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Limit theorems for arrays of maximal order statistics

Adler A.

Probability and Mathematical Statistics

2002

Vol. 22, Fasc. 2

211--220

Let {X, Xnj,1≤j≤mn, n≥1} be independent and identically distributed random variables with the Pareto distribution. Let Xn(k) be the k-th largestorder statistic from then-th row of our array. This paper establishes unusual limit theorems involving weighted sums for the sequence {Xn(k), n≥1}.

Locations of extreme values of the empirical process

Randjiou Y.

Probability and Mathematical Statistics

2001

Vol. 21, Fasc. 1

57--70

Let αn be a uniform empirical process and μn (respectively, νn the unique location of its maximum (respectively, minimum). We establish a “liminf” iterated logarithm law for |μn – νn|