Penalized maximum likelihood estimation of a stochastic multivariate regression model

We study the large-sample properties of the penalized maximum likelihood estimator of a multivariate stochastic regression model with contemporaneously correlated data. The penalty is in terms of the square norm of some (vector) linear function of the regression coefficients. The model subsumes the so-called common transfer function model useful for extracting common signals in a panel of short time series. We show that, under mild regularity conditions, the penalized maximum likelihood estimator is consistent and asymptotically normal. The asymptotic bias of the regression coefficient estimator is also derived.     

A new approach for technical efficiency estimation in multiple output production

The nonparametric technique of Data Envelopment Analysis (DEA) has been used to measure technical efficiency. This approach has proven useful because, unlike regression analyses, it allows multiple outputs and does not require a priori functional form specification. DEA does, however, require correct model specification; inclusion of inappropriate variables or omission of relevant variables leads to distortions. The purpose of this paper is to develop an alternative methodology based on canonical correlation to measure technical efficiency for multiple output production correspondences. Using simulated data, the new methodology is compared with DEA. The results indicate that the canonical regression approach outperforms DEA in most cases.     

Variational iteration method for solving cubic nonlinear Schrödinger equation

The variational iteration method is applied to solve the cubic nonlinear Schrödinger (CNLS) equation in one and two space variables. In both cases, we will reduce the CNLS equation to a coupled system of nonlinear equations. Numerical experiments are made to verify the efficiency of the method. Comparison with the theoretical solution shows that the variational iteration method is of high accuracy.     

The training institution efficiency of the semiconductor institute programme in Taiwan—application of spatiotemporal ICA with DEA approach

Despite the fact that Taiwan’s high-tech industry has gradually secured a leading position in the world, enterprises in Taiwan have striven to strengthen their technical advancement by providing employees with various internal or external training programmes. These institutional training programmes are designed to sustain competitive advantage, enhance the quality of manpower and improve operational efficiency. Much literature assesses the efficiency of an internal training programme that is initiated by a firm, but only a little literature studies the efficiency of an external training programme that is led by a government. Various efficiency measurement tools, such as conventional statistical methods and non-parametric methods, have been successfully developed in the literature. Among these tools, the data envelopment analysis (DEA) approach is one of the most widely discussed. However, the DEA's capability to discriminate efficient decision-making units from inefficient decision-making units requires much improvement (Adler and Yazhemsky). In this paper, a two-stage approach of integrating spatiotemporal independent component analysis (stICA) and DEA is developed for efficiency measurement. stICA is used to search for latent source signals where no relevant signal mixture mechanisms are available; and DEA is used to measure the relative efficiencies of decision-making units (DMUs). We suggest using stICA first to extract the input variables for generating independent components (IC), then selecting the ICs representing the independent sources of input variables, and finally inputting the selected ICs as new variables in the DEA model. To find the effects of environmental variables on the estimated efficiency scores, the Tobit–Bayes (censored) regression is applied. A simulated dataset and the training institution dataset provided by the Semiconductor Institute in Taiwan is used for analysis. The empirical result shows that the proposed method can not only separate performance differences between the training institutions but also improve the discriminatory capability of the DEA's efficiency measurement. The study results can serve as a reference for training institutions wishing to enhance their training efficiency.     

A bias corrected nonparametric regression estimator

In this article, we propose a new method of bias reduction in nonparametric regression estimation. The proposed new estimator has asymptotic bias order h⁴, where h is a smoothing parameter, in contrast to the usual bias order h² for the local linear regression. In addition, the proposed estimator has the same order of the asymptotic variance as the local linear regression. Our proposed method is closely related to the bias reduction method for kernel density estimation proposed by Chung and Lindsay (2011). However, our method is not a direct extension of their density estimate, but a totally new one based on the bias cancelation result of their proof.     

Double penalized variable selection procedure for partially linear models with longitudinal data

Based on the double penalized estimation method,a new variable selection procedure is proposed for partially linear models with longitudinal data.The proposed procedure can avoid the effects of the nonparametric estimator on the variable selection for the parameters components.Under some regularity conditions,the rate of convergence and asymptotic normality of the resulting estimators are established.In addition,to improve efficiency for regression coefficients,the estimation of the working covariance matrix is involved in the proposed iterative algorithm.Some simulation studies are carried out to demonstrate that the proposed method performs well.     

