The Study Of Unbiased Ratio Estimator

In sampling survey, use of the auxiliary variable can increase the precision of estimation so as to achieve a more satisfactory effect. Ratio estimation which is a kind of estimation using auxiliary variable is a nonlinear estimation. As to a simple random sampling, the usual ratio estimator is biased which should not be ignored in certain conditions. So I studied unbiased estimators in this essay, and got approximate estimators of variances of some estimators.The first chapter enumerates some of the extant theories in this field. The second chapter comments on the traditional ratio estimator, and shows its bias through an example. The third chapter is the core of this essay which consists of four sections: The first section enumerates several types of unbiased ratio estimator; the second part introduces the methods of educing variance and estimator of variance; the third section studies four unbiased ratio estimators, using two methods to educe its variances and estimators of variances; moreover, I studied four unbiased product estimators in the fourth section. The fourth chapter compares five ratio estimators in an example. The fifth chapter ends the essay as a summary.This essay have some new achieves as follows: obtaining the Harley_Ross estimator' approximate variance and approximate estimator of variance; constructing another unbiased ratio estimator and obtaining its approximate variance and approximate estimator of variance by referring to Harley_Ross estimator; constructing two unbiased product estimators and obtaining their approximate variances and approximate estimators of variances with reference to Harley_Ross estimator; constructing another unbiased ratio estimator and other two unbiased product estimators according to Mickey estimator.The ratio estimator has much to study. What a pity. Because of my limited ability, there are still many problems which are not solved. For instances: the bias degree of the estimators' approximate variances and approximate estimators of variances are not theoretically studied; no comparison is made between the five ratio estimators' variances or between the five product estimators' variances. Detailed weaknesses of this essay can be found in the second section of the fifth chapter.