Minimum average deviance estimation for sufficient dimension reduction

Sufficient dimension reduction methods aim to reduce the dimensionality of predictors while preserving regression information relevant to the response. In this article, we develop Minimum Average Deviance Estimation (MADE) methodology for sufficient dimension reduction. The purpose of MADE is to generalize Minimum Average Variance Estimation (MAVE) beyond its assumption of additive errors to settings where the outcome follows an exponential family distribution. As in MAVE, a local likelihood approach is used to learn the form of the regression function from the data and the main parameter of interest is a dimension reduction subspace. To estimate this parameter within its natural space, we propose an iterative algorithm where one step utilizes optimization on the Stiefel manifold. MAVE is seen to be a special case of MADE in the case of Gaussian outcomes with a common variance. Several procedures are considered to estimate the reduced dimension and to predict the outcome for an arbitrary covariate value. Initial simulations and data analysis examples yield encouraging results and invite further exploration of the methodology.     

Estimation and prediction for an inverted exponentiated Rayleigh distribution under hybrid censoring

In this paper we consider estimation of unknown parameters of an inverted exponentiated Rayleigh distribution when it is known that data are hybrid Type I censored. The maximum likelihood and Bayes estimates are derived. In sequel interval estimates are also constructed. We further consider one- and two-sample prediction of future observations and also obtain prediction intervals. The performance of proposed methods of estimation and prediction is studied using simulations and an illustrative example is discussed in support of the suggested methods.     

The Complexity of Forecast Testing

Consider a weather forecaster predicting a probability of rain for the next day. We consider tests that, given a finite sequence of forecast predictions and outcomes, will either pass or fail the forecaster. Sandroni showed that any test which passes a forecaster who knows the distribution of nature can also be probabilistically passed by a forecaster with no knowledge of future events. We look at the computational complexity of such forecasters and exhibit a linear‐time test and distribution of nature such that any forecaster without knowledge of the future who can fool the test must be able to solve computationally difficult problems. Thus, unlike Sandroni's work, a computationally efficient forecaster cannot always fool this test independently of nature.     

大学生心理健康现状及发展趋势探讨——基于南华大学学生心理咨询状况的分析

大学生心理健康教育问题日益突出,已经成为高校教育的重要组成部分。文章首先探讨了国内大学生心理健康教育的现状,而后就南华大学学生心理咨询状况展开探讨,采用多项式拟合的方法就未来发展趋势进行预测,结论表明大学生心理问题已经日益突出,需要寻找合理的解决途径。通过研究分析,对南华大学学生心理健康教育提出了若干建议。     

内蒙古自治区人口总量的时间序列拟合与预测

以1950-2007年内蒙古自治区人口总量数据为依据,利用ARIMA（1,1,1）与GM（1,1）模型分别对内蒙古人口总量的时间序列进行了拟合、分析与预测。分析结果表明：两种模型的拟合程度都比较高,但灰色模型的拟合度更高。因此用GM（1,1）模型对内蒙古自治区2010-2012年的人口总量进行了预测。     

NONPARAMETRIC META‐ANALYSIS FOR MINIMAL‐REPAIR SYSTEMS

We consider the situation that repair times of several identically structured technical systems are observed. As an example of such data we discuss the Boeing air conditioner data, consisting of successive failures of the air conditioning system of each member of a fleet of Boeing jet airplanes. The repairing process is assumed to be performed according to a minimal‐repair strategy. This reflects the idea that only those operations are accomplished that are absolutely necessary to restart the system after a failure. The ‘after‐repair‐state’ of the system is the same as it was shortly before the failure. Clearly, the observed repair times contain valuable information about the repair times of an identically structured system put into operation in the future. Thus, for statistical analysis and prediction, it is certainly favourable to take into account all repair times from each system. The resulting pooled sample is used to construct nonparametric prediction intervals for repair times of a future minimal‐repair system. To illustrate our results we apply them to the above‐mentioned data set. As expected, the maximum coverage probabilities of prediction intervals based on two samples exceed those based on one sample. We show that the relative gain for a two‐sample prediction over a one‐sample prediction can be substantial. One of the advantages of the present approach is that it allows nonparametric prediction intervals to be constructed directly. This provides a beneficial alternative to existing nonparametric methods for minimal‐repair systems that construct prediction intervals via the asymptotic distribution of quantile estimators. Moreover, the prediction intervals presented here are exact regardless of the sample size.     

基于小波分析的基金净值预测模型

基于小波分析提出了一种基金净值预测模型。此模型利用小波分析理论用改进的小波阈值去噪方法对基金净值数据进行去噪处理,再对经过去噪处理后得到的较为平稳的数据,利用计量经济学中时间序列自回归模型进行短期预测。研究证明：该预测模型能较好地预测基金净值的短期趋势,预测结果优于传统的基金净值预测模型。     

New 3-level response surface designs constructed from incomplete block designs

Box and Behnken [1958. Some new three level second-order designs for surface fitting. Statistical Technical Research Group Technical Report No. 26. Princeton University, Princeton, NJ; 1960. Some new three level designs for the study of quantitative variables. Technometrics 2, 455–475.] introduced a class of 3-level second-order designs for fitting the second-order response surface model. These 17 Box–Behnken designs (BB designs) are available for 3–12 and 16 factors. Although BB designs were developed nearly 50 years ago, they and the central-composite designs of Box and Wilson [1951. On the experimental attainment of optimum conditions. J. Royal Statist. Soc., Ser. B 13, 1–45.] are still the most often recommended response surface designs. Of the 17 aforementioned BB designs, 10 were constructed from balanced incomplete block designs (BIBDs) and seven were constructed from partially BIBDs (PBIBDs). In this paper we show that these seven BB designs constructed from PBIBDs can be improved in terms of rotatability as well as average prediction variance, D$D$- and G$G$-efficiency. In addition, we also report new orthogonally blocked solutions for 5, 8, 9, 11 and 13 factors. Note that an 11-factor BB design is available but cannot be orthogonally blocked. All new designs can be found at http://www.math.montana.edu/∼$\sim$jobo/bbd/.     

Partial least squares Cox regression for genome-wide data

Most methods for survival prediction from high-dimensional genomic data combine the Cox proportional hazards model with some technique of dimension reduction, such as partial least squares regression (PLS). Applying PLS to the Cox model is not entirely straightforward, and multiple approaches have been proposed. The method of Park et al. (Bioinformatics 18(Suppl. 1):S120–S127, 2002) uses a reformulation of the Cox likelihood to a Poisson type likelihood, thereby enabling estimation by iteratively reweighted partial least squares for generalized linear models. We propose a modification of the method of park et al. (2002) such that estimates of the baseline hazard and the gene effects are obtained in separate steps. The resulting method has several advantages over the method of park et al. (2002) and other existing Cox PLS approaches, as it allows for estimation of survival probabilities for new patients, enables a less memory-demanding estimation procedure, and allows for incorporation of lower-dimensional non-genomic variables like disease grade and tumor thickness. We also propose to combine our Cox PLS method with an initial gene selection step in which genes are ordered by their Cox score and only the highest-ranking k% of the genes are retained, obtaining a so-called supervised partial least squares regression method. In simulations, both the unsupervised and the supervised version outperform other Cox PLS methods.     

天命、国运与预言

“一姓不再兴”和“五百年必有王者兴”是东周时代最流行的两条预言 ,它们相互为用 ,影响了一代人心和政治。本文探其源而析其用 ,从两条预言的流变看人心向背 ,国运兴衰 ,说明天命即民命 ,人心即天心 ,得民心者得天下