Hazhir Homei
Stochastic linear combinations of some random vectors are studied where the distribution of the random vectors and the joint distribution of their coefficients are Dirichlet. A method is provided for calculating the distribution of these combinations which has been studied before by some authors. Our main result is a generalization of some existing results with a simpler proof.
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In the multivariate one-sample location model, we propose a class of flexible robust, affine-equivariant L-estimators of location, for distributions invoking affine-invariance of Mahalanobis distances of individual observations. An involved iteration process for their computation is numerically illustrated.
A Novel Extension of Randomly Weighted Average
研究了一个关于随机变量$Z$均匀分布在两个独立随机变量之间的问题。本文对这个问题作了一个新的推广，并利用广义斯蒂尔切斯变换识别了相当大的一类随机加权平均分布。在这篇文章中，我们采用施瓦茨分布理论来寻找这种扩展的分布，我们还研究了它们的一些性质。
This article gives a synopsis on new developments in affine invariant tests for multivariate normality in an i.i.d.-setting, with special emphasis on asymptotic properties of several classes of weighted $L^2$-statistics. Since weighted $L^2$-statistics typically have limit normal distributions under fixed alternatives to normality, they open ground for a neighborhood of model validation for normality. The paper also reviews several other invariant tests for this problem, notably the energy test, and it presents the results of a large-scale simulation study. All tests under study are implemente…
We study weighted M-estimators for $\mathbb{R}^d$-valued clustered data and give sufficient conditions for their consistency. Their asymptotic normality is established with estimation of the asymptotic covariance matrix. We address the robustness of these estimators in terms of their breakdown point. Comparison with the unweighted case is performed with some numerical studies. They highlight that optimal weights maximizing the relative efficiency have a bad impact on the breakdown point.
Asymptotics of Randomly Weighted u- and v-statistics: Application to Bootstrap
本文主要研究u-统计量和v-统计量的加权自助法的渐近性质。我们推导出的一致性加权自助u-和v-统计量，基于独立同分布。和非I.I.D.观察，从一些更一般的结果，我们首先建立的总和随机加权阵列的随机变量。本文的一些结果推广了u-统计量的相合性以及随机变量阵列和的相合性的一些著名结果。我们还采用了一种新的方法来调理，以获得一个有条件的CLT的加权自助u-和v-统计量，假设相同的条件，为经典的中心极限定理定期u-和v-统计量。
We give the exact distribution of the average of n independent beta random variables weighted by the selected cuts of (0, 1) by the order statistics of a random sample of size n-1 from the uniform distribution U(0,1), for each n. A new integral transformation that is similar to generalized Stieltjes transform is given with various properties. The result of Soltani and Roozegar [On distribution of randomly ordered uniform incremental weighted averages: Divided difference approach. Statist Probab Lett. 2012, 82(5):1012-1020] with this new transform and also integral representation of the Gauss-h…
Tail asymptotics of randomly weighted large risks
在本文中，我们关注的是一个样本的渐近独立的风险。随机加权顺序统计量的线性组合的尾渐近概率近似在各种假设下，其中个人的尾部行为有一个至关重要的作用。提供了对数正态风险的应用程序。
Deriving Lehmer and Hölder means as maximum weighted likelihood estimates for the multivariate exponential family
本文将 Lehmer 和 Hölder 均值族与加权最大似然估计的联系从一元指数族推广到多元指数族，为这些均值族提供概率解释并拓展其应用。
Strong uniform laws of large numbers for bootstrap means and other randomly weighted sums
本文为自助法均值等随机加权和建立了新颖的强一致大数定律，扩展了加权程序适用性与样本量灵活性，涵盖负正交相依权重等多种方案。
A multivariable measurement error model $AX \approx B$ is considered. Here $A$ and $B$ are input and output matrices of measurements and $X$ is a rectangular matrix of fixed size to be estimated. The errors in $[A,B]$ are row-wise independent, but within each row the errors may be correlated. Some of the columns are observed without errors and the error covariance matrices may differ from row to row. The total covariance structure of the errors is known up to a scalar factor. The fully weighted total least squares estimator of $X$ is studied. We give conditions for asymptotic normality of the …
On weighted Poincar{é} inequalities for multivariate Liouville distributions -- Application to Global Sensitivity Analysis
本文建立了多元Liouville分布的加权Poincaré不等式，并通过传输论证将其推广到连续椭圆等高分布，最后应用于全局敏感性分析，在洪水模型案例中展示了实际用途。
A tail empirical process for heavy-tailed and right-censored data is introduced and its Gaussian approximation is established. In this context, a (weighted) new Hill-type estimator for positive extreme value index is proposed and its consistency and asymptotic normality are proved by means of the aforementioned process in the framework of second-order conditions of regular variation. In a comparative simulation study, the newly defined estimator is seen to perform better than the already existing ones in terms of both bias and mean squared error. As a real data example, we apply our estimation…
Approximation by mixtures of multivariate Erlang distributions
本文证明了具有相同速率参数的有限多元Erlang混合密度在概率密度类中是稠密的，并通过构造性论证得出多项量化结果，包括统一逼近界和局部Hölder条件下的逼近速率。
Two-stage weighted least squares estimator of multivariate non-negative observation-driven models
本文针对多元非负时间序列的半参数观测驱动模型，提出两阶段多元加权最小二乘估计量（MWLSEs），在保持与拟最大似然估计一致性的同时，通过选择适当的加权矩阵序列提高估计效率，并通过模拟和实际数据验证了其优越性。
Multivariate root-n-consistent smoothing parameter free matching estimators and estimators of inverse density weighted expectations
针对多维下常用最近邻和匹配估计量的偏差问题，提出基于K阶Voronoi镶嵌单元多项式最小二乘拟合的修改版本，实现√n速率收敛且无需平滑参数，还通过下界验证了回归函数平滑性的必要性并经模拟验证可行性。
We apply the holonomic gradient method to compute the distribution function of a weighted sum of independent noncentral chi-square random variables. It is the distribution function of the squared length of a multivariate normal random vector. We treat this distribution as an integral of the normalizing constant of the Fisher-Bingham distribution on the unit sphere and make use of the partial differential equations for the Fisher-Bingham distribution.
