Asymptotic Results for U-Functions of Concomitants of Order Statistics

Statistics ◽  
1992 ◽  
Vol 23 (3) ◽  
pp. 257-264 ◽  
Author(s):  
Noël Veraverbeke
Keyword(s):  
Order Statistics ◽  
Asymptotic Results ◽  
Concomitants Of Order Statistics

Choice, Order Statistics and the Distribution of Earnings

1997 ◽  
Author(s):  
Michael Sattinger
Keyword(s):  
Order Statistics ◽  
Order Statistic ◽  
Occupational Choice ◽  
Earnings Inequality ◽  
Limiting Distribution ◽  
Asymptotic Results ◽  
Expected Earnings

This paper analyzes the distribution of earnings as being generated by workers choosing among occupations on the basis of earnings maximization. A worker’s earnings then have characteristics of an order statistic. The extension to multiple occupations leads to the revision results from A.D. Roy’s two-occupation case. An additional occupation raises expected earnings while in general reducing earnings inequality. Asymptotic results from order statistics suggest that the process of occupational choice determines a limiting distribution of earnings independently of underlying distributions of occupational abilities.

The asymptotic theory of concomitants of order statistics

1974 ◽  
Vol 11 (04) ◽  
pp. 762-770 ◽  
Author(s):  
H. A. David ◽  
J. Galambos
Keyword(s):  
Order Statistics ◽  
Asymptotic Distribution ◽  
Random Sample ◽  
Order Statistic ◽  
Asymptotic Theory ◽  
Selection Procedures ◽  
Concomitants Of Order Statistics ◽  
Bivariate Normal ◽  
Independent Identically Distributed

In a random sample of n pairs (X r , Y r ), r = 1, 2, …, n, drawn from a bivariate normal distribution, let Xr :n be the rth order statistic among the Xr and let Y [r:n] be the Y-variate paired with Xr :n . The Y[r:n] , which we call concomitants of the order statistics, arise most naturally in selection procedures based on the Xr :n . It is shown that asymptotically the k quantities k fixed, are independent, identically distributed variates. In addition, putting Rt,n for the number of integers j for which , the asymptotic distribution and all moments of n– 1 Rt, n are determined for t such that t/n → λ with 0 < λ < 1.

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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