014b) propose a plug-in selection method for recursive kernel distribution estimators, Slaoui (2015) propose a plug-in selection method for recursive kernel regression estimators with a fixed design setting, and Slaoui (2016) propose a plug-in selection algorithm for the semi-recursive kernel regression estimators, all of this works suppose that the full data are observed. Here, we developed a specific second-generation plug-in bandwidth selection method of the Recursive KDE under missing data.…”

Section: Introductionmentioning

confidence: 99%

Recursive kernel density estimators under missing data

Communications in Statistics - Theory and Methods

2017

Self Cite

In this paper we propose an automatic bandwidth selection of the recursive kernel density estimators with missing data in the context of global and local density estimation. We showed that, using the selected bandwidth and a special stepsize, the proposed recursive estimators outperformed the nonrecursive one in terms of estimation error in the case of global estimation. However, the recursive estimators are much better in terms of computational costs. We corroborated these theoretical results through simulation studies and on the simulated data of the Aquitaine cohort of HIV-1 infected patients and on the coriell cell lines using the chromosome number 11.

“…This estimator was proposed by Slaoui (2015c) to estimate recursively the regression function with a fixed design setting. The recursive property (1) is particularly useful in large sample size since a n can be easily updated with each additional observation.…”

Section: Introductionmentioning

confidence: 99%

Optimal bandwidth selection for semi-recursive kernel regression estimators

Statistics and Its Interface

2016

Self Cite

In this paper we propose an automatic selection of the bandwidth of the semi-recursive kernel estimators of a regression function defined by the stochastic approximation algorithm. We showed that, using the selected bandwidth and some special stepsizes, the proposed semi-recursive estimators will be very competitive to the nonrecursive one in terms of estimation error but much better in terms of computational costs. We corroborated these theoretical results through simulation study and a real dataset.