农民行为逻辑与合作能力：一个新的阐释视角

首先对农民的行为逻辑、合作意愿与合作能力进行系统文献回顾,结果发现,虽然这些理论观点都具有一定的现实解释力,但未能全面反映事实,问题不在于这些事是而非的现象,而在于现有理论不能框架性和系统地解释这些矛盾性现象.农民的经济行为会形成一个以自我利益为中心、以经济利益为半径的经济生活圈,其理性程度、合作意愿和合作能力与经济生活圈呈正相关关系.     

用牛顿环实验测量凸透镜曲率半径的误差分析

对牛顿环测量凸透镜曲率半径实验中的误差进行了理论分析和半定量分析,指出了误差的主要来源及相应的处理方法.对于测量曲率半径P>lm的平凸透镜,公式R=Dm2-Dn2/4（m-n）λ的理论相对误差小于10-8;逐差法可以消除形变带来的系统误差;由于形变的影响应从第5级以后开始计数,对于R>1m的凸透镜要得到小于10-3的相对误差,级数应小于50,级数差值应大于30.钠光灯作为光源的系统相对误差为7.1×10-4.     

中国大宗商品现货价格指数的构建及预测能力研究

本文首先选取了我国国民经济中八个主要行业,首次提出并采用成分商品的“三重筛选”标准,选取了72种成分商品,先以成分商品的表观消费量为权重构建了行业商品现货价格指数,然后以行业规模以上工业企业的工业总产值为权重综合行业指数得到中国大宗商品现货价格指数。其次,基于已构建指数,采用谱分析方法研究发现：中国大宗商品现货价格指数领先CPI、PPI、CI三个国内宏观经济指数的期数依次为2.48个月、0.66个月、0.89个月,领先BPI、MyBCIC、CCPI三个国内大宗商品现货价格指数的期数依次为1.54天、1天、1.21周,领先上证综合指数的期数为13天,说明中国大宗商品现货价格指数具有很好的预警和预测能力。最后,本文用时差相关系数法对CSCPI的预测能力进行了定量检验,检验结果与谱分析结果一致,说明谱分析结果是稳健的。     

On proximity between PCA in the frequency domain and usual PCA

The principal components analysis (PCA) in the frequency domain of a stationary p-dimensional time series (X _n ) _n∈? leads to a summarizing time series written as a linear combination series X′ _n =∑ _m C _m ° X _n?m . Therefore, we observe that, when the coefficients C _m , m≠0, are close to 0, this PCA is close to the usual PCA, that is the PCA in the temporal domain. When the coefficients tend to 0, the corresponding limit is said to satisfy a property noted 𝒫, of which we will study the consequences. Finally, we will examine, for any series, the proximity between the two PCAs.     

Nonparametric estimation of multivariate extreme-value copulas

Extreme-value copulas arise in the asymptotic theory for componentwise maxima of independent random samples. An extreme-value copula is determined by its Pickands dependence function, which is a function on the unit simplex subject to certain shape constraints that arise from an integral transform of an underlying measure called spectral measure. Multivariate extensions are provided of certain rank-based nonparametric estimators of the Pickands dependence function. The shape constraint that the estimator should itself be a Pickands dependence function is enforced by replacing an initial estimator by its best least-squares approximation in the set of Pickands dependence functions having a discrete spectral measure supported on a sufficiently fine grid. Weak convergence of the standardized estimators is demonstrated and the finite-sample performance of the estimators is investigated by means of a simulation experiment.     

谱检验的Wild Bootstrap方法

 本文考察了基于谱估计的拟合优度检验在判断时间序列鞅差性质方面的应用,提出了利用Wild Bootstrap来近似该类检验统计量渐近分布的方法,通过模拟试验揭示出新的方法改进了检验的水平并提高了其功效,最后比较了不同方法在分析实际金融数据时的不同效果。     

The cost of not knowing the radius

Robust Statistics considers the quality of statistical decisions in the presence of deviations from the ideal model, where deviations are modelled by neighborhoods of a certain size about the ideal model. We introduce a new concept of optimality (radius-minimaxity) if this size or radius is not precisely known: for this notion, we determine the increase of the maximum risk over the minimax risk in the case that the optimally robust estimator for the false neighborhood radius is used. The maximum increase of the relative risk is minimized in the case that the radius is known only to belong to some interval [r _l ,r _u ]. We pursue this minmax approach for a number of ideal models and a variety of neighborhoods. Also, the effect of increasing parameter dimension is studied for these models. The minimax increase of relative risk in case the radius is completely unknown, compared with that of the most robust procedure, is 18.1% versus 57.1% and 50.5% versus 172.1% for one-dimensional location and scale, respectively, and less than 1/3 in other typical contamination models. In most models considered so far, the radius needs to be specified only up to a factor , in order to keep the increase of relative risk below 12.5%, provided that the radius–minimax robust estimator is employed. The least favorable radii leading to the radius–minimax estimators turn out small: 5–6% contamination, at sample size 100.      

Lévy Processes,Phase-Type Distributions,and Martingales

Lévy processes are defined as processes with stationary independent increments and have become increasingly popular as models in queueing, finance, etc.; apart from Brownian motion and compound Poisson processes, some popular examples are stable processes, variance gamma processes, CGMY Lévy processes (tempered stable processes), NIG (normal inverse Gaussian) Lévy processes, and hyperbolic Lévy processes. We consider here a dense class of Lévy processes, compound Poisson processes with phase-type jumps in both directions and an added Brownian component. Within this class, we survey how to explicitly compute a number of quantities that are traditionally studied in the area of Lévy processes, in particular two-sided exit probabilities and associated Laplace transforms, the closely related scale function, one-sided exit probabilities and associated Laplace transforms coming up in queueing problems, and similar quantities for a Lévy process with reflection in 0. The solutions are in terms of roots to polynomials, and the basic equations are derived by purely probabilistic arguments using martingale optional stopping; a particularly useful martingale is the so-called Kella-Whitt martingale. Also, the relation to fluid models with a Brownian component is discussed.     

BLLac天体谱的性质

本以喷流加速模型为基础，从有效谱指数出发讨论两种选择BLLac天体（RBLs，XBLs）的统一性。