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Copula 密度的半参数贝叶斯估计AI 解读

We propose a semiparametric Bayesian estimator for copula density, formulated as a generalized exponential family that combines a parametric baseline copula with a flexible adjustment modeled by a Gaussian Process (GP). The baseline captures the main features of dependence and accommodates possibly unbounded densities, while the GP component introduces nonparametric refinement. To modulate the influence of the baseline, we further introduce a tuning parameter that adjusts…

Copula 密度的非参数贝叶斯估计及金融市场应用AI 解读

We propose a nonparametric Bayesian estimator of copula density based on the Logistic Gaussian Process density estimation method. A Gaussian process prior with flexible mean and covariance functions is placed on the underlying latent function. To avoid the typical boundary issues in copula density estimation, a transformation approach is adopted, allowing the latent process to be defined on an unrestricted support and then back-transformed to obtain the posterior copula…

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…

核密度估计的稳健似然交叉验证AI 解读

Likelihood cross-validation for kernel density estimation is known to be sensitive to extreme observations and heavy-tailed distributions. We propose a robust likelihood-based cross-validation method to select bandwidths in multivariate density estimations. We derive this bandwidth selector within the framework of robust maximum likelihood estimation. This method establishes a smooth transition from likelihood cross-validation for nonextreme observations to least squares…

引导式非参数拟合优度检验及其收入分布应用AI 解读

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…

预测密度设定的序贯检验AI 解读

We develop a specification test of predictive densities, based on the fact that the generalized residuals of correctly specified predictive density models are independent and identically distributed uniform. The proposed sequential test examines the hypotheses of serial independence and uniformity in two stages, wherein the first‐stage test of serial independence is robust to violation of uniformity. The approach of the data‐driven smooth test is employed to construct the…

数据驱动的平滑对称性检验AI 解读

In this paper we propose a data driven smooth test of symmetry. We first transform the raw data via the probability integral transformation according to a symmetrized empirical distribution, and show that under the null hypothesis of symmetry, the transformed data has a limiting uniform distribution, reducing testing for symmetry to testing for uniformity. Employing Neyman’s smooth test of uniformity, we show that only odd-ordered orthogonal moments of the transformed data…

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…

Copula 模型设定的光滑检验AI 解读

We present a family of smooth tests for the goodness of fit of semiparametric multivariate copula models. The proposed tests are distribution free and can be easily implemented. They are diagnostic and constructive in the sense that when a null distribution is rejected, the test provides useful pointers to alternative copula distributions. We then propose a method of copula density construction, which can be viewed as a multivariate extension of Efron and Tibshirani. We…

多元密度的指数级数估计量AI 解读

We present an Exponential Series Estimator (ESE) of multivariate densities, which has an appealing information-theoretic interpretation. For a d dimensional random variable with density p0, the ESE takes the form , where are some real-valued, linearly independent functions defined on the support of p0. We derive the convergence rate of the ESE in terms of the Kullback-Leibler Information Criterion, the integrated squared error and some other metrics. We also derive its…

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基于最大熵密度的部分自适应估计AI 解读

We propose a partially adaptive estimator based on information theoretic maximum entropy estimates of the error distribution. The maximum entropy (maxent) densities have simple yet flexible functional forms to nest most of the mathematical distributions. Unlike the non-parametric fully adaptive estimators, our parametric estimators do not involve choosing a bandwidth or trimming, and only require estimating a small number of nuisance parameters, which is desirable when the…

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