Rate of strong uniform convergence of k-NN density estimates

Let f_n(x) be the univariate k-nearest neighbor (k-NN) density estimate proposed by Loftsgaarden and Quesenberry (1965). By using similar techniques as in Bahadur's representation of sample quantiles (1966), and by the recent results on the oscillation of empirical processes by Stute (1982), we derive the rate of strong uniform convergence of f_n(x) on some suitably chosen interval J_δ. Some comparison with the kernel estimates is given, as well as the choice of the bandwidth sequence relative to the sample size.     

Sequential Estimation of Dynamic Discrete Games: A Comment

Recursive procedures which are based on iterating on the best response mapping have difficulties converging to all equilibria in multi‐player games. We illustrate these difficulties by revisiting the asymptotic properties of the iterative nested pseudo maximum likelihood method for estimating dynamic games introduced by Aguirregabiria and Mira (2007). An example shows that the iterative method may not be consistent.     

中国粮食流通与粮食安全：关键节点的风险识别

粮食安全不仅取决于粮食生产的量和自给率,还取决于可获性,包括“买得起”和“买得到”。当前中国粮食总量安全,但粮食生产的区域结构性矛盾突出,粮食生产日渐向优势区域集中,主销区的粮食消费日益依赖于主产区的粮食调运,粮食运达的及时性对于粮食安全愈发重要。粮食调运必然面临长距离运输问题,这其中尤以在粮食运输网络中起枢纽作用的关键节点的平稳有序运行最为关键。当前实现粮食调运的运输方式主要依靠铁路、水路以及铁水联运,但是这一运输网络存在运力不足、物流方式落后、基础设施建设不足等风险因素,与粮食运输量的增长速度以及运输的顺畅性、及时性要求不相匹配,因此亟待通过加快铁路、水路基础设施建设、推动粮食物流方式变革和健全粮食物流应急响应机制等措施,保障粮食的稳定供给和粮食安全。     

A permutation test approach to the choice of size k for the nearest neighbors classifier

The k nearest neighbors (k-NN) classifier is one of the most popular methods for statistical pattern recognition and machine learning. In practice, the size k, the number of neighbors used for classification, is usually arbitrarily set to one or some other small numbers, or based on the cross-validation procedure. In this study, we propose a novel alternative approach to decide the size k. Based on a k-NN-based multivariate multi-sample test, we assign each k a permutation test based Z-score. The number of NN is set to the k with the highest Z-score. This approach is computationally efficient since we have derived the formulas for the mean and variance of the test statistic under permutation distribution for multiple sample groups. Several simulation and real-world data sets are analyzed to investigate the performance of our approach. The usefulness of our approach is demonstrated through the evaluation of prediction accuracies using Z-score as a criterion to select the size k. We also compare our approach to the widely used cross-validation approaches. The results show that the size k selected by our approach yields high prediction accuracies when informative features are used for classification, whereas the cross-validation approach may fail in some cases.     

Edge Estimation in the Population of a Binary Tree Using Node-Sampling

Suppose a finite population of several vertices, each connected to single or multiple edges. This constitutes a structure of graphical population of vertices and edges. As a special case, the graphical population like a binary tree having only two child vertices associated to parent vertex is taken into consideration. The entire binary tree is divided into two sub-graphs such as a group of left-nodes and a group of right-nodes. This paper takes into account a mixture of graph structured and population sampling theory together and presents a methodology for mean-edge-length estimation of left sub-graph using right edge sub-graph as an auxiliary source of information. A node-sampling procedure is developed for this purpose and a class of estimators is proposed containing several good estimators. Mathematical conditions for minimum bias and optimum mean squared error of the class are derived and theoretical results are numerically supported with a test of 99% confidence intervals. It is shown that suggested class has a sub-class of optimum estimators, and sample-based estimates are closer to the true value of the population parameter.     

社会转型期农村邻里冲突的解构分析

社会转型期农村邻里冲突增多,影响了农村社会秩序的稳定。探究起来,这些冲突源于农民生活、生产方式和场域的变化,价值观与追求的变化,社会分层的发生与部分人在较前陡增的社会压力下产生的心理畸变。     

C93. The relevance of imaginary alternatives

Some practical approaches to the problem of choosing parameters which control the smoothness of kernel-based density estimators are investigated. Fixed and variable kernels are considered, and particularly simple approaches are investigated in the latter case. The performances of a wide range of estimators are compared in a simulation study.     

Inference in Dynamic Discrete Choice Models With Serially orrelated Unobserved State Variables

This paper develops a method for inference in dynamic discrete choice models with serially correlated unobserved state variables. Estimation of these models involves computing high‐dimensional integrals that are present in the solution to the dynamic program and in the likelihood function. First, the paper proposes a Bayesian Markov chain Monte Carlo estimation procedure that can handle the problem of multidimensional integration in the likelihood function. Second, the paper presents an efficient algorithm for solving the dynamic program suitable for use in conjunction with the proposed estimation procedure.     

Comparison of multiple imputation and two-phase logistic regression to analyse two-phase case–control studies with rich phase 1: a simulation study

Two-phase case–control studies cope with the problem of confounding by obtaining required additional information for a subset (phase 2) of all individuals (phase 1). Nowadays, studies with rich phase 1 data are available where only few unmeasured confounders need to be obtained in phase 2. The extended conditional maximum likelihood (ECML) approach in two-phase logistic regression is a novel method to analyse such data. Alternatively, two-phase case–control studies can be analysed by multiple imputation (MI), where phase 2 information for individuals included in phase 1 is treated as missing. We conducted a simulation of two-phase studies, where we compared the performance of ECML and MI in typical scenarios with rich phase 1. Regarding exposure effect, MI was less biased and more precise than ECML. Furthermore, ECML was sensitive against misspecification of the participation model. We therefore recommend MI to analyse two-phase case–control studies in situations with rich phase 1 data.