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.

中文翻译：

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给定权重下概率密度的小波估计的中心极限定理

考虑在给定权重下估计概率密度的问题。这种类型的概率密度出现在不同的情况下，例如，在可靠性理论，保险和其他领域的问题中分析订单统计数据并研究随机大小的样本。在构造估计器时，基于具有有限频谱的小波函数，针对小波基础使用扩展。证明了当展开项的数目固定并增长时，考虑的估计量是渐近正态的。