Multivariate density estimation using dimension reducing information and tail flattening transformations

We propose a nonparametric multiplicative bias corrected transformation estimator designed for heavy tailed data. The multiplicative correction is based on prior knowledge and has a dimension reducing effect at the same time as the original dimension of the estimation problem is retained. Adding a tail flattening transformation improves the estimation significantly-particularly in the tail-and provides significant graphical advantages by allowing the density estimation to be visualized in a simple way. The combined method is demonstrated on a fire insurance data set and in a data-driven simulation study.     

Testing Lack-of-fit for a Polynomial Errors-in-variables Model

When a regression model is applied as an approximation of underlying model of data, the model checking is important and relevant. In this paper, we investigate the lack-of-fit test for a polynomial error-in-variables model. As the ordinary residuals are biased when there exist measurement errors in covariables,we correct them and then construct a residual-based test of score type. The constructed test is asymptotically chi-squared under null hypotheses. Simulation study shows that the test can maintain the significance level well.The choice of weight functions involved in the test statistic and the related power study are also investigated.The application to two examples is illustrated. The approach can be readily extended to handle more general models.     

数据变换参数的渐近置信域的曲率表示

该文首次用几何方法研究回归模型中数据变换参数及其子集参数的渐近置信域问题．由于文中讨论的是一般的数据变换多参数的渐近置信域的曲率表示，从而有关结论适用于各种数据变换如著名的Box-Cox变换、带有漂移参数的幂变换等变换中变换参数的渐近置信域的曲率表示．     

Robust and asymptotically unbiased estimation of extreme quantiles for heavy tailed distributions

A robust and asymptotically unbiased extreme quantile estimator is derived from a second order Pareto-type model and its asymptotic properties are studied under suitable regularity conditions. The finite sample properties of the proposed estimator are investigated with a small simulation experiment.     

非线性随机效应模型的置信域

本文对非线性随机效应模型,建立了微分几何框架,推广了Bates＆Wates关于非线性模型几何结构．在吡基础上,我们导出了关于固定效应参数和子集参数的置信域的曲率表示,这些结果是BatesandWates(1980),Hamilton(1986)与Wei(1994)等的推广．     

非线性再生散度模型参数置信域的曲率表示

本文对非线性再生散度模型在Ｅｕｃｌｉｄ空间建立了几何结构。在此基础上,研究了该模型参数和子集参数的三种近似置信域,推广了Ｈａｍｉｌｔｏｎ和韦博成等人的工作。     

Second- and third-order bias reduction for one-parameter family models

In this paper we derive second- and third-order bias-corrected maximum likelihood estimates in general uniparametric models. We compare the corrected estimates and the usual maximum likelihood estimate in terms of their mean squared errors. We also obtain closed-form expressions for bias-corrected estimates in one-parameter exponential family models. Our results cover many important and commonly used distributions. Simulation results are also given.     

Marginal density estimation for linear processes with cyclical long memory

Some convergence results on the kernel density estimator are proven for a class of linear processes with cyclic effects. In particular, we extend the results of Ho and Hsing (1996), Mielniczuk (1997) and Hall and Hart (1990) to the stationary processes for which the singularities of the spectral density are not limited to the origin. We show that the convergence rates and the limiting distribution may be different in this context.     

Asymptotically unbiased estimation of the second order tail parameter

We introduce a class of asymptotically unbiased estimators for the second order parameter in extreme value statistics. The estimators are constructed by means of an appropriately chosen linear combination of two simple, but biased, kernel estimators for the second order parameter. Asymptotic normality is proven under a third order condition on the tail behavior, some conditions on the kernel functions and for an intermediate number of upper order statistics. A specific member from the proposed class, obtained with power kernel functions, is derived and its finite sample behavior studied in a small simulation experiment.     

条件密度置信区间的覆盖精度

本文用经验似然方法讨论了条件密度的置信区间的构造. 通过对覆盖概率的Edgeworth展开得到了经验似然置信区间的覆盖精度, 同时证明了条件密度的经验似然置信区间的Bartlett可修正性     

Computing the variance of a conditional expectation via non-nested Monte Carlo

Computing the variance of a conditional expectation has often been of importance in uncertainty quantification. Sun et al. has introduced an unbiased nested Monte Carlo estimator, which they call $1\frac{1}{2}$-level simulation since the optimal inner-level sample size is bounded as the computational budget increases. In this letter, we construct unbiased non-nested Monte Carlo estimators based on the so-called pick-freeze scheme due to Sobol’. An extension of our approach to compute higher order moments of a conditional expectation is also discussed.     

