On Some Useful “Inefficient” Statistics
Several statistical techniques are proposed for economically analyzing large masses of data by means of punched-card equipment; most of these techniques require only a counting sorter. The methods proposed are designed especially for situations where data are inexpensive compared to the cost of analysis by means of statistically “efficient” or “most powerful” procedures. The principal technique is the use of functions of order statistics, which we call systematic statistics.
It is demonstrated that certain order statistics are asymptotically jointly distributed according to the normal multivariate law.
for estimating the mean by using 1, 2, …, 10 suitably chosen order statistics;
for estimating the standard deviation by using 2, 4, or 8 suitably chosen order statistics;
for estimating the correlation coefficient whether other parameters of the normal bivariate distribution are known or not (three sorting and three counting operations are involved).
KeywordsCovariance Sorting Estima Glean Metron
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- E.J. Gumbel, “Statische Theorie der grössten Werte,” Zeitschrift für schweizerische Statistik und Volkswirtschaft. Vol. 75. part 2 (1939) P- 250.Google Scholar
- M.G. Kendall, The Advanced Theory of Statistics, J.B. Lippineott Co., 1943.Google Scholar
- K. Pearson. “On the probable errors of frequency constants. Part 111.” Biometrika, Vol. 13 (1920), p. 113.Google Scholar
- K. Pearson (Editor), Tables for Statisticians and Biomeiricians. Part II. 1931, p. 78. Table VIII.Google Scholar
- N. Smirnoff. “Sur la dépendance des membres d’un series de variations,” Bull. Unto. État Moscou. Series Int., Sect. A.. Math, et Mécan., Vol. I, fasc. 4. p. 1.Google Scholar