Weak convergence of the linear rank statistics under strong mixing conditions

2018 ◽  
Vol 132 ◽  
pp. 28-34
Author(s):  
Lucia Tabacu
Keyword(s):  
Weak Convergence ◽  
Strong Mixing ◽  
Mixing Conditions ◽  
Rank Statistics ◽  
Linear Rank

scholarly journals Weak convergence of linear rank statistics

1980 ◽  
Vol 6 (1) ◽  
pp. 141-149
Author(s):  
Béla Gyires
Keyword(s):  
Weak Convergence ◽  
Rank Statistics ◽  
Linear Rank

ON THE SPECTRAL MEASURES OF SOME WEAKLY STATIONARY SEQUENCES INVOLVING RANDOMLY SPACED OBSERVATIONS

2012 ◽  
Vol 12 (01) ◽  
pp. 1150004
Author(s):  
RICHARD C. BRADLEY
Keyword(s):  
Spectral Density ◽  
Density Function ◽  
Spectral Density Function ◽  
Strong Mixing ◽  
Spectral Measures ◽  
Mixing Conditions ◽  
Stationary Sequences ◽  
Second Moments ◽  
The Central Limit Theorem ◽  
Complex Valued

In an earlier paper by the author, as part of a construction of a counterexample to the central limit theorem under certain strong mixing conditions, a formula is given that shows, for strictly stationary sequences with mean zero and finite second moments and a continuous spectral density function, how that spectral density function changes if the observations in that strictly stationary sequence are "randomly spread out" in a particular way, with independent "nonnegative geometric" numbers of zeros inserted in between. In this paper, that formula will be generalized to the class of weakly stationary, mean zero, complex-valued random sequences, with arbitrary spectral measure.

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