Nonparametric kernel estimation of the probability density function of\n regression errors using estimated residuals

2010/10/03 by Rawane Samb, Samb, Rawane
Engineering · Mathematics · #Advanced Statistical Methods and Models #Control Systems and Identification #FOS: Mathematics #Fault Detection and Control Systems #Statistical Methods and Inference #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.1010.0439

openalex publication_date 2010/10/03 · openalex created_date 2022/10/05 · openalex updated_date 2026/07/28

Abstract

This paper deals with the nonparametric density estimation of the regression\nerror term assuming its independence with the covariate. The difference between\nthe feasible estimator which uses the estimated residuals and the unfeasible\none using the true residuals is studied. An optimal choice of the bandwidth\nused to estimate the residuals is given. We also study the asymptotic normality\nof the feasible kernel estimator and its rate-optimality.\n

Citations

• A note on the estimation of a distribution function and quantiles by a kernel method
• Robust Estimation of a Location Parameter
• Consistent Nonparametric Regression
• Bandwith selection for the smoothing of distribution functions

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