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Consistency of the frequency polygon estimators of density mode for strongly mixing processes

Abstract : We consider a simple estimator of the density mode using the frequency polygon estimate. We investigate strong consistency of the estimator for strong mixing sequence of real variables under mild assumptions. We study the almost sure rate of convergence and we show that the estimator can achieve optimal almost sure rates of convergence for appropriate choices of the bin widths. The asymptotic normality of the simple estimator is given and a simulation study is performed. Our asymptotic results are obtained without any differentiability condition assumed on the density around the mode.
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https://hal.inrae.fr/hal-03295522
Contributor : Christelle Raynaud <>
Submitted on : Thursday, July 22, 2021 - 11:04:06 AM
Last modification on : Friday, July 23, 2021 - 3:50:29 AM

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Ahmad Younso. Consistency of the frequency polygon estimators of density mode for strongly mixing processes. Communications in Statistics - Theory and Methods, Taylor & Francis, 2021, pp.1-16. ⟨10.1080/03610926.2021.1945633⟩. ⟨hal-03295522⟩

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