×

The minimum inaccuracy principle in estimating population parameters from grouped data. (English) Zbl 0613.62038

In a previous paper [Stochastica 8, 63-81 (1984; Zbl 0599.62010)] the authors suggested the minimum inaccuracy principle as an operative method for estimating population parameters when the available experimental information could not be perceived as an exact outcome, but rather as fuzzy information. This principle is an extension of the maximum likelihood principle of estimating from exact experimental data.
In this paper, the particularization of the first method to the case in which each fuzzy information reduces to a class of exact observations is developed. We then analyze certain correspondences between the maximum likelihood and minimum inaccuracy principles in estimating parameters after grouping data. In addition, we prove that the second method approximates to the first one when a certain natural grouping, or choice of classes, is accomplished. Finally, in order to illustrate the preceding results, some relevant particular cases are examined.

MSC:

62F10 Point estimation
62F99 Parametric inference

Citations:

Zbl 0599.62010
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Corral N., Stochastica VIII 1 pp 63– (1984)
[2] DOI: 10.1016/0377-2217(85)90112-2 · Zbl 0576.90003 · doi:10.1016/0377-2217(85)90112-2
[3] Tanaka H., Advances in Fuzzy Sets Theory and Applications (North-Holland pp 303– (1979)
[4] DOI: 10.1016/0165-0114(78)90029-5 · Zbl 0377.04002 · doi:10.1016/0165-0114(78)90029-5
[5] DOI: 10.1016/0022-247X(68)90078-4 · Zbl 0174.49002 · doi:10.1016/0022-247X(68)90078-4
[6] Casals M. R., Fuzzy Sets and Systems 19 pp 3– (1986)
[7] DOI: 10.1080/01969727408546075 · Zbl 0319.02060 · doi:10.1080/01969727408546075
[8] DOI: 10.1016/0165-0114(78)90032-5 · Zbl 0378.94001 · doi:10.1016/0165-0114(78)90032-5
[9] Kerridge D. F., J. Royal Stat. Soc. Ser. B 23 pp 184– (1961)
[10] Mathai A. M., Basic Concepts in Information Theory and Statistics (1975) · Zbl 0346.94014
[11] DOI: 10.1007/BF02479370 · Zbl 0338.94016 · doi:10.1007/BF02479370
[12] Cramér H., Mathematical Methods of Statistics (1946) · Zbl 0063.01014
[13] DOI: 10.2307/2341292 · doi:10.2307/2341292
[14] DOI: 10.1214/aoms/1177728726 · Zbl 0056.37103 · doi:10.1214/aoms/1177728726
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.