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密度导数核估计的根号 n 带宽选择方法AI 解读

Based on a random sample of size n from an unknown density f on the real line, the problem of adaptively selecting the bandwidth in kernel estimation of f (k) is investigated, where f (k) denotes the kth derivative of f. The estimates of density derivatives can be used to evaluate modes and inflection points of f and can be applied to the estimation of scores in certain additive models and to the empirical verification of the law of demand in econometrics. For all k, the…

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密度导数平方积分的自适应平方根样本量估计AI 解读

Based on a random sample of size $n$ from an unknown density $f$ on the real line, the nonparametric estimation of $\theta_k = \int\{f^{(k)}(x)\}^2 dx, k = 0, 1,\ldots$, is considered. These functionals are important in a number of contexts. The proposed estimates of $\theta_k$ is constructed in the frequency domain by using the sample characteristic function. It is known that the sample characteristic function at high frequency is dominated by sample variation and does not…

对称性假设下符号线性秩统计量的大偏差结果AI 解读

A Cramer type large deviation theorem for signed linear rank statistics under the symmetry hypothesis is obtained. The theorem is proved for a wide class of scores covering most of the commonly used ones (including the normal scores). Furthermore, the optimal range $0 < x \leq o(n^{1/4})$ can be obtained for bounded scores, whereas the range $0 < x \leq o(n^\delta), \delta \in (0, \frac{1}{4})$ is obtainable for many unbounded ones. This improves the earlier result under the…