Sankhya: The Indian Journal of Statistics

1994, Volume 56, Series B, Pt. 3 , pp. 400 -- 414

SUFFICIENT CONDITIONS FOR MOMENT APPROXIMATIONS FOR A SAMPLE RATIO OR REGRESSION COEFFICIENT UNDER SIMPLE RANDOM SAMPLING

By

JOHN L. ELTINGE, *Texas A \& M University*

SUMMARY. This paper discusses sufficient conditions for standard Taylor-expansion based approximations of the bias and mean squared error of a sample ratio or sample regression coefficient in finite population random sampling. No superpopulation model is used. For a sample ratio, the sufficient conditions permit some population units to have denominator terms $X_i$ equal to zero; and require the other population units to have $X_i$ values above bounds that are decreasing in the sample size *n*. For the regression case, the conditions involve trade-offs between sample size and spacing of the population of $X_i$ values. For both the ratio and regression cases, the proposed conditions give relatively simple forms to the intuitive idea that standard moment approximations are satisfactory except in certain extreme cases, where the definition of ``extreme case'' depends on the sample size.

*AMS (1980) subject classification.* Primary 62D05, secondary 63F12, 62J05.

*Key words and phrases.* Asymptotics, bias approximation, finite population sampling, sampling without replacement, survey sampling, variance approximation.