Multivariate bandwidth selection for local linear regression

The existence and properties of optimal bandwidths for multivariate local linear regression are established, using either a scalar bandwidth for all regressors or a diagonal bandwidth vector that has a different bandwidth for each regressor. Both involve functionals of the derivatives of the unknown multivariate regression function. Estimating these functionals is difficult primarily because they contain multivariate derivatives. In this paper, an estimator of the multivariate second derivative is obtained via local cubic regression with most cross-terms left out. This estimator has the optimal rate of convergence but is simpler and uses much less computing time than the full local estimator. Using this as a pilot estimator, we obtain plug-in formulae for the optimal bandwidth, both scalar and diagonal, for multivariate local linear regression. As a simpler alternative, we also provide rule-of-thumb bandwidth selectors. All these bandwidths have satisfactory performance in our simulation study.     

z Test for the significance of the mean of a stable probability distribution with 1<α≤2

The analysis of data using a stable probability distribution with tail parameter α<2 (sometimes called a Pareto–Levy distribution) seems to have been avoided in the past in part because of the lack of a significance test for the mean, even though it appears to be the correct distribution to use for describing returns in the financial markets. A z test for the significance of the mean of a stable distribution with tail parameter 1<α≤2 is defined. Tables are calculated and displayed for the 5% and 1% significance levels for a range of tail and skew parameters α and β. Through the use of maximum likelihood estimates, the test becomes a practical tool even when α and β are not that accurately determined. As an example, the z test is applied to the daily closing prices for the Dow Jones Industrial average from 2 January 1940 to 19 March 2010.     

Parameter estimation of nonlinear mixed-effects models using first-order conditional linearization and the EM algorithm

Nonlinear mixed-effects (NLME) models are flexible enough to handle repeated-measures data from various disciplines. In this article, we propose both maximum-likelihood and restricted maximum-likelihood estimations of NLME models using first-order conditional expansion (FOCE) and the expectation–maximization (EM) algorithm. The FOCE-EM algorithm implemented in the ForStat procedure SNLME is compared with the Lindstrom and Bates (LB) algorithm implemented in both the SAS macro NLINMIX and the S-Plus/R function nlme in terms of computational efficiency and statistical properties. Two realworld data sets an orange tree data set and a Chinese fir (Cunninghamia lanceolata) data set, and a simulated data set were used for evaluation. FOCE-EM converged for all mixed models derived from the base model in the two realworld cases, while LB did not, especially for the models in which random effects are simultaneously considered in several parameters to account for between-subject variation. However, both algorithms had identical estimated parameters and fit statistics for the converged models. We therefore recommend using FOCE-EM in NLME models, particularly when convergence is a concern in model selection.     

On the recoding of continuous and bounded indexes to a binomial form: an application to quality-of-life scores

The statistical analysis of patient-reported outcomes (PROs) as endpoints has shown to be of great practical relevance. The resulting scores or indexes from the questionnaires used to measure PROs could be treated as continuous or ordinal. The goal of this study is to propose and evaluate a recoding process of the scores, so that they can be treated as binomial outcomes and, therefore, analyzed using logistic regression with random effects. The general methodology of recoding is based on the observable values of the scores. In order to obtain an optimal recoding, the evaluation of the recoding method is tested for different values of the parameters of the binomial distribution and different probability distributions of the random effects. We illustrate, evaluate and validate the proposed method of recoding with the Short Form-36 (SF-36) Survey and real data. The optimal recoding approach is very useful and flexible. Moreover, it has a natural interpretation, not only for ordinal scores, but also for questionnaires with many dimensions and different profiles, where a common method of analysis is desired, such as the SF-36.     

Improving TAIEX forecasting using fuzzy time series with Box–Cox power transformation

Box–Cox together with our newly proposed transformation were implemented in three different real world empirical problems to alleviate noisy and the volatility effect of them. Consequently, a new domain was constructed. Subsequently, universe of discourse for transformed data was established and an approach for calculating effective length of the intervals was then proposed. Considering the steps above, the initial forecasts were performed using frequently used fuzzy time series (FTS) methods on transformed data. Final forecasts were retrieved from initial forecasted values by proper inverse operation. Comparisons of the results demonstrate that the proposed method produced more accurate forecasts compared with existing FTS on original data.     

组织支持、组织文化认同和情绪工作作用机制研究

以服务行业工作人员为研究对象,通过实证分析对组织支持、组织文化认同和情绪工作间的作用机制进行研究。结果表明：同事支持、上级支持和企业支持对表层行为有显著负向影响,上级支持和企业支持对深层行为有显著正向影响;组织文化认同的行为性认同维度对表层行为有抑制作用,认知性认同、情感性认同和行为性认同则能有效激发员工的深层行为;组织支持通过组织文化认同的部分中介作用对表层行为和深层行为产生影响。     

判别企业生命周期的新方法——构面偏差法

企业生命周期的判别方法存在指标单一、可操作性不强等诸多的问题,成为制约基于生命周期的相关企业管理研究的一个瓶颈。将构面偏差的方法应用到企业生命周期的判别中,详细阐述了基于构面偏差的企业生命周期判别方法的基本原理及应用,并以478个企业数据为例,详细说明了此方法的操作步骤,为基于生命周期的相关研究提供了科学的依据。     

Power-divergence-type measure of departure from diagonals-parameter symmetry for square contingency tables with ordered categories

For the analysis of square contingency tables with ordered categories, Goodman considered the diagonals-parameter symmetry (DPS) model. This paper proposes a measure to represent the degree of departure from the DPS model. The proposed measure is expressed by applying Read and Cressie’s power-divergence or Patil and Taillie’s diversity index. The measure would be useful for comparing the degree of departure from the DPS model in several tables. Examples are given.     

Parameter selection in modified histogram estimates

A multivariate modified histogram density estimate depending on a reference density g and a partition P has been proved to have good consistency properties according to several information theoretic criteria. Given an i.i.d. sample, we show how to select automatically both g and P so that the expected L ₁ error of the corresponding selected estimate is within a given constant multiple of the best possible error plus an additive term which tends to zero under mild assumptions. Our method is inspired by the combinatorial tools developed by Devroye and Lugosi [Devroye, L. and Lugosi, G., 2001, Combinatorial Methods in Density Estimation (New York, NY: Springer–Verlag)] and it includes a wide range of reference density and partition models. Results of simulations are also presented.