A Note on Limit Theorems for Joint Distributions with Applications to Linear Signed Rank Statistics

1981 ◽  
Vol 43 (1) ◽  
pp. 61-64
Author(s):  
Michael A. Fligner
Keyword(s):  
Limit Theorems ◽  
Rank Statistics ◽  
Joint Distributions ◽  
Signed Rank

Limit theorems for threshold-stopped random variables with applications to optimal stopping

1990 ◽  
Vol 22 (2) ◽  
pp. 396-411 ◽  
Author(s):  
Douglas P. Kennedy ◽  
Robert P. Kertz
Keyword(s):  
Asymptotic Behaviour ◽  
Optimal Stopping ◽  
Limit Theorems ◽  
Random Variables ◽  
Limit Distributions ◽  
Joint Distributions ◽  
Normalizing Constants

The extremal types theorem identifies asymptotic behaviour for the maxima of sequences of i.i.d. random variables. A parallel theorem is given which identifies the asymptotic behaviour of sequences of threshold-stopped random variables. Three new types of limit distributions arise, but normalizing constants remain the same as in the maxima case. Limiting joint distributions are also given for maxima and threshold-stopped random variables. Applications to the optimal stopping of i.i.d. random variables are given.

Asymptotic Normality of a Class of Nonparametric Statistics

1987 ◽  
Vol 3 (3) ◽  
pp. 313-347 ◽  
Author(s):  
Munsup Seoh ◽  
Madan L. Puri
Keyword(s):  
Asymptotic Normality ◽  
Order Statistics ◽  
Linear Combination ◽  
Linear Function ◽  
Random Variables ◽  
Weighted Sum ◽  
Rank Statistics ◽  
Concomitants Of Order Statistics ◽  
Signed Rank ◽  
Special Cases

Asymptotic normality is established for a class of statistics which includes as special cases weighted sum of independent and identically distributed (i.i.d.) random variables, unsigned linear rank statistics, signed rank statistics, linear combination of functions of order statistics, and linear function of concomitants of order statistics. The results obtained unify as well as extend a number of known results.

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