On the asymptotic mean integrated squared error of a kernel density estimator for dependent data
AbstractHall and Hart (1990) proved that the mean integrated squared error (MISE) of a marginal kernel density estimator from an infinite moving average process X1, X2, … may be decomposed into the sum of MISE of the same kernel estimator for a random sample of the same size and a term proportional to the variance of the sample mean. Extending this, we show here that the phenomenon is rather general: the same result continues to hold if dependence is quantified in terms of the behaviour of a remainder term in a natural decomposition of the densities of (X1, X1+i), i = 1, 2, ….
|Journal series||Statistics & Probability Letters, [Statistics and Probability Letters], ISSN 0167-7152, e-ISSN 1879-2103|
|Publication size in sheets||0.5|
|Keywords in English||Kernel estimator; Long-range dependence; Mean integrated square error|
|Publication indicators||= 11; = 12.0; : 1999 = 0.735; : 2006 = 0.286 (2) - 2007=0.443 (5)|
|Citation count*||12 (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.