Bootstrap procedures under some non-i.i.d. models. (English) Zbl 0655.62031

Liu, Regina Y.

Ann. Stat. 16, No. 4, 1696-1708 (1988).

Summary: It is shown that the classical i.i.d. bootstrap remains a valid procedure for estimating the sampling distributions of certain symmetric estimators of location, as long as the random observations are independently drawn from distributions with (essentially) a common location. This may be viewed as a robust property of the classical i.i.d. bootstrap. Also included is a study of the second order properties of a different bootstrap procedure proposed by C. F. J. Wu [ibid. 14, 1261-1295 (1986; Zbl 0618.62072)] in the context of heteroscedasticity in regression.

MSC:

62G05

Nonparametric estimation

Keywords:

asymptotics; L-statistics; Edgeworth expansions; sampling distributions; symmetric estimators of location; second order properties; bootstrap procedure; heteroscedasticity; regression

Citations:

Zbl 0618.62072