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.
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This work is supported by the National Natural Sciences Foundation of China.
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Chen, X., Jin, M. A randomly weighted estimate of the population mean. Acta Mathematicae Applicatae Sinica 10, 274–287 (1994). https://doi.org/10.1007/BF02006858
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DOI: https://doi.org/10.1007/BF02006858