A new per-field classification method using mixture discriminant analysis

In this study, a new per-field classification method is proposed for supervised classification of remotely sensed multispectral image data of an agricultural area using Gaussian mixture discriminant analysis (MDA). For the proposed per-field classification method, multivariate Gaussian mixture models constructed for control and test fields can have fixed or different number of components and each component can have different or common covariance matrix structure. The discrimination function and the decision rule of this method are established according to the average Bhattacharyya distance and the minimum values of the average Bhattacharyya distances, respectively. The proposed per-field classification method is analyzed for different structures of a covariance matrix with fixed and different number of components. Also, we classify the remotely sensed multispectral image data using the per-pixel classification method based on Gaussian MDA.     

A new approach to statistical efficiency of weighted least squares fitting algorithms for reparameterization of nonlinear regression models

We study nonlinear least-squares problem that can be transformed to linear problem by change of variables. We derive a general formula for the statistically optimal weights and prove that the resulting linear regression gives an optimal estimate (which satisfies an analogue of the Rao-Cramer lower bound) in the limit of small noise.     

拓展训练课程与大学生创新能力培养探析

以培养大学生创新能力为切入点,以拓展训练课程项目创新、模块教学和课程分享为主线,拓展训练课程与大学生创新能力的培养模式为：通过项目创新,改变学生惯性思维;利用模块教学,改变学生思维定势;运用头脑风暴法,激发学生联想能力;依托实践教学,铸就学生创新能力.     

Column generation with free replicability in DEA

The evaluation of efficiency scores in data envelopment analysis is based on the construction of artificial decision making units subject to some assumptions, usually requiring convexity of the production possibility set. This demands divisibility in input and output, which is not always possible. The so-called free replicability model, proposed by Henry Tulkens, permits input and output to enter in only discrete amounts. The model is of a mixed integer programming type, for which the number of variables, here corresponding to the decision making units, may be critical in order to reach an optimal solution.     

Effects of correlated covariates on the asymptotic efficiency of matching and inverse probability weighting estimators for causal inference

In observational studies, the overall aim when fitting a model for the propensity score is to reduce bias for an estimator of the causal effect. To make the assumption of an unconfounded treatment plausible researchers might include many, possibly correlated, covariates in the propensity score model. In this paper, we study how the asymptotic efficiency of matching and inverse probability weighting estimators for average causal effects change when the covariates are correlated. We investigate the case with multivariate normal covariates, a logistic model for the propensity score and linear models for the potential outcomes and show results under different model assumptions. We show that the correlation can both increase and decrease the large sample variances of the estimators, and that the correlation affects the asymptotic efficiency of the estimators differently, both with regard to direction and magnitude. Moreover, the strength of the confounding towards the outcome and the treatment plays an important role.     

Non uniform exponential bounds on normal approximation by Stein’s method and monotone size bias couplings

It is known that the normal approximation is applicable for sums of non negative random variables, W, with the commonly employed couplings. In this work, we use the Stein’s method to obtain a general theorem of non uniform exponential bound on normal approximation base on monotone size bias couplings of W. Applications of the main result to give the bound on normal approximation for binomial random variable, the number of bulbs on at the terminal time in the lightbulb process, and the number of m runs are also provided.     

Uniformly strong consistency and Berry-Esseen bound of frequency polygons for α-mixing samples

In this article, the frequency polygon investigated by Scott is studied as a nonparametric estimator for α-mixing samples. By some known exponent and moment inequalities, we obtain the uniformly strong consistency and Berry-Esseen bound of the estimator. The present results relax the relevant conditions used by Carbon et al. Furthermore, the convergence rate of the uniformly asymptotic normality is derived, which is O(n^{? 1/11}) under the given conditions.     

On partial linear additive isotonic regression

In this paper we discuss semiparametric additive isotonic regression models. We discuss the efficiency bound of the model and the least squares estimator under this model. We show that the ordinary least square estimator studied by Huang (2002) and Cheng (2009) for the semiparametric isotonic regression achieves the efficiency bound for the regular estimator when the true parameter belongs to the interior of the parameter space. We also show that the result by Cheng (2009) can be generalized to the case that the covariates are dependent on each other.     

A Lower Bound for the Wrap-around L2-discrepancy on Combined Designs of Mixed Two- and Three-level Factorials

The objective of this article is to study the issue of employing the uniformity criterion measured by wrap-around L₂-discrepancy to assess the optimal foldover plans. For mixed two- and three-level fractional factorials as the original designs, general foldover plan and combined design under a foldover plan are defined, and the equivalence between any foldover plan and its complementary foldover plan is investigated. A lower bound of wrap-around L₂-discrepancy of combined designs under a general foldover plan is obtained, which can be used as a benchmark for searching optimal foldover plans. Moreover, it also provides a theoretical justification for optimal foldover plans in terms of uniformity criterion.     

Book Reviews

Book Reviews
Chris Wild & George Seber, Chance Encounters: a First Course in Data Analysis and Inference
A. J. Underwood, Experiments in Ecology
Lawrence L. Lapin, Modern Engineering Statistics
M. E. Thompson, Theory of Sample Surveys
Fima C. Klebaner, Introduction to Stochastic Calculus with Applications
Frank Lad, Operational Subjective Statistical Methods: a Mathematical, Philosophical, and Historical Introduction