Numbers of near-maxima for the bivariate case

作者：Bairamov I^*; Stepanov A

来源：Statistics & Probability Letters, 2010, 80(3-4): 196-205.

DOI：10.1016/j.spl.2009.10.007

Let (Z) over bar (1) = (X(1), Y(1))....(Z) over bar (n) = (X(n), Y(n)) be independent and identically distributed random vectors with continuous distribution. Let K(n)(a, b(1), b(2)) be the number of sample elements that belong to the open rectangle (X(max)((n)) - a, X(max)((n))) x (Y(max)((n)) - b(1), Y(max)((n)) + b(2)) - numbers of near-maxima in the bivariate case. in the present paper, we discuss asymptotic properties of K(n) (a, b(1), b(2)) and K(n)(infinity, 0, infinity).

• 出版日期2010-2-1