On the consistency of mode estimate for spatially dependent data

Ahmad Younso ()
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Ahmad Younso: Université Montpellier

Metrika: International Journal for Theoretical and Applied Statistics, 2023, vol. 86, issue 3, No 4, 343-372

Abstract: Abstract This paper is concerned with estimating the density mode for random field by kernel method under some $$\alpha $$ α -mixing condition. The almost sure uniform convergence of the density estimator is proved. The rate of almost sure uniform convergence of the density gradient estimator is given under mild conditions. The unknown density is supposed unimodal and its mode is estimated by a kernel estimate. The strong consistency of the mode estimate is investigated and the rate of convergence is given. An optimal bandwidth selection procedure is proposed and a simulation study is used to obtain empirical results.

Keywords: Random field; Density; Mode; Kernel estimate; Bandwidth; Consistency (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s00184-022-00879-w

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