Some properties of random stationary sequences with bivariate densities having diagonal expansions and nonparametric estimators based on them*

Jan Mielniczuk

Abstract

We consider bivariate densities having diagonal expansions and review and generalize some of its known properties. In particular, Mehler's equality and Gebelein's inequality are generalized. Moreover, we consider stationary processes with a covariance function r(i) and with bivariate densities of (X1, X1+i) having diagonal form with coefficients a k (i), k = 0,1,… and state general conditions under which sequences subordinated to (X i )∞ i=1 are long-range dependent and obey the reduction principle. Furthermore, in the special case a k (i) = r(i) k , k = 0,1,… estimates based on such sequences enjoy some common asymptotic properties under long-range dependence.
Author Jan Mielniczuk (FMIS / DSPFM)
Jan Mielniczuk,,
- Department of Stochastic Processes and Financial Mathematics
Journal seriesJournal of Nonparametric Statistics, ISSN 1048-5252, e-ISSN 1029-0311
Issue year2000
Vol12
No2
Pages223-243
Publication size in sheets1
Keywords in English Diagonal expansion of bivariate density, long-range dependence, orthonor-mal system, mixing coefficients, subordinated sequence, time series
ASJC Classification1804 Statistics, Probability and Uncertainty; 2613 Statistics and Probability
DOIDOI:10.1080/10485250008832806
URL https://www.tandfonline.com/doi/abs/10.1080/10485250008832806
Languageen angielski
Score (nominal)15
Score sourcejournalList
Publication indicators WoS Citations = 2; GS Citations = 4.0; Scopus SNIP (Source Normalised Impact per Paper): 2000 = 0.456; WoS Impact Factor: 2006 = 0.277 (2) - 2007=0.574 (5)
Citation count*4 (2015-02-21)
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* presented citation count is obtained through Internet information analysis and it is close to the number calculated by the Publish or Perish system.
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