A note on testing the regression functions via nonparametric smoothing

The authors present a consistent lack‐of‐fit test in nonlinear regression models. The proposed procedure possesses some nice properties of Zheng's test such as the consistency, the ability to detect any local alternatives approaching the null at rates slower than the parametric rate. What's more, for a predetermined kernel function, the proposed test is more powerful than Zheng's test and the validity of these findings is confirmed by the simulation studies and a real data example. In addition, the authors find out a close connection between the choices of normal kernel functions and the bandwidths. The Canadian Journal of Statistics 39: 108–125; 2011 © 2011 Statistical Society of Canada     

城市防灾绿地现状调查与分析——以黄山市为例

以黄山市中心城区为例,综合黄山市中心城区绿地现状以及灾害发生点,对城区内防灾绿地的选址进行合理安排,确定黄山学院南区、世纪广场等区域为灾害发生的避难点,并依据黄山市道路结构系统,提出了恰当的一级、二级避难通道。灾害发生点、避难通道、防灾绿地点三者有机结合,形成完善的避难系统。     

Inductive Inference: An Axiomatic Approach

A predictor is asked to rank eventualities according to their plausibility, based on past cases. We assume that she can form a ranking given any memory that consists of finitely many past cases. Mild consistency requirements on these rankings imply that they have a numerical representation via a matrix assigning numbers to eventuality–case pairs, as follows. Given a memory, each eventuality is ranked according to the sum of the numbers in its row, over cases in memory. The number attached to an eventuality–case pair can be interpreted as the degree of support that the past case lends to the plausibility of the eventuality. Special instances of this result may be viewed as axiomatizing kernel methods for estimation of densities and for classification problems. Interpreting the same result for rankings of theories or hypotheses, rather than of specific eventualities, it is shown that one may ascribe to the predictor subjective conditional probabilities of cases given theories, such that her rankings of theories agree with rankings by the likelihood functions.     

一种基于PIM与核方法的模糊聚类新算法

本文针对模糊C均值聚类在大数据量时收敛较慢以及不能对多种数据结构有效聚类的缺点,结合PIM算法与核方法提出了一种新的高效聚类算法———KPIM算法,并从理论上证明了该算法的收敛性.最后利用标准实验数据IRIS数据集测试,结果表明KPIM算法在保证收敛速度的同时,聚类效果更有效.     

同种商品不同月份期货组合风险评价模型研究及应用

以期货合约的每一交易日的对数涨跌率来反映市场风险,借助VaR风险价值法,运用加权核估计技术(WKDE)和指数加权滑动模型(EWMA),建立了基于期货组合中持有头寸不同且可以进行风险对冲的期货组合市场风险非线性叠加评价模型,解决了同种商品、不同月份期货组合每一交易日最大损失的确定问题,并通过实证研究验证了模型的实用性.该模型的特点一是借助WKDE法预测组合中单个合约每一交易日涨跌率最大日亏损值,充分体现了期货合约涨跌率的实际走势,使VaR估计更加精确.二是通过动态迁移相关系数矩阵的计算保证了模型的精确性.采用EWMA模型预测动态变化的方差-协方差矩阵,从实证的角度得到更精准的动态迁移相关系数矩阵.三是考虑了组合中多头和空头不同头寸之间的风险对冲,避免了实际中期货组合风险的线性相加而造成放大风险或减少风险的不准确性,从而能较好地保证了模型的预测精度及准确性.四是通过基于风险非线性叠加建立的期货组合风险评价模型解决了SPAN系统中期货组合风险的线性叠加问题,从而得到更合理的组合风险预测值.     

Estimation of Nonparametric Models With Simultaneity

We introduce methods for estimating nonparametric, nonadditive models with simultaneity. The methods are developed by directly connecting the elements of the structural system to be estimated with features of the density of the observable variables, such as ratios of derivatives or averages of products of derivatives of this density. The estimators are therefore easily computed functionals of a nonparametric estimator of the density of the observable variables. We consider in detail a model where to each structural equation there corresponds an exclusive regressor and a model with one equation of interest and one instrument that is included in a second equation. For both models, we provide new characterizations of observational equivalence on a set, in terms of the density of the observable variables and derivatives of the structural functions. Based on those characterizations, we develop two estimation methods. In the first method, the estimators of the structural derivatives are calculated by a simple matrix inversion and matrix multiplication, analogous to a standard least squares estimator, but with the elements of the matrices being averages of products of derivatives of nonparametric density estimators. In the second method, the estimators of the structural derivatives are calculated in two steps. In a first step, values of the instrument are found at which the density of the observable variables satisfies some properties. In the second step, the estimators are calculated directly from the values of derivatives of the density of the observable variables evaluated at the found values of the instrument. We show that both pointwise estimators are consistent and asymptotically normal.     

Nonparametric Instrumental Regression

The focus of this paper is the nonparametric estimation of an instrumental regression function ϕ defined by conditional moment restrictions that stem from a structural econometric model E[Y−ϕ(Z)|W]=0, and involve endogenous variables Y and Z and instruments W. The function ϕ is the solution of an ill‐posed inverse problem and we propose an estimation procedure based on Tikhonov regularization. The paper analyzes identification and overidentification of this model, and presents asymptotic properties of the estimated nonparametric instrumental regression function.     

基于最优支持向量机模型的经营失败预警研究

根据中国资本市场的实际和样本数据特点,设计一套从样本准备到模型参数优化、再到模型比较的集成解决方案,对上市公司经营失败进行预警,通过实验分析参数调整和核函数选择对支持向量机建模的影响,寻求最优的支持向量机模型.实证结果表明,经营失败预警应用中,参数和核函数的选择对预警模型有较大影响,基于最优支持向量机模型的预测效果优于统计方法和神经网络方法,支持向量机适合中国上市公司分行业小样本的实际.特别处理事件作为经营失败样本切分标准对模型产生一定影响.     

有核网络型集群中知识共享深度与知识型企业的创新资源投入关系研究

针对我国由国内小企业对大企业(国外跨国公司)的依附关系而形成的有核网络型集群.建立集群中知识溢出、知识共享所形成的不同深度组织知识和企业的私有知识对产出的影响分析模型,通过仿真计算,研究了不同知识共享深度及私有知识产出弹性对企业知识共享行为和创新资源投入的影响.研究表明,对大企业而言.只有当公共知识产出弹性超过一定阈值时,才会进行主动知识共享,且该阈值随着知识共享深度的增加而增大:且当公共知识产出弹性超过该阈值时,大企业创新投入将随公共知识产出弹性的增加而显著增加;但此时公共知识产出弹性的增加反而会抑制小企业的创新投入.相关研究结论对促进集群持续发展提供了有益的启示.     

DO NOT WEIGHT FOR HETEROSCEDASTICITY IN NONPARAMETRIC REGRESSION

The potential role of weighting in kernel regression is examined. The concept that weighting has something to do with heteroscedastic errors is shown to be false. However, weighting does affect bias, and ways in which this might be exploited are indicated.