Star-Shaped deviations

We propose the Star-Shaped deviation measures in the same vein as Star-Shaped risk measures and Star-Shaped acceptability indexes. We characterize Star-Shaped deviation measures through Star-Shaped acceptance sets and as the minimum of a family of Convex deviation measures. We also expose an interplay between Star-Shaped risk measures and deviation measures.     

Large deviations of realized volatility

This paper studies large and moderate deviation properties of a realized volatility statistic of high frequency financial data. We establish a large deviation principle for the realized volatility when the number of high frequency observations in a fixed time interval increases to infinity. Our large deviation result can be used to evaluate tail probabilities of the realized volatility. We also derive a moderate deviation rate function for a standardized realized volatility statistic. The moderate deviation result is useful for assessing the validity of normal approximations based on the central limit theorem. In particular, it clarifies that there exists a trade-off between the accuracy of the normal approximations and the path regularity of an underlying volatility process. Our large and moderate deviation results complement the existing asymptotic theory on high frequency data. In addition, the paper contributes to the literature of large deviation theory in that the theory is extended to a high frequency data environment.     

Moderate Deviation for the Rightmost Position in a Branching Brownian Motion

We study the moderate deviation probability of the position of the rightmost particle in a branching Brownian motion and obtain its moderate deviation function. Firstly, Chauvin and Rouault studied the large deviation probability for the rightmost position in a branching Brownian motion. Recently, Derrida and Shiconsidered lower deviation for the same model. By contrast, Our main result is more extensive.     

Distributions of rectilinear deviation distance to visit a facility

This paper deals with the deviation distance to visit a facility from pre-planned routes. Facilities are approximated by both points and lines on a continuous plane. To see the relationship between the deviation distance and the availability of facilities, we derive the distributions of the rectilinear deviation distance for regular and random patterns of facilities. These distributions demonstrate how the shortest distance and the relative position of origin and destination affect the deviation distance. We also show that the deviation distance is a generalization of the nearest neighbour distance.     

Optimality conditions in portfolio analysis with general deviation measures

Optimality conditions are derived for problems of minimizing a general measure of deviation of a random variable, with special attention to situations where the random variable could be the rate of return from a portfolio of financial instruments. General measures of deviation go beyond standard deviation in satisfying axioms that do not demand symmetry between ups and downs. The optimality conditions are applied to characterize the generalized ``master funds' which elsewhere have been developed in extending classical portfolio theory beyond the case of standard deviation. The consequences are worked out for deviation based on conditional value-at-risk and its variants, in particular.     

函数变换缩小数据级比偏差效果的比较原则

针对缩小序列级比偏差的单调变换,研究了在函数的和变换与每一个变换缩小级比偏差效果优劣的比较原则基础上证明了两函数之正线性和变换缩小级比偏差效果介于这两个函数缩小级比偏差效果之间.因此如果两函数之正线性和变换不比任何一个单独变换效果差,其实质是两函数商的比值是常数,即两函数变换缩小级比偏差效果一样好,并通过实例验证了结论.     

Large deviation results for the nonparametric regression function estimator on functional data

This paper is devoted to the study of large deviation behavior in the setting of the estimation of the regression function on functional data. A large deviation principle is stated for a process Z _n , defined below, allowing to derive a pointwise large deviation principle for the Nadaraya- Watson-type l-indexed regression function estimator as a by-product. Moreover, a uniform over VC-classes Chernoff type large deviation result is stated for the deviation of the l-indexed regression estimator.     

基于半参数回归模型的最小一乘局部线性算法

根据最小一乘准则,推导出最小一乘局部线性估计的计算方法,并通过对模拟数据的计算和分析,对比最小一乘核算法和最小二乘局部线性算法,验证了最小一乘局部线性算法是一种有效的,稳健的估计方法,并且有降低边界效应的作用．     

带小随机扰动的中偏差原理(英文)

本文研究了带小随机扰动的中偏差原理.运用收缩原理和指数逼近方法,Freidlin-Wentzell定理给出了Xε的大偏差原理,从而得到了Xε的中偏差原理.     

Large deviations for Glauber dynamics of continuous gas

This paper is devoted to the large deviation principles of the Glauber-type dynamics of finite or infinite volume continuous particle systems.We prove that the level-2 empirical process satisfies the large deviation principles in the weak convergence topology,while it does not satisfy the large deviation principles in the T-topology.     

Moderate Deviations for Longest Increasing Subsequences: The Lower Tail

We derive a moderate deviation principle for the lower tail probabilities of the length of a longest increasing subsequence in a random permutation. It refers to the regime between the lower tail large deviation regime and the central limit regime. The present article together with the upper tail moderate deviation principle in Ref. 12 yields a complete picture for the whole moderate deviation regime. Other than in Ref. 12, we can directly apply estimates by Baik, Deift, and Johansson, who obtained a (non-standard) Central Limit Theorem for the same quantity.     

