An Esséen-type inequality for probability density functions, with an application

George G. Roussas

Statistics & Probability Letters, 2001, vol. 51, issue 4, 397-408

Abstract: In this note, an upper bound is provided for the supremum of the absolute value of the difference of the probability density functions of two k-dimensional random vectors. The bound involves integrals of the absolute value of the characteristic functions of the random vectors, and shares a general similarity with a bound obtained by Sadikova for distribution functions of two-dimensional random vectors. Sadikova's paper provided the impetus for this note. Special cases are considered, and an application is presented, regarding consistency of a kernel estimate in the framework of associated random variables.

Keywords: Associated; processes; Consistent; estimate; Esséen-type; inequality; Sadikova; inequality (search for similar items in EconPapers)
Date: 2001
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Citations: View citations in EconPapers (3)

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