A new proposed model of restricted data envelopment analysis by correlation coefficients

The concept of efficiency in data envelopment analysis (DEA) is defined as weighted sum of outputs/weighted sum of inputs. In order to calculate the maximum efficiency score, each decision making unit (DMU)’s inputs and outputs are assigned to different weights. Hence, the classical DEA allows the weight flexibility. Therefore, even if they are important, the inputs or outputs of some DMUs can be assigned zero (0) weights. Thus, these inputs or outputs are neglected in the evaluation. Also, some DMUs may be defined as efficient even if they are inefficient. This situation leads to unrealistic results. Also to eliminate the problem of weight flexibility, weight restrictions are made in DEA. In our study, we proposed a new model which has not been published in the literature. We describe it as the restricted data envelopment analysis ((ARIII(COR))) model with correlation coefficients. The aim for developing this new model, is to take into account the relations between variables using correlation coefficients. Also, these relations were added as constraints to the CCR and BCC models. For this purpose, the correlation coefficients were used in the restrictions of input–output each one alone and their combination together. Inputs and outputs are related to the degree of correlation between each other in the production. Previous studies did not take into account the relationship between inputs/outputs variables. So, only with expert opinions or an objective method, weight restrictions have been made. In our study, the weights for input and output variables were determined, according to the correlations between input and output variables. The proposed new method is different from other methods in the literature, because the efficiency scores were calculated at the level of correlations between the input and/or output variables.     

On the Bias of the Generalized Regression Estimator in Survey Sampling

It is well known that the generalized regression (GREG) estimator of the finite population total is asymptotically unbiased. Consequently, bias is negligible when the sample size is large. But the magnitude of the bias is not known, if we are estimating small areas or operating with small samples. Furthermore, beside the sample size, the bias depends on the auxiliary variables, on their relation to the study variable and on the sampling design. In small samples it is important to know sources of the bias and in some cases to use a bias-corrected regression estimator. The aim of the present paper is to derive approximate bias expressions of the GREG estimator under different population models and different sampling designs to study the magnitude of the bias.      

The impact of supervisory monitoring on high-end retail sales productivity

Based on a two-stage analysis of a panel of data on 12 outlets of a high-end retailer for 24 months, we investigate how the level of supervisory monitoring affects retail sales productivity. In the first stage, we use Data Envelopment Analysis (DEA) to compute the relative productivity of retail outlets in using their labor and capital resources to generate store sales. In the second stage, we regress the logarithm of DEA scores on contextual variables to obtain consistent estimators of the impact of contextual variables on productivity (Banker and Natarajan in Operation Research 56:48–58, 2008). Contrary to agency theoretic prediction that supervisory monitoring leads to an increase in retail sales productivity, our empirical results indicate that the higher the level of supervisory monitoring, the lower is the retail sales productivity for high-end retail outlets.     

Randomly censored partially linear single-index models

This paper proposes a method for estimation of a class of partially linear single-index models with randomly censored samples. The method provides a flexible way for modelling the association between a response and a set of predictor variables when the response variable is randomly censored. It presents a technique for “dimension reduction” in semiparametric censored regression models and generalizes the existing accelerated failure-time models for survival analysis. The estimation procedure involves three stages: first, transform the censored data into synthetic data or pseudo-responses unbiasedly; second, obtain quasi-likelihood estimates of the regression coefficients in both linear and single-index components by an iteratively algorithm; finally, estimate the unknown nonparametric regression function using techniques for univariate censored nonparametric regression. The estimators for the regression coefficients are shown to be jointly root-n consistent and asymptotically normal. In addition, the estimator for the unknown regression function is a local linear kernel regression estimator and can be estimated with the same efficiency as all the parameters are known. Monte Carlo simulations are conducted to illustrate the proposed methodology.     

Frontier estimation with local polynomials and high power-transformed data

We present a new method for estimating the frontier of a sample. The estimator is based on a local polynomial regression on the power-transformed data. We assume that the exponent of the transformation goes to infinity while the bandwidth goes to zero. We give conditions on these two parameters for obtaining almost complete convergence. The asymptotic conditional bias and variance of the estimator are provided and its good performance is illustrated for some finite sample situations.     

New conservative difference schemes for a coupled nonlinear Schrödinger system

In this paper, two conservative difference schemes for solving a coupled nonlinear Schrödinger (CNLS) system are numerically analyzed. Firstly, a nonlinear implicit two-level finite difference scheme for CNLS system is studied, then a linear three-level difference scheme for CNLS system is presented. An induction argument and the discrete energy method are used to prove the second-order convergence and unconditional stability of the linear scheme. Numerical examples show the efficiency of the new scheme.     

