Moment density estimation for positive random variables |
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| Authors: | R M Mnatsakanov F H Ruymgaart |
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| Institution: | 1. Department of Statistics , West Virginia University , P.O. Box 6330, Morgantown , WV , 26506 , USA;2. Health Effects Laboratory Division , National Institute for Occupational Safety and Health , Morgantown , WV , 26505 , USA rmnatsak@stat.wvu.edu;4. Department of Mathematics and Statistics , Texas Tech University , P.O. Box 41042, Lubbock , TX , 79409 , USA |
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| Abstract: | An unknown moment-determinate cumulative distribution function or its density function can be recovered from corresponding moments and estimated from the empirical moments. This method of estimating an unknown density is natural in certain inverse estimation models like multiplicative censoring or biased sampling when the moments of unobserved distribution can be estimated via the transformed moments of the observed distribution. In this paper, we introduce a new nonparametric estimator of a probability density function defined on the positive real line, motivated by the above. Some fundamental properties of proposed estimator are studied. The comparison with traditional kernel density estimator is discussed. |
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| Keywords: | moment density estimator mean-squared error δ-sequence L 1-consistency |
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