Abstract
The problem of estimating a probability density with a given weight is considered. Probability densities of this type arise in different cases, e.g., analyzing order statistics and studying random-size samples in problems of reliability theory, insurance, and other areas. When constructing an estimator, expansion is used with respect to a wavelet basis based on wavelet functions with bounded spectrum. It is proved that the considered estimator is asymptotically normal when the number of terms of the expansion is fixed and growing.
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Funding
This work was supported by the Russian Science Foundation, project no. 18-11-00155.
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Russian Text © The Author(s), 2019, published in Vestnik Moskovskogo Universiteta, Seriya 15: Vychislitel’naya Matematika i Kibernetika, 2019, No. 2, pp. 56–60.
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Shestakov, O.V. Central Limit Theorem for a Wavelet Estimator of a Probability Density with a Given Weight. MoscowUniv.Comput.Math.Cybern. 43, 143–147 (2019). https://doi.org/10.3103/S0278641918040088
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DOI: https://doi.org/10.3103/S0278641918040088