Pointwise Adaptive Estimation of the MarginalDensity of a Weakly\n Dependent Process

2016/03/31 by Karine Bertin, Bertin, Karine, Nicolas Klutchnikoff +1 · 1 citation
Computer Science · Economics, Econometrics and Finance · Mathematics · #Bayesian Methods and Mixture Models #FOS: Mathematics #Financial Risk and Volatility Modeling #Statistical Methods and Inference #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.1604.00039

openalex publication_date 2016/03/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper is devoted to the estimation of the common marginal density\nfunction of weakly dependent processes. The accuracy of estimation is measured\nusing pointwise risks. We propose a datadriven procedure using kernel rules.\nThe bandwidth is selected using the approach of Goldenshluger and Lepski and we\nprove that the resulting estimator satisfies an oracle type inequality. The\nprocedure is also proved to be adaptive (in a minimax framework) over a scale\nof H "older balls for several types of dependence: stong mixing processes,\n\λ-dependent processes or i.i.d. sequences can be considered using a\nsingle procedure of estimation. Some simulations illustrate the performance of\nthe proposed method.\n

Citations

• Remarks on Some Nonparametric Estimates of a Density Function
• On Estimation of a Probability Density Function and Mode

Cited by

• Adaptive estimation in regression models for weakly dependent data and explanatory variable with known density

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