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Copula 密度的变换核估计AI 解读

The standard kernel estimator of copula densities suffers from boundary biases and inconsistency due to unbounded densities. Transforming the domain of estimation into an unbounded one remedies both problems, but also introduces an unbounded multiplier that may produce erratic boundary behaviors in the final density estimate. We propose an improved transformation-kernel estimator that employs a smooth tapering device to counter the undesirable influence of the multiplier. We…

Summary We have developed a customizable goodness-of-fit test of a parametric density based on its distance to a consistently estimated density. This consistent estimate is obtained via a nonparametric density estimator with a parametric start, wherein the start is set to be the hypothesized parametric density. To cope with the influence of nonparametric estimation bias, nonparametric goodness-of-fit tests have resorted to remedies such as undersmoothing or convolution of…

单位区间密度的改进变换核估计AI 解读

The kernel density estimator (KDE) suffers boundary biases when applied to densities on bounded supports, which are assumed to be the unit interval. Transformations mapping the unit interval to the real line can be used to remove boundary biases. However, this approach may induce erratic tail behaviors when the estimated density of transformed data is transformed back to its original scale. We propose a modified, transformation-based KDE that employs a tapered and tilted…