## Estimation in the general linear model when the accuracy is specified before data collection.(English)Zbl 0589.62067

The author uses a concept of accuracy saying that an estimator $${\hat \beta}$$ of $$\beta$$ is ”accurate with accuracy A and confidence c”, $$0<c<1$$, if P($${\hat \beta}$$-$$\beta\in A)\geq c$$ for all $$\beta$$. Note that A need only be any Borel set having an interior point at zero.
Given a sequence $$Y_ 1,Y_ 2,..$$. of independent vector-valued homoscedastic normally-distributed random variables generated via the general linear model $$Y_ i=X_ i\beta +\epsilon$$, the k-dimensional parameter $$\beta$$ is accurately estimated using a sequential version of the well-known maximum probability estimator developed by L. Weiss and J. Wolfowitz [Ann. Inst. Stat. Math. 19, 193-206 (1967; Zbl 0183.212); see also ”Maximum probability estimators and related topics.” (1974; Zbl 0297.62015)]. The procedure also generalizes C. Stein’s [Ann. Math. Stat. 16, 243-258 (1945; Zbl 0060.304)] fixed-width confidence sets to several dimensions. Some examples are given to illustrate the procedure.
Reviewer: V.Mammitzsch

### MSC:

 62L12 Sequential estimation 62E20 Asymptotic distribution theory in statistics 60G40 Stopping times; optimal stopping problems; gambling theory

### Citations:

Zbl 0183.212; Zbl 0297.62015; Zbl 0060.304
Full Text: