Kernel density estimators for random fields satisfying an interlaced mixing condition

Tone, Cristina

doi:10.1016/j.jspi.2013.02.003

Cited by 3 publications

(2 citation statements)

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“…For a sequence of strictly stationary random fields that are uniformly ρ ′mixing and satisfy a Lindeberg condition, a central limit theorem is obtained in [7] for sequences of "rectangular" sums from the given random fields. The "Lindeberg CLT" is then used to prove a CLT for some kernel estimators of probability density for some strictly stationary random fields satisfying ρ ′ -mixing, and whose probability density and joint densities are absolutely continuous, generalizing the results in [2], under ρ * -mixing.…”

Section: Introductionmentioning

confidence: 99%

A Central Limit Theorem for Non-stationary Strongly Mixing Random Fields

Bradley

Tone

2015

J Theor Probab

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In this paper we extend a central limit theorem of Peligrad for uniformly strong mixing random fields satisfying the Lindeberg condition in the absence of stationarity property. More precisely, we study the asymptotic normality of the partial sums of uniformly α-mixing non-stationary random fields satisfying the Lindeberg condition, in the presence of an extra dependence assumption involving maximal correlations.

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Section: Introductionmentioning

confidence: 99%

A Central Limit Theorem for Non-stationary Strongly Mixing Random Fields

Bradley

Tone

2015

J Theor Probab

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“…They [7] also, proved a CLT and law of large numbers under near-epoch dependence. A Lindeberg CLT for strictly stationary RFs was provided by Cristina Tone in 2013 [8]. Maltz and Samur [9] worked on a uniform CLT on rectangles for functions of mixing RFs.…”

Section: Introductionmentioning

confidence: 99%