Tail Functions and Iterative Weights in Binary Regression

In interpreting the binary regression models often used in the analysis of dose-response data, it is common to introduce the idea of an underlying continuous tolerance distribution. Different choices of link function lead to different tolerance distributions. A useful way of comparing these alternatives is to compare the hazard functions or tail functions associated with each tolerance distribution. Tail functions can also be applied to give numerically preferable formulas for the iterative weights and the adjusted dependent variable in the fitting of binary regression models by the iteratively reweighted least-squares algorithm.     

Missing data in principal component analysis of questionnaire data: a comparison of methods

Principal component analysis (PCA) is a widely used statistical technique for determining subscales in questionnaire data. As in any other statistical technique, missing data may both complicate its execution and interpretation. In this study, six methods for dealing with missing data in the context of PCA are reviewed and compared: listwise deletion (LD), pairwise deletion, the missing data passive approach, regularized PCA, the expectation-maximization algorithm, and multiple imputation. Simulations show that except for LD, all methods give about equally good results for realistic percentages of missing data. Therefore, the choice of a procedure can be based on the ease of application or purely the convenience of availability of a technique.     

基于PLS的R＆D投入效果的实证分析

运用偏最小二乘(PLS)回归方法,建立Cobb-Douglas生产函数,分析了影响天津市经济发展的各投入要素,在投入向量中引入研究与发展存量T,并充分考虑了研究与发展投资效用的滞后性与长期性。对天津市研究与发展投资收益与边际收益进行分析计算,认为加大研究与发展投入力度是提高天津市科技综合竞争力,实现经济持续稳定、快速增长的最有效途径,为天津市制订不确定条件下研究与发展风险投资战略提供有益的参考。     

EFFICIENT BLOCK DESIGNS FOR CORRELATED OBSERVATIONS

Current methods for the design of efficient incomplete block experiments when the observations within a block are dependent usually involve computer searches of binary designs. These searches give little insight into the features that lead to efficiency, and can miss more efficient designs. This paper aims to develop some approximations which give some insight into the features of a design that lead to high efficiency under a generalized least-squares analysis for a known dependence structure, and to show that non-binary designs can be more efficient for some dependence structures. In particular, we show how neighbour balance and end plot balance are related to the design efficiency for low-order autoregressions, and that under moderate positive dependence, replication at lag two can sometimes increase efficiency.     

Consistency and robustness properties of the S-nonnegative garrote estimator

This paper concerns a robust variable selection method in multiple linear regression: the robust S-nonnegative garrote variable selection method. In this paper the consistency of the method, both in terms of estimation and in terms of variable selection, is established. Moreover, the robustness properties of the method are further investigated by providing a lower bound for the breakdown point, and by deriving the influence function. The provided expressions nicely reveal the impact that the choice of an initial estimator has on the robustness properties of the variable selection method. Illustrative examples of influence functions for the S-nonnegative garrote as well as for the original (non-robust) nonnegative garrote variable selection method are provided.     

Using restricted CCA for cross-language information retrieval

Canonical correlation analysis is a method of correlating linear relationship between two sets of variables. When not any linear combination of variables is allowed, restricted canonical correlation analysis is appropriate. The method was implemented with alternating least-squares and applied to the cross-language information retrieval on a dataset with officially translated and aligned documents in eight European languages.     

An Efficient Algorithm for the Least-Squares Cross-Validation with Symmetric and Polynomial Kernels

The least-squares cross-validation is a completely automatic method for choosing the smoothing parameter in probability density estimation but this method consume large amounts of computer time. This article concerns an efficient computational algorithm for this method when the kernel is symmetric and polynomial functions.     

Theoretical limits of component identification in a separable nonlinear least-squares problem

We provide theoretical insights into component identification in a separable nonlinear least-squares problem in which the model is a linear combination of nonlinear functions (called components in this paper). Within this research, we assume that the number of components is unknown. The objective of this paper is to understand the limits of component discovery under the assumed model. We focus on two aspects. One is sensitivity analysis referring to the ability of separating regression components from noise. The second is resolution analysis referring to the ability of de-mixing components that have similar location parameters. We use a wavelet transformation that allows to zoom in at different levels of details in the observed data. We further apply these theoretical insights to provide a road map on how to detect components in more realistic settings such as a two-dimensional nuclear magnetic resonance experiment for protein structure determination.     

Border estimation of a two-dimensional uniform distribution if data are measured with additive error

The paper considers estimation of the boundary of an elliptical domain when the data without a measurement error are distributed uniformly on this domain but are superimposed by random errors. The problem is solved in two phases. In the first phase the domain is subdivided into thin slices and the endpoints of these slices are estimated within the framework of a corresponding one-dimensional problem. In the second phase the estimated endpoints are used to estimate the boundary using the total least-squares curve fitting procedure.     

On additive and block decompositions of WLSEs under a multiple partitioned regression model

While considering the mechanism of weighted least-squares estimators (WLSEs) of regression coefficients in a partitioned linear model, Tian and Takane [On sum decompositions of weighted least-squares estimators under the partitioned linear model, Comm. Statist. Theory Methods 37 (2008), pp. 55–69] gave some identifying conditions for the WLSEs to be the sum of WLSEs under its two small models based on orthogonality of regressors with respect to the given weight matrix. The purpose of this paper is to show how to establish additive and block decompositions of WLSEs under a multiple partitioned linear model and its k small models based on orthogonality of regressors with respect to a given weight matrix.