Sensitivity analysis of the newsvendor model

Quality of decisions in inventory management models depends on the accuracy of parameter estimates used for decision making. In many situations, error in decision making is unavoidable. In such cases, sensitivity analysis is necessary for better implementation of the model. Though the newsvendor model is one of the most researched inventory models, little is known about its robustness. In this paper, we perform sensitivity analysis of the classical newsvendor model. Conditions for symmetry/skewness of cost deviation (i.e., deviation of expected demand–supply mismatch cost from its minimum) have been identified. These conditions are closely linked with symmetry/skewness of the demand density function. A lower bound of cost deviation is established for symmetric unimodal demand distributions. Based on demonstrations of the lower bound, we found the newsvendor model to be sensitive to sub-optimal ordering decisions, more sensitive than the economic order quantity model. Order quantity deviation (i.e., deviation of order quantity from its optimum) is explored briefly. We found the magnitude of order quantity deviation to be comparable with that of parameter estimation error. Mean demand is identified as the most influential parameter in deciding order quantity deviation.     

基于序数偏差融合度的动态匹配决策方法

针对具有不确定偏好序信息的动态匹配决策问题,提出了一种决策方法。首先,给出了序数偏差的相关描述;然后,把在同一时刻的不同方案间或同一方案在不同时刻间的序数偏差关系作为证据,并通过证据组合求出双边序数偏差融合度;在此基础上,构建了优化模型,获得双边匹配方案。最后,通过一个算例说明了该方法的可行性和有效性。     

Restricted Robust Uniform Matroid Maximization Under Interval Uncertainty

For the problem of selecting p items with interval objective function coefficients so as to maximize total profit, we introduce the r-restricted robust deviation criterion and seek solutions that minimize the r-restricted robust deviation. This new criterion increases the modeling power of the robust deviation (minmax regret) criterion by reducing the level of conservatism of the robust solution. It is shown that r-restricted robust deviation solutions can be computed efficiently. Results of experiments and comparisons with absolute robustness, robust deviation and restricted absolute robustness criteria are reported. This work is supported by a grant from Turkish Academy of Science(TUBA).     

A large deviation principle for bootstrapped sample means

A large deviation principle for bootstrapped sample means is established. It relies on the Bolthausen large deviation principle for sums of i.i.d. Banach space valued random variables. The rate function of the large deviation principle for bootstrapped sample means is the same as the classical one.

     

Limit theorems for the median deviation

Summary In this paper, we obtain a strong law and central limit theorem for the median deviation under only very mild smoothness conditions on the underlying distribution. Under an additional condition implied by symmetry, we derive a weak Bahadur representation for the median deviation and establish the asymptotic equivalence of the median deviation and the semi-interquartile range.     

业绩补偿承诺对定增并购双价格偏离的影响机理

业绩补偿承诺制度的初衷是降低估值溢价,引入盈利预测增长率探究其对定增并购双价格偏离的影响机理进而揭示制度发挥作用的路径。采用层级回归分析表明:业绩补偿承诺对双价格偏离具有正向影响,对盈利预测增长率具有负向影响;盈利预测增长率对双价格偏离具有正向影响,其在业绩承诺与价格偏离之间的作用机制呈现出“遮掩效应”;进一步分析发现,业绩补偿承诺对定增并购绩效具有价值促进作用,并提升了并购双方互利共赢的空间,大股东因业绩承诺所获得的高价格偏离是价值补偿的体现。研究结果丰富和拓展了业绩补偿承诺和双价格偏离的相关研究,对制度的合理安排及契约价值的发挥具有重要的意义。     

Veljan-Korchmaros不等式的稳定性

关于Euclidean空间E~n(n■2)中单形的几何不等式,由于支撑函数或径向函数的表达式很难找到,因此一般很难用Hausdorff度量或径向度量来度量两个单形的"偏差",使得涉及单形的几何不等式的稳定性的研究一直为空白.本文利用单形棱长在确定单形时起决定性作用这一事实,引进了两个单形"偏正"度量的概念,从而较好地解决了单形偏正度量的问题,由此建立了著名的Veljan-Korchmaros不等式的稳定性版本,作为推论,导出了单形中著名的Weitzenb■ck不等式和Euler不等式的稳定性版本,最后提出了几个有待解决的问题.     

Deviation inequalities,moderate deviation principles for certain Gaussian functionals,and their applications in parameter estimation

In this article, we study the deviation inequalities, moderate deviation principle (MDP) and Berry–Esseen bounds for certain Gaussian functionals arising from the Ornstein-Uhlenbeck process without tears. As an application, several asymptotic properties for the minimum distance estimator are obtained. The main methods include the MDP and deviation inequality for multiple Wiener–Itô integrals.     

Groups with small deviation for non-subnormal subgroups

We introduce the notion of the non-subnormal deviation of a group G. If the deviation is 0 then G satisfies the minimal condition for nonsubnormal subgroups, while if the deviation is at most 1 then G satisfies the so-called weak minimal condition for such subgroups (though the converse does not hold). Here we present some results on groups G that are either soluble or locally nilpotent and that have deviation at most 1. For example, a torsion-free locally nilpotent with deviation at most 1 is nilpotent, while a Baer group with deviation at most 1 has all of its subgroups subnormal.