On the theory of ratio estimates. (English. Czech, Russian summaries) Zbl 0156.39804

Summary: Estimated variances, yielded by large sample approach, are adjusted by a proportional regression approach; subsequently, under the assumption of normality, exact statements on confidence intervals are arrived at. The paper deals too, with complex types of ratio estimates, as well as with modifications needed, when stratification, multiple stages, or some special methods of first-stage sampling are present.


62D05 Sampling theory, sample surveys
62F25 Parametric tolerance and confidence regions


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[1] Fieller E. C.: A fundamental formula in the statistics of biological assay, and some applications. Quart. Journ. Pharm. 17 (1944), 117- 123.
[2] Hansen M. H., Hurwitz W. N., Madow W. G.: Sample Survey Methods and Theory. vol. I, II, New York, London, 1953. · Zbl 0052.14801
[3] Hansen M. H., Hurwitz W. N.: On the theory of sampling from finite populations. Ann. Math. Stat. 14 (1943), p. 393. · Zbl 0060.30104 · doi:10.1214/aoms/1177731356
[4] Yeates F., Grundy P. M.: Selection without replacement from within strata with probability proportional to size. Journ. Royal. Stat. Soc., B, XV, 1953, 253-261. · Zbl 0052.15301
[5] Keyfitz W.: Estimates of sampling variance where two units are selected from each stratum. Journ. Am. Stat. Ass. 52 (1957), 503-510. · Zbl 0078.33502 · doi:10.2307/2281699
[6] Madow W. G.: On the limiting distributions of estimates based on samples from finite universes. Ann. Math. Stat. 19 (1948), 535-545. · Zbl 0037.08602 · doi:10.1214/aoms/1177730149
[7] Cramer H.: Mathematical methods of statistics. Princeton 1946. · Zbl 0063.01014
[8] Hájek J.: Nerovnosti pro zobecněné Studentovo rozdělení a jejich použití. Časopis pro pěstování matematiky 82 (1957), 182-194.
[9] Hájek J.: Representativní výbor skupin metodou dvou fází. Statistický obzor, XXIX, 1949, 384-394.
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