Tail Behavior of Randomly Weighted Sums
设$\{X_t, t \geq 1\}$是同分布的两两渐近独立的随机变量序列，$\{ Θ_t, t\geq1 \}$是独立于序列$\{X_t, t \geq 1\}$的正随机变量序列.我们将讨论$\xinf=\sum_{t=1}^{\infty}Θ_t X_t^{+}$（其中$X^+=\max\{0,X\}$）和$\max_{1\leq k<\infty} \sum_{t=1}^{k}Θ_t X_t$的尾概率和几乎处处收敛性，并提供Denisov和Zwart（2007）提出的一些充分条件作为通常矩条件的替代。特别是，我们说明了$X_1$的尾部概率中涉及的慢变函数的条件如何有助于控制随机加权和的尾部行为。注意，上述结果允许我们选择$X_1, X_2,...$作为独立同分布的正随机变量。若$X_1$具有指数$-α$的规则变化尾，其中$α>0$，且$\{Θ_t,t\geq1\}$是与$\{X_t\}$无关的正随机变量序列，则已知，也可由上述充分条件得到，在$\{Θ_t,t\geq1\}$上的某些适当矩条件下，$\xinf=\sum_{t=1}^{\infty}Θ_t X_t$以概率1收敛且具有指数$-α$的规则变化尾。受Jacobsen等人（2009）的逆问题的启发，我们提出了这样一个问题：如果$\xinf$具有规则变化的尾部，那么在某些适当的条件下，$X_1$是否具有规则变化的尾部？我…
A weighted likelihood technique for robust estimation of a multivariate Wrapped Normal distribution for data points scattered on a p-dimensional torus is proposed. The occurrence of outliers in the sample at hand can badly compromise inference for standard techniques such as maximum likelihood method. Therefore, there is the need to handle such model inadequacies in the fitting process by a robust technique and an effective down-weighting of observations not following the assumed model. Furthermore, the employ of a robust method could help in situations of hidden and unexpected substructures i…
This paper addresses the problem of estimating the extreme value index in presence of random censoring for distributions in the Weibull domain of attraction. The methodologies introduced in [Worms (2014)], in the heavy-tailed case, are adapted here to the negative extreme value index framework, leading to the definition of weighted versions of the popular moments of relative excesses with arbitrary exponent. This leads to the definition of two families of estimators (with an adaptation of the so called Moment estimator as a particular case), for which the consistency is proved under a first or…
Ensemble estimators for multivariate entropy estimation
熵和互信息等密度泛函的估计问题在统计学和信息论界引起了广泛的关注。概率密度泛函的一大类估计量遭受维数灾难，其中，随着样本的维数$d$增加，均方误差（MSE）作为样本大小$T$的函数衰减得越来越慢。特别地，速率通常是$O(T^{-γ/{d}})$阶的冰川慢，其中$γ>0$是速率参数。这样的估计器的示例包括核密度估计器、$k$ -最近邻（$k$ -NN）密度估计器、$k$ -NN熵估计器、固有维数估计器和其他示例。在本文中，我们提出了一个加权仿射组合的合奏，这样的估计，其中最佳的权重可以选择这样的加权估计收敛速度快得多的尺寸不变率$O(T^{-1})$。此外，我们表明，这些最佳的权重可以通过解决一个凸优化问题，可以离线进行，不需要训练数据。我们说明了我们的加权估计两个重要的应用程序的优越性能：（i）估计Panter-Dite失真率因子和（ii）估计香农熵测试的概率分布的随机样本。
The contribution of this study is twofold: First, we propose an efficient algorithm for the computation of the (weighted) maximum likelihood estimators for the parameters of the multivariate Student-$t$ distribution, which we call generalized multivariate myriad filter. Second, we use the generalized multivariate myriad filter in a nonlocal framework for the denoising of images corrupted by different kinds of noise. The resulting method is very flexible and can handle heavy-tailed noise such as Cauchy noise, as well as the other extreme, namely Gaussian noise. Furthermore, we detail how the li…
We study a novel class of affine invariant and consistent tests for multivariate normality. The tests are based on a characterization of the standard $d$-variate normal distribution by means of the unique solution of an initial value problem connected to a partial differential equation, which is motivated by a multivariate Stein equation. The test criterion is a suitably weighted $L^2$-statistic. We derive the limit distribution of the test statistic under the null hypothesis as well as under contiguous and fixed alternatives to normality. A consistent estimator of the limiting variance under …
We employ a general Monte Carlo method to test composite hypotheses of goodness-of-fit for several popular multivariate models that can accommodate both asymmetry and heavy tails. Specifically, we consider weighted L2-type tests based on a discrepancy measure involving the distance between empirical characteristic functions and thus avoid the need for employing corresponding population quantities which may be unknown or complicated to work with. The only requirements of our tests are that we should be able to draw samples from the distribution under test and possess a reasonable method of esti…
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