Some properties of random stationary sequences with bivariate densities having diagonal expansions and nonparametric estimators based on them*
AbstractWe 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.
|Journal series||Journal of Nonparametric Statistics, ISSN 1048-5252, e-ISSN 1029-0311|
|Publication size in sheets||1|
|Keywords in English||Diagonal expansion of bivariate density, long-range dependence, orthonor-mal system, mixing coefficients, subordinated sequence, time series|
|Publication indicators||= 2; = 4.0; : 2000 = 0.456; : 2006 = 0.277 (2) - 2007=0.574 (5)|
|Citation count*||4 (2015-02-21)|
* presented citation count is obtained through Internet information analysis and it is close to the number calculated by the Publish or Perish system.