Stabilizing the asymptotic covariance of an estimate

作者：Withers Christopher^*; Nadarajah Saralees

来源：Electronic Journal of Statistics, 2010, 4: 161-171.

DOI：10.1214/10-EJS562

• Asymptotic
• confidence regions
• distribution-free
• estimates
• influence function
• multivariate normal
• stabilizing

Suppose n(1/2)((theta) over cap (n)-theta)-> N-p(0, V(theta)) as n -> infinity for some estimate (theta) over cap (n), of theta in R-p. If p = 1 and g(theta) = integral(theta)(0) V(x)(-1/2)dx, it is well known that n(1/2)(g((theta) over cap (n)) - g(theta)) -> N(0, 1) as n -> infinity, the distribution often being less skew so that inference based on the approximation n(1/2)(g((theta) over cap (n))-g(theta)) similar to N(0, 1) should he more accurate than inference based on the approximation V((theta) over cap (n))(-1/2)n(1/2) ((theta) over cap (n)-theta) similar to N(0, 1). If p > 1 there is generally no such one to one transformation g(.). We consider three different types of stabilization of V(theta). We also consider the problem of finding, g(.) so that the components of g((theta) over cap (n)) are asymptotically independent.

• 出版日期2010