Modeling spatial overdispersion via the generalized Waring point process

Modeling spatial overdispersion requires point process models with finite‐dimensional distributions that are overdisperse relative to the Poisson distribution. Fitting such models usually heavily relies on the properties of stationarity, ergodicity, and orderliness. In addition, although processes based on negative binomial finite‐dimensional distributions have been widely considered, they typically fail to simultaneously satisfy the three required properties for fitting. Indeed, it has been conjectured by Diggle and Milne that no negative binomial model can satisfy all three properties. In light of this, we change perspective and construct a new process based on a different overdisperse count model, namely, the generalized Waring (GW) distribution. While comparably tractable and flexible to negative binomial processes, the GW process is shown to possess all required properties and additionally span the negative binomial and Poisson processes as limiting cases. In this sense, the GW process provides an approximate resolution to the conundrum highlighted by Diggle and Milne.     

航线网络中需求无约束估计的非参数选择模型

传统的航空客运需求无约束估计方法仅针对平行直达航班中的顾客需求“溢出”和“再 现”问题，未能考虑航空网络中直达和中转联程航班之间的网络替代效应． 基于顾客偏好排序列表定义了航空网络顾客类型集合，建立了考虑顾客策略行为的网络型非参数离散选择模型．考虑到网络环境下历史预售数据的不完备性，站在线上和线下交易平台的角度，分别建立了非截尾和截尾需求情况下的完备数据对数似然函数． 采用 EM 算法对顾客到达率和概率质量函数进行联合估计，并提出了网络环境下的顾客“初始需求”、“再现需求”和“溢出需求”无约束估计计算方法．通过数值模拟验证了所提方法的可行性和有效性，相较于现有方法能准确反映产品间网络替代效应对顾客选择行为影响，从而更加有效地避免对历史顾客“初始需求”的高估问题．     

Uniform consistency rate of kNN regression estimation for functional time series data

In this paper, we investigate the k-nearest neighbours (kNN) estimation of nonparametric regression model for strong mixing functional time series data. More precisely, we establish the uniform almost complete convergence rate of the kNN estimator under some mild conditions. Furthermore, a simulation study and an empirical application to the real data analysis of sea surface temperature (SST) are carried out to illustrate the finite sample performances and the usefulness of the kNN approach.     

Strong law of large numbers and complete convergence for non-identically distributed WOD random variables

In this paper, we establish the strong law of large numbers and complete convergence for non-identically distributed WOD random variables. We derive some new inequalities of Fuk–Nagaev type for the sums of non-identically distributed WD random variables. All these results further extend and refine previous ones.     

On Hotelling’s T2 test in a special paired sample case

In a special paired sample case, Hotelling’s T² test based on the differences of the paired random vectors is the likelihood ratio test for testing the hypothesis that the paired random vectors have the same mean; with respect to a special group of affine linear transformations it is the uniformly most powerful invariant test for the general alternative of a difference in mean. We present an elementary straightforward proof of this result. The likelihood ratio test for testing the hypothesis that the covariance structure is of the assumed special form is derived and discussed. Applications to real data are given.     

Complete convergence and the strong laws of large numbers for pairwise NQD random variables

The authors study the strong convergence for sequences of pairwise negatively quadrant dependent (NQD) random variables under some wide conditions, and present some new theorems on the complete convergence and the strong laws of large numbers. The obtained results extend and improve some theorems in existing literature.     

Complete consistency for the estimator of nonparametric regression models based on extended negatively dependent errors

In this paper, we provide some exponential inequalities for extended negatively dependent (END) random variables. By using these exponential inequalities and the truncated method, we investigate the complete consistency for the estimator of nonparametric regression model based on END errors. As an application, the complete consistency for the nearest neighbour estimator is obtained.     

多主体权责分配与大学科研评价的科学性

针对权责界限不确定的多主体共享事物权责分配的科学性问题进行研究,提出多主体共享权责分配方式的封闭性、序列性、均称性和关联性等概念,将同时具备一致封闭性、一致序列性、一致均称性和一致关联性作为完备型权责分配方式的条件,并以完备性作为权责界限不确定的多主体权责分配的科学性的标准.通过一系列数学论证,给出完备型权责分配方式的基本性质,得出由黄金分割法诱导出来的多主体共享事物权责的“黄金分配法”的完备性,既得到了一般多主体共享权责问题的完备型分配方式的存在性结论,也证明了武书连在《2010中国大学评价》中关于大学科研获奖成果评价计分方法的科学性.     

正常商品的替代效应与收入效应研究

目前,国内外的微观经济学教科书中,关于正常商品的替代效应和收入效应的图形说明很不一致。主要是关于正常商品降价后新的预算线上的均衡点和原始预算线上的均衡点的位置不同。为此,在给定消费者效用函数和预算线方程的基础上,通过对正常商品降价(涨价)后带来的总效应、替代效应以及收入效应进行数理分析,使人们达到完整准确地理解和掌握正常商品的替代效应和收入效应的目的。     

Complete moment convergence and Lr convergence for asymptotically almost negatively associated random variables

In this paper, we investigate the complete moment convergence and L_r convergence for maximal partial sums of asymptotically almost negatively associated random variables under some general conditions. The results obtained in the paper generalize some corresponding ones for negatively associated random variables.