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Warianty tytułu
O klasie estymatorów odwrotności prawdopodobieństwa
Języki publikacji
Abstrakty
In this paper a class of estimators for inverse probability indexed by a parameter c∈(0,+∞) was considered. All estimators in the class are consistent. They always take finite values, as opposed to the simple reciprocal of the sampling fraction. The class incorporates the well-known Fattorini's [2006] statistic for c = 1. The formulas for bias of these estimators were derived for c = 1,...,4 and a method for computing the bias for c = 5,6,... was suggested. The bias of estimators depends on sample size n, parameter c and unknown probability p. It turns out that there is no single value of c that would nullify the bias or minimize the mean square error for all possible values of p. In other words, no estimator in the class dominates others in terms of accuracy for a fixed n and all values of p. This also applies to the Fattorini's statistic. However, it seems that values of c greater than one do not nullify bias for any possible p so they should be avoided. If the exact formula (or upper bound) for MSE or absolute bias when c is not integer and the sample is large were known, then some partial knowledge on p taking e.g. form of inequality constraints might be explored to set the value of c in such a way that MSE or bias for most pessimistic (unfavorable) p is minimized. This justifies further efforts aimed at finding such a formula. (fragment of text)
Powszechnie znany estymator odwrotności prawdopodobieństwa zaproponowany przez Fattoriniego uogólniono poprzez dopuszczenie zmian wartości jednostkowej stałej występującej we wzorze definiującym go. Prowadzi to do konstrukcji klasy estymatorów odwrotności prawdopodobieństwa. Własności tych estymatorów zbadano analitycznie. Zaproponowano metodę wyznaczania asymptotycznego obciążenia dla całkowitych wartości zmodyfikowanej stałej. Własności estymatorów dla małych prób wyznaczono numerycznie, korzystając z własności rozkładu dwumianowego. (abstrakt oryginalny)
Słowa kluczowe
Rocznik
Strony
71--85
Opis fizyczny
Twórcy
autor
- Uniwersytet Ekonomiczny w Katowicach
Bibliografia
- Berry C.J. (1989): Bayes Minimax Estimation of a Bernoulli p in a Restricted Parameter Space. "Communications in Statistics - Theory and Methods", No. 18(12).
- Fattorini L. (2006): Applying the Horvitz-Thompson Criterion in Complex Designs: A Computer-Intensive Perspective for Estimating Inclusion Probabilities. "Biometrika", No. 93(2).
- Fattorini L. (2009): An Adaptive Algorithm for Estimating Inclusion Probabilities and Performing the Horvitz-Thompson Criterion in Complex Designs. "Computational Statistics", No. 24.
- Marciniak E., Wesołowski J. (1999): Asymptotic Eulerian Expansions for Binomial and Negative Binomial Reciprocals. "Proceedings of the American Mathematical Society", No. 127(11).
- Marchand E., Perron F., Gueye R. (2005): Minimax Estimation of a Constrained Binomial Proportion p When |p-1/2| is Small. "Sankhya", No. 67(3).
- Marchand E., MacGibbon B. (2000): Minimax Estimation of a Constrained Binomial Proportion. "Statistics & Decisions", No. 18.
- Rempała G., Szekely G.J. (1998): On Estimation with Elementary Symmetric Polynomials. "Random Operations and Stochastic Equations", No. 6.
- Stephan F.F. (1946): The Expected Value and Variance of the Reciprocal and Other Negative Powers of a Positive Bernoullian Variate. "Annals of Mathematical Statistics", No. 16.
- Thompson M.E., Wu C. (2008): Simulation-based Randomized Systematic PPS Sampling under Substitution of Units. "Survey Methodology", No. 34 (1).
Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.ekon-element-000171252269