Asymptotic convergence of dimension reduction based boosting in classification

In high dimensional classification problem, two stage method, reducing the dimension of predictor first and then applying the classification method, is a natural solution and has been widely used in many fields. The consistency of the two stage method is an important issue, since errors induced by dimension reduction method inevitably have impacts on the following classification method. As an effective method for classification problem, boosting has been widely used in practice. In this paper, we study the consistency of two stage method–dimension reduction based boosting algorithm (briefly DRB) for classification problem. Theoretical results show that Lipschitz condition on the base learner is required to guarantee the consistency of DRB. This theoretical findings provide useful guideline for application.     

A MONTE CARLO COMPARISON OF VARIOUS ASYMPTOTIC APPROXIMATIONS TO THE DISTRIBUTION OF INSTRUMENTAL VARIABLES ESTIMATORS

ABSTRACT

We examine empirical relevance of three alternative asymptotic approximations to the distribution of instrumental variables estimators by Monte Carlo experiments. We find that conventional asymptotics provides a reasonable approximation to the actual distribution of instrumental variables estimators when the sample size is reasonably large. For most sample sizes, we find Bekker[11] Bekker, P. A. 1994. Alternative Approximations to the Distributions of Instrumental Variable Estimators. Econometrica, 62: 657–681. [Crossref], [Web of Science ®] , [Google Scholar] asymptotics provides reasonably good approximation even when the first stage R ² is very small. We conclude that reporting Bekker[11] Bekker, P. A. 1994. Alternative Approximations to the Distributions of Instrumental Variable Estimators. Econometrica, 62: 657–681. [Crossref], [Web of Science ®] , [Google Scholar] confidence interval would suffice for most microeconometric (cross-sectional) applications, and the comparative advantage of Staiger and Stock[5] Staiger, D. and Stock, J. H. 1997. Instrumental Variables Regression with Weak Instruments. Econometrica, 65: 556–586. [Crossref], [Web of Science ®] , [Google Scholar] asymptotic approximation is in applications with sample sizes typical in macroeconometric (time series) applications.     

我国行业分类与国际标准行业分类的比较研究

 本文通过对我国行业分类和国际标准行业分类两项分类标准最新版本的比较,对两项分类的基本构成、应用原则、门类和大类的条目结构以及对照转换等方面的情况进行了比较分析研究。详细解析了在若干行业领域中,二者存在典型差异的情况。最后,对我国的行业分类的科学性和国际可比性做出了分析评价,对如何进一步提升分类水平提出了改进意见,另外还提出了未来修订的思路和方法等建议。     

A Genetic Algorithm Based Modification on the LTS Algorithm for Large Data Sets

The authors introduce an algorithm for estimating the least trimmed squares (LTS) parameters in large data sets. The algorithm performs a genetic algorithm search to form a basic subset that is unlikely to contain outliers. Rousseeuw and van Driessen (2006 Rousseeuw , P. J. , van Driessen , K. ( 2006 ). Computing LTS regression for large data sets . Data Mining and Knowledge Discovery 12 : 29 – 45 .[Crossref], [Web of Science ®] , [Google Scholar]) suggested drawing independent basic subsets and iterating C-steps many times to minimize LTS criterion. The authors 'algorithm constructs a genetic algorithm to form a basic subset and iterates C-steps to calculate the cost value of the LTS criterion. Genetic algorithms are successful methods for optimizing nonlinear objective functions but they are slower in many cases. The genetic algorithm configuration in the algorithm can be kept simple because a small number of observations are searched from the data. An R package is prepared to perform Monte Carlo simulations on the algorithm. Simulation results show that the performance of the algorithm is suitable for even large data sets because a small number of trials is always performed.     

Multi-Step Classification Trees

Many algorithms originated from decision trees have been developed for classification problems. Although they are regarded as good algorithms, most of them suffer from loss of prediction accuracy, namely high misclassification rates when there are many irrelevant variables. We propose multi-step classification trees with adaptive variable selection (the multi-step GUIDE classification tree (MG) and the multi-step CRUISE classification tree (MC) to handle this problem. The variable selection step and the fitting step comprise the multi-step method.

We compare the performance of classification trees in the presence of irrelevant variables. MG and MC perform better than Random Forest and C4.5 with an extremely noisy dataset. Furthermore, the prediction accuracy of our proposed algorithm is relatively stable even when the number of irrelevant variables increases, while that of other algorithms worsens.     

Multiplicative Algorithms for Maximum Penalized Likelihood Inversion with Non Negative Constraints and Generalized Error Distributions

In many linear inverse problems the unknown function f (or its discrete approximation Θ _p×1), which needs to be reconstructed, is subject to the non negative constraint(s); we call these problems the non negative linear inverse problems (NNLIPs). This article considers NNLIPs. However, the error distribution is not confined to the traditional Gaussian or Poisson distributions. We adopt the exponential family of distributions where Gaussian and Poisson are special cases. We search for the non negative maximum penalized likelihood (NNMPL) estimate of Θ. The size of Θ often prohibits direct implementation of the traditional methods for constrained optimization. Given that the measurements and point-spread-function (PSF) values are all non negative, we propose a simple multiplicative iterative algorithm. We show that if there is no penalty, then this algorithm is almost sure to converge; otherwise a relaxation or line search is necessitated to assure its convergence.     

Bayesian,MLE, and GMM Estimation of a Spot Rate Model

ABSTRACT

We develop Markov chain Monte Carlo algorithms for estimating the parameters of the short-term interest rate model. Using Monte Carlo experiments we compare the Bayes estimators with the maximum likelihood and generalized method of moments estimators. We estimate the model using the Japanese overnight call rate data.     

Application of a non-homogeneous Markov chain with seasonal transition probabilities to ozone data

In this work, we assume that the sequence recording whether or not an ozone exceedance of an environmental threshold has occurred in a given day is ruled by a non-homogeneous Markov chain of order one. In order to account for the possible presence of cycles in the empirical transition probabilities, a parametric form incorporating seasonal components is considered. Results show that even though some covariates (namely, relative humidity and temperature) are not included explicitly in the model, their influence is captured in the behavior of the transition probabilities. Parameters are estimated using the Bayesian point of view via Markov chain Monte Carlo algorithms. The model is applied to ozone data obtained from the monitoring network of Mexico City, Mexico. An analysis of how the methodology could be used as an aid in the decision-making is also given.     

Facility Location with Dynamic Distance Functions

Facility location problems have always been studied with theassumption that the edge lengths in the network are static anddo not change over time. The underlying network could be used to model a city street networkfor emergency facility location/hospitals, or an electronic network for locating information centers. In any case, it is clear that due to trafficcongestion the traversal time on links changes with time. Very often, we have estimates as to how the edge lengths change over time, and our objective is to choose a set of locations (vertices) ascenters, such that at every time instant each vertex has a center close to it (clearly, the center close to a vertex may change over time). We also provide approximation algorithms as well as hardness results forthe K-center problem under this model. This is the first comprehensive study regarding approximation algorithmsfor facility location for good time-invariant solutions.