基于奇异值分解的岭型回归(英文)

本文基于设计阵的奇异值分解(SVD),从LS估计出发,应用岭回归估计方法,构造了回归系数的一个新的有偏估计,称为基于SVD的岭型回归估计,简称RRSVD估计,讨论了其性质和偏参数的选取问题,得到了许多重要结论.计算结果表明,在设计阵呈病态时,RRS善岭回归估计.     

Bayes估计与最小二乘估计的一个新的相对效率

考虑在错误的先验假定下线性模型回归系数的Bayes估计,将其与最小二乘估计进行比较,提出了Bayes估计与LSE的一种新的相对效率e5,给出了e5的基本性质,同时导出了它的上下界．     

Reduced‐bias kernel estimators of a positive extreme value index

In this paper, we deal with the semi‐parametric estimation of the extreme value index, an important parameter in extreme value analysis. It is well known that many classic estimators, such as the Hill estimator, reveal a strong bias. This problem motivated the study of two classes of kernel estimators. Those classes generalize the classical Hill estimator and have a tuning parameter that enables us to modify the asymptotic mean squared error and eventually to improve their efficiency. Since the improvement in efficiency is not very expressive, we also study new reduced bias estimators based on the two classes of kernel statistics. Under suitable conditions, we prove their asymptotic normality. Moreover, an asymptotic comparison, at optimal levels, shows that the new classes of reduced bias estimators are more efficient than other reduced bias estimator from the literature. An illustration of the finite sample behaviour of the kernel reduced‐bias estimators is also provided through the analysis of a data set in the field of insurance.     

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This paper concerns with the estimation of a fixed effects panel data partially linear regression model with the idiosyncratic errors being an autoregressive process. For fixed effects short time series panel data, the commonly used autoregressive error structure fitting method will not result in a consistent estimator of the autoregressive coefficients. Here we propose an alternative estimation and show that the resulting estimator of the autoregressive coefficients is consistent and this method is workable for any order autoregressive error structure. Moreover, combining the B-spline approximation, profile least squares dummy variable (PLSDV) technique and consistently estimated the autoregressive error structure, we develop a weighted PLSDV estimator for the parametric component and a weighted B-spline series (BS) estimator for the nonparametric component. The weighted PLSDV estimator is shown to be asymptotically normal and more asymptotically efficient than the one which ignores the error autoregressive structure. In addition, this paper derives the asymptotic bias of the weighted BS estimator and establish its asymptotic normality as well. Simulation studies and an example of application are conducted to illustrate the finite sample performance of the proposed procedures.     

关于DEA有效性“新方法”的探讨

主要指出文献[1],[2]中所用的"新方法"不能完全区分决策单元的DEA有效性和弱DEA有效性.同时,"新方法"中所使用的DEA模型(即文献[3]中超效率DEA模型)的最优解不一定存在,这也是"新方法"使用中的一大缺陷.本文同时指出"新方法"虽然是可以扩充的,但扩充后,某些"新模型"仍然会出现上述问题.如果单纯的去评价决策单元的DEA有效性、弱DEA有效性和非弱DEA有效性时,建议还是使用传统的经典模型为好;如果需要进一步对DEA有效性再进行分析,是可以象最早提出超效率DEA模型的文献[3]中那样去应用超效率DEA模型。     

回归系数的混合估计与最小二乘估计的两种相对效率

本文研究了线性回归模型中,回归系数的混合估计与最小二乘估计的相对效率,利用矩阵的相关性质和运算,导出了两者之间两种新的相对效率的上下界.     

Data sharpening methods in multivariate local quadratic regression

This paper is concerned with the conditional bias and variance of local quadratic regression to the multivariate predictor variables. Data sharpening methods of nonparametric regression were first proposed by Choi, Hall, Roussion. Recently, a data sharpening estimator of local linear regression was discussed by Naito and Yoshizaki. In this paper, to improve mainly the fitting precision, we extend their results on the asymptotic bias and variance. Using the data sharpening estimator of multivariate local quadratic regression, we are able to derive higher fitting precision. In particular, our approach is simple to implement, since it has an explicit form, and is convenient when analyzing the asymptotic conditional bias and variance of the estimator at the interior and boundary points of the support of the density function.     

Linear Least Squares Estimation of Regression Models for Two-Dimensional Random Fields

We consider the problem of estimating regression models of two-dimensional random fields. Asymptotic properties of the least squares estimator of the linear regression coefficients are studied for the case where the disturbance is a homogeneous random field with an absolutely continuous spectral distribution and a positive and piecewise continuous spectral density. We obtain necessary and sufficient conditions on the regression sequences such that a linear estimator of the regression coefficients is asymptotically unbiased and mean square consistent. For such regression sequences the asymptotic covariance matrix of the linear least squares estimator of the regression coefficients is derived.