# A randomly weighted estimate of the population mean

A randomly weighted estimate of the population mean Consider the model (1.6), whereE ij (j=1, ...,N i,i=1,2,...) are i.i.d. with mean 0 and variance 1. Introduce a randomly weighted estimateβ n defined by (1.8). Assuminge 11 ∼N(0, 1) andN i ≥ 6, the paper gives a necessary and sufficient condition forβ n to be a consistent estimate ofβ 0, and under some further restrictions a normal approximation foβ n is established which can be used in constructing a large sample confidence interval ofβ 0. Finally, in the non-normal case a theorem about the consistency ofβ n is proved. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

# A randomly weighted estimate of the population mean

, Volume 10 (3) – Jul 13, 2005
14 pages

/lp/springer-journals/a-randomly-weighted-estimate-of-the-population-mean-wpTW07cf6u
Publisher
Springer Journals
Copyright © 1994 by Science Press, Beijing, China and Allerton Press, Inc., New York, U.S.A.
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/BF02006858
Publisher site
See Article on Publisher Site

### Abstract

Consider the model (1.6), whereE ij (j=1, ...,N i,i=1,2,...) are i.i.d. with mean 0 and variance 1. Introduce a randomly weighted estimateβ n defined by (1.8). Assuminge 11 ∼N(0, 1) andN i ≥ 6, the paper gives a necessary and sufficient condition forβ n to be a consistent estimate ofβ 0, and under some further restrictions a normal approximation foβ n is established which can be used in constructing a large sample confidence interval ofβ 0. Finally, in the non-normal case a theorem about the consistency ofβ n is proved.

### Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Jul 13, 2005

### References

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