Bias correction for estimated distortion risk measure using the bootstrap

The bias of the empirical estimate of a given risk measure has recently been of interest in the risk management literature. In particular, Kim and Hardy (2007) showed that the bias can be corrected for the Conditional Tail Expectation (CTE, a.k.a. Tail-VaR or Expected Shortfall) using the bootstrap. This article extends their result to the distortion risk measure (DRM) class where the CTE is a special case. In particular, through the exact bootstrap, it is analytically proved that the bias of the empirical estimate of DRM with concave distortion function is negative and can be corrected on the bootstrap, using the fact that the bootstrapped loss is majorized by the original loss vector. Since the class of DRM is a subset of the L-estimator class, the result provides a sufficient condition for the bootstrap bias correction for L-estimators. Numerical examples are presented to show the effectiveness of the bootstrap bias correction. Later a practical guideline to choose the estimate with a lower mean squared error is also proposed based on the analytic form of the double bootstrapped estimate, which can be useful in estimating risk measures where the bias is non-cumulative across loss portfolio.     

用修正重标极差法对上证指数长期记忆性的研究

本文以上证指数周收益率为研究对象,分别采用重标极差分析法和修正重标极差分析法,通过计算V统计量的值对其进行长期记忆性的检验。由于不能排除V统计量的值存在超出上侧分位点的可能性,本文进行了双侧检验,并分析了R/S分析法产生偏差的原因。得出上证指数周收益率时间序列并未表现出显著的长期记忆性的结论。     

Higher order representations of the Robbins–Monro process

For quasi-linear regression functions, the Robbins–Monro process X_n is decomposed in a sum of a linear form and a quadratic form both defined in the observation errors. Under regularity conditions, the remainder term is of order O(n^−3/2) with respect to the L_p-norm. If a cubic form is added, the remainder term can be improved up to an order of O(n⁻²). As a corollary the expectation of X_n is expanded up to an error of order O(n⁻²). This is used to correct the bias of X_n up to an error of order O(n^−3/2 log n).     

Trajectories of efficiency measurement: A bibliometric analysis of DEA and SFA

This study surveys the increasing research field of performance measurement by making use of a bibliometric literature analysis. We concentrate on two approaches, namely Data Envelopment Analysis (DEA) and Stochastic Frontier Analysis (SFA) as the most important methods to evaluate the efficiency of individual and organizational performance. It is the first literature survey that analyses DEA and SFA publications jointly, covering contributions published in journals, indexed by the Web of Science database from 1978 to 2012. Our aim is to identify seminal papers, playing a major role in DEA and SFA development and to determine areas of adoption. We recognized a constant growth of publications during the years identifying DEA as a standard technique in Operations Research, whereas SFA is mainly adopted in Economic research fields. Making use of document co-citation analysis we identify Airports and Supplier Selection (DEA) as well as Banking and Agriculture (SFA) as most influential application areas. Furthermore, Sensitivity and Fuzzy Set Theory (DEA) as well as Bayesian Analysis and Heterogeneity (SFA) are found to be most influential research areas and seem to be methodological trends. By developing an adoption rate of knowledge we identify that research, in terms of citations, is more focusing on relatively old and recent research at the expenses of middle-aged contributions, which is a typical phenomenon of a fast developing discipline.     

Bayes局部影响分析<英>

本文从Bayes观点出发,利用Kullback-Leibler距离和微分几何方法,系统地讨论了微小扰动对于Bayes统计推断的局部影响,给出了Bayes局部影响分析的一般公式作为应用,具体讨论了线性回归模型的Bayes估计和Bayes预测的局部影响问题,数值计算的结果表明,本文的方法是比较有效的。     

Spin actions in Euclidean and Hermitian Clifford analysis in superspace

In [4] we studied the group invariance of the inner product of supervectors as introduced in the framework of Clifford analysis in superspace. The fundamental group ${\mathrm{SO}}_0$ leaving invariant such an inner product turns out to be an extension of $\text{SO}(m)\times \text{Sp}(2n)$ and gives rise to the definition of the spin group in superspace through the exponential of the so-called extended superbivectors, where the spin group can be seen as a double covering of ${\mathrm{SO}}_0$ by means of the representation $h(s)[x]=sx\stackrel{￣}{s}$. In the present paper, we study the invariance of the Dirac operator in superspace under the classical H and L actions of the spin group on superfunctions. In addition, we consider the Hermitian Clifford setting in superspace, where we study the group invariance of the Hermitian inner product of supervectors introduced in [3]. The group of complex supermatrices leaving this inner product invariant constitutes an extension of $\text{U}(m)\times \text{U}(n)$ and is isomorphic to the subset ${\text{SO}}_0^J$ of ${\text{SO}}_0$ of elements that commute with the complex structure J. The realization of ${\text{SO}}_0^J$ within the spin group is studied together with the invariance under its actions of the super Hermitian Dirac system. It is interesting to note that the spin element leading to the complex structure can be expressed in terms of the n-dimensional Fourier transform.     

Resampling DEA estimates of investment fund performance

Data envelopment analysis (DEA) is attractive for comparing investment funds because it handles different characteristics of fund distribution and gives a way to rank funds. There is substantial literature applying DEA to funds, based on the time series of funds’ returns. This article looks at the issue of uncertainty in the resulting DEA efficiency estimates, investigating consistency and bias. It uses the bootstrap to develop stochastic DEA models for funds, derive confidence intervals and develop techniques to compare and rank funds and represent the ranking. It investigates how to deal with autocorrelation in the time series and considers models that deal with correlation in the funds’ returns.