Analysis of robust design experiments with time-dependent ordinal response characteristics: a quality improvement study from the horticulture industry

An approach to the analysis of time-dependent ordinal quality score data from robust design experiments is developed and applied to an experiment from commercial horticultural research, using concepts of product robustness and longevity that are familiar to analysts in engineering research. A two-stage analysis is used to develop models describing the effects of a number of experimental treatments on the rate of post-sales product quality decline. The first stage uses a polynomial function on a transformed scale to approximate the quality decline for an individual experimental unit using derived coefficients and the second stage uses a joint mean and dispersion model to investigate the effects of the experimental treatments on these derived coefficients. The approach, developed specifically for an application in horticulture, is exemplified with data from a trial testing ornamental plants that are subjected to a range of treatments during production and home-life. The results of the analysis show how a number of control and noise factors affect the rate of post-production quality decline. Although the model is used to analyse quality data from a trial on ornamental plants, the approach developed is expected to be more generally applicable to a wide range of other complex production systems.     

论虚实关系在舞美设计中的运用

虚与实是艺术创作技巧的美学原则,在舞台美术设计中,更显示出虚实结合的独特性和必要性,具体来说,表现在几个方面:在布景设置上,要以实带虚,以虚衬实;在意境表达上,要虚实对比,和谐产生;在光色处理上,要虚实变幻,以景托人;在舞台布局上,要讲究整体,统筹协调.     

Another look at Huber's estimator: A new minimax estimator in regression with stochastically bounded noise

Huber's estimator has had a long lasting impact, particularly on robust statistics. It is well known that under certain conditions, Huber's estimator is asymptotically minimax. A moderate generalization in rederiving Huber's estimator shows that Huber's estimator is not the only choice. We develop an alternative asymptotic minimax estimator and name it regression with stochastically bounded noise (RSBN). Simulations demonstrate that RSBN is slightly better in performance, although it is unclear how to justify such an improvement theoretically. We propose two numerical solutions: an iterative numerical solution, which is extremely easy to implement and is based on the proximal point method; and a solution by applying state-of-the-art nonlinear optimization software packages, e.g., SNOPT. Contribution: the generalization of the variational approach is interesting and should be useful in deriving other asymptotic minimax estimators in other problems.     

The t-information and its use in multivariate problems and time-series analysis

The second moment of recently introduced scalar inference function can be viewed as generalized Fisher information of the continuous probability distributions. In this paper we call it the t-information and give some possible applications of the new concept.     

A variable-neighbourhood search algorithm for finding optimal run orders in the presence of serial correlation

The responses obtained from response surface designs that are run sequentially often exhibit serial correlation or time trends. The order in which the runs of the design are performed then has an impact on the precision of the parameter estimators. This article proposes the use of a variable-neighbourhood search algorithm to compute run orders that guarantee a precise estimation of the effects of the experimental factors. The importance of using good run orders is demonstrated by seeking D-optimal run orders for a central composite design in the presence of an AR(1) autocorrelation pattern.     

Cumulative correspondence analysis of ordered categorical data from industrial experiments

Most studies of quality improvement deal with ordered categorical data from industrial experiments. Accounting for the ordering of such data plays an important role in effectively determining the optimal factor level of combination. This paper utilizes the correspondence analysis to develop a procedure to improve the ordered categorical response in a multifactor state system based on Taguchi's statistic. Users may find the proposed procedure in this paper to be attractive because we suggest a simple and also popular statistical tool for graphically identifying the really important factors and determining the levels to improve process quality. A case study for optimizing the polysilicon deposition process in a very large-scale integrated circuit is provided to demonstrate the effectiveness of the proposed procedure.     

Forecasting obesity trends in England

Summary.  Forecasts of trends in obesity in England for 2010 are produced by treating the available data, which contain the proportions of the population, categorized by age and sex, falling into different body mass index ranges, as compositional data sets, so that the implicit simplex restrictions are automatically satisfied. Forecasts are calculated by using linear trend models for the log-ratio transformations and are accompanied by prediction regions. The advantages of treating data on proportions compositionally are emphasized and compared with forecasts that have been obtained by ignoring this restriction.     

Doubly adaptive biased coin designs with heterogeneous responses

Doubly adaptive biased coin design (DBCD) is an important family of response-adaptive randomization procedures for clinical trials. It uses sequentially updated estimation to skew the allocation probability to favor the treatment that has performed better thus far. An important assumption for the DBCD is the homogeneity assumption for the patient responses. However, this assumption may be violated in many sequential experiments. Here we prove the robustness of the DBCD against certain time trends in patient responses. Strong consistency and asymptotic normality of the design are obtained under some widely satisfied conditions. Also, we propose a general weighted likelihood method to reduce the bias caused by the heterogeneity in the inference after a trial. Some numerical studies are also presented to illustrate the finite sample properties of DBCD.     

Estimating a sensitive proportion through randomized response procedures based on auxiliary information

Randomized response techniques are widely employed in surveys dealing with sensitive questions to ensure interviewee anonymity and reduce nonrespondents rates and biased responses. Since Warner’s (J Am Stat Assoc 60:63–69, 1965) pioneering work, many ingenious devices have been suggested to increase respondent’s privacy protection and to better estimate the proportion of people, π _A , bearing a sensitive attribute. In spite of the massive use of auxiliary information in the estimation of non-sensitive parameters, very few attempts have been made to improve randomization strategy performance when auxiliary variables are available. Moving from Zaizai’s (Model Assist Stat Appl 1:125–130, 2006) recent work, in this paper we provide a class of estimators for π _A , for a generic randomization scheme, when the mean of a supplementary non-sensitive variable is known. The minimum attainable variance bound of the class is obtained and the best estimator is also identified. We prove that the best estimator acts as a regression-type estimator which is at least as efficient as the corresponding estimator evaluated without allowing for the auxiliary variable. The general results are then applied to Warner and Simmons’ model.     

Covariance-regularized regression and classification for high dimensional problems

Summary.  We propose covariance-regularized regression, a family of methods for prediction in high dimensional settings that uses a shrunken estimate of the inverse covariance matrix of the features to achieve superior prediction. An estimate of the inverse covariance matrix is obtained by maximizing the log-likelihood of the data, under a multivariate normal model, subject to a penalty; it is then used to estimate coefficients for the regression of the response onto the features. We show that ridge regression, the lasso and the elastic net are special cases of covariance-regularized regression, and we demonstrate that certain previously unexplored forms of covariance-regularized regression can outperform existing methods in a range of situations. The covariance-regularized regression framework is extended to generalized linear models and linear discriminant analysis, and is used to analyse gene expression data sets with multiple class and survival outcomes.