里耶秦简所见秦统一衡制新证

秦在统一六国的过程中,即已逐步展开度量衡制统一,并非等到统一六国以后才开始统一度量衡制。里耶秦简简8-109+8-386既是秦统一衡制的重要物证,也是研究中国古代度量衡发展史的重要历史文物,该简反映了秦在统一六国过程中,在新占领地即已开始统一衡制的史实。里耶秦简简8-109+8-386还为我们更加全面了解秦朝推行度量衡制统一提供了重要的新资料,反映了秦地方机构如何具体开展衡制统一,即由官府传送度量衡标准器,逐县厘定。     

民国福建度政考论

度量衡与天文立法、音律三者是我国中华古老文明的基础,是民众从事经济活动的重要凭借,是百物制度的标准,也是国家政权统一的象征与经济社会发展的保障。自民国建立,福建在中央的统一部署下,开始了全省度量衡标准的划一与度量衡新器的推行工作,促进了民国时期福建经济社会的发展。     

Predictor relative importance and matching regression parameters

Predictor importance in applied regression modeling gives the main operational tools for managers and decision-makers. The paper considers estimation of predictors' importance in regression using measures introduced in works by Gibson and R. Johnson (GJ), then modified by Green, Carroll, and DeSarbo, and developed further by J. Johnson (JJ). These indices of importance are based on the orthonormal decomposition of the data matrix, and the work shows how to improve this approximation. Using predictor importance, the regression coefficients can also be adjusted to reach the best data fit and to be meaningful and interpretable. The results are compared with the robust to multicollinearity, but computationally difficult, Shapley value regression (SVR). They show that the JJ index is good for importance estimation, but the GJ index outperforms it if both predictor importance and coefficients of regression are needed; hence, this index (GJ) can be used in place of the more computationally intensive estimation by SVR. The results can be easily estimated by the considered approach that is very useful in practical regression modeling and analysis, especially for big data.     

About an adaptively weighted Kaplan-Meier estimate

The minimum averaged mean squared error nonparametric adaptive weights use data from m possibly different populations to infer about one population of interest. The definition of these weights is based on the properties of the empirical distribution function. We use the Kaplan-Meier estimate to let the weights accommodate right-censored data and use them to define the weighted Kaplan-Meier estimate. The proposed estimate is smoother than the usual Kaplan-Meier estimate and converges uniformly in probability to the target distribution. Simulations show that the performances of the weighted Kaplan-Meier estimate on finite samples exceed that of the usual Kaplan-Meier estimate. A case study is also presented.     

Evaluating bias correction in weighted proportional hazards regression

Often in observational studies of time to an event, the study population is a biased (i.e., unrepresentative) sample of the target population. In the presence of biased samples, it is common to weight subjects by the inverse of their respective selection probabilities. Pan and Schaubel (Can J Stat 36:111–127, 2008) recently proposed inference procedures for an inverse selection probability weighted (ISPW) Cox model, applicable when selection probabilities are not treated as fixed but estimated empirically. The proposed weighting procedure requires auxiliary data to estimate the weights and is computationally more intense than unweighted estimation. The ignorability of sample selection process in terms of parameter estimators and predictions is often of interest, from several perspectives: e.g., to determine if weighting makes a significant difference to the analysis at hand, which would in turn address whether the collection of auxiliary data is required in future studies; to evaluate previous studies which did not correct for selection bias. In this article, we propose methods to quantify the degree of bias corrected by the weighting procedure in the partial likelihood and Breslow-Aalen estimators. Asymptotic properties of the proposed test statistics are derived. The finite-sample significance level and power are evaluated through simulation. The proposed methods are then applied to data from a national organ failure registry to evaluate the bias in a post-kidney transplant survival model.     

Pseudo‐R2 statistics under complex sampling

Model summaries based on the ratio of fitted and null likelihoods have been proposed for generalised linear models, reducing to the familiar R² coefficient of determination in the Gaussian model with identity link. In this note I show how to define the Cox–Snell and Nagelkerke summaries under arbitrary probability sampling designs, giving a design‐consistent estimator of the population model summary. It is also shown that for logistic regression models under case–control sampling the usual Cox–Snell and Nagelkerke R² are not design‐consistent, but are systematically larger than would be obtained with a cross‐sectional or cohort sample from the same population, even in settings where the weighted and unweighted logistic regression estimators are similar or identical. Implementation of the new estimators is straightforward and code is provided in R.     

On extremal behavior of aggregation of largest claims

In this paper some dependent risks are considered, and tail asymptotic probabilities for linear combinations of finite number or random number of randomly weighted order statistics are estimated under various assumptions, where the primary random variables have long and dominatedly varying tails. Our findings are highly motivated by the need of the investigation of extremal behavior of aggregation of large claims, which has been shown in Asimit et al. (2012) Asimit, A.V., Hashorva, E., Kortschak, D. (2012). Exact tail asymptotics of the total loss of largest claim reinsurance treaties. Available at SSRN: http://ssrn.com/abstract=1993114 or http://dx.doi.org/10.2139/ssrn.1993114. [Google Scholar].     

多属性决策决问题的满意度与赋权研究

多属性决策问题的决策中,决策者往往对属性上的数值存在一定的心理预期。首先,通过心理预期与实际数据获得决策对象在每个属性上的满意度,对决策对象进行筛选过滤;其次,提出属性值信息相容关系,利用属性值之间的相容度进行赋权,信息融合对满足决策者心理预期的决策对象排序择优;再次,提出决策对象满意度,并指出传统的排序方法获取的最优决策对象与决策者总体满意度最大的决策对象并不等价。具体算例表明,该方法科学有效且可行。     

An iterative algorithm for optimal variable weighting in K-means clustering

The K-means clustering method is a widely adopted clustering algorithm in data mining and pattern recognition, where the partitions are made by minimizing the total within group sum of squares based on a given set of variables. Weighted K-means clustering is an extension of the K-means method by assigning nonnegative weights to the set of variables. In this paper, we aim to obtain more meaningful and interpretable clusters by deriving the optimal variable weights for weighted K-means clustering. Specifically, we improve the weighted k-means clustering method by introducing a new algorithm to obtain the globally optimal variable weights based on the Karush-Kuhn-Tucker conditions. We present the mathematical formulation for the clustering problem, derive the structural properties of the optimal weights, and implement an recursive algorithm to calculate the optimal weights. Numerical examples on simulated and real data indicate that our method is superior in both clustering accuracy and computational efficiency.     

论周易哲学与度量衡制度

周易哲学是河洛文化的精髓。它既是塑造中华文明的理论基础,也是中国古代度量衡制度的指导原则。中国古代度量衡理论萌芽于原始社会末期,形成于春秋,定型于西汉,成熟于东汉。周易哲学"阴阳和合"的辩证法则和"天人合一"的宇宙观念,则贯穿于我国度量衡理论形成和发展的始终。这种具有鲜明东方思想色彩的度量衡制度,在世界度量衡史上占据着独特的重要地位。