Canonical Correlation Analysis Through Linear Modeling

In this paper, we introduce linear modeling of canonical correlation analysis, which estimates canonical direction matrices by minimising a quadratic objective function. The linear modeling results in a class of estimators of canonical direction matrices, and an optimal class is derived in the sense described herein. The optimal class guarantees several of the following desirable advantages: first, its estimates of canonical direction matrices are asymptotically efficient; second, its test statistic for determining the number of canonical covariates always has a chi‐squared distribution asymptotically; third, it is straight forward to construct tests for variable selection. The standard canonical correlation analysis and other existing methods turn out to be suboptimal members of the class. Finally, we study the role of canonical variates as a means of dimension reduction for predictors and responses in multivariate regression. Numerical studies and data analysis are presented.     

Latent variable model for mixed correlated power series and ordinal longitudinal responses with non ignorable missing values

We propose a joint model based on a latent variable for analyzing mixed power series and ordinal longitudinal data with and without missing values. A bivariate probit regression model is used for the missing mechanisms. Random effects are used to take into account the correlation between longitudinal responses. A full likelihood-based approach is used to yield maximum-likelihood estimates of the model parameters. Our model is applied to a medical data set, obtained from an observational study on women where the correlated responses are the ordinal response of osteoporosis of the spine and the power series response of the number of joint damages. Sensitivity analysis is also performed to study the influence of small perturbations of the parameters of the missing mechanisms and overdispersion of the model on likelihood displacement.     

Technology selection in the absence of standardised materials and processes: a survey in the UK composite materials supply chain

Composite materials is an industry where technology selection has major consequences as there is not a standard manufacturing process, nor are there standardised materials with defined or proscribed properties for companies to select as multiple solutions are technically viable. This research aims to identify key factors for manufacturing technology selection in the UK composite materials supply chain. Literature review and managers’ opinions were used to identify 18 factors affecting manufacturing technology selection. This was followed by a survey comprising the multi-tier supply chain of the composite materials industry. The results of the survey show ‘on time deliveries/service level to customers’, ‘improve quality’ and ‘reduce cycle time’ received the highest average ratings. In this study a correlation analysis was performed to identify the underlying dependencies between the factors investigated. The identification and use of underlying dependencies rather than highest average provided a more comprehensive picture of the factors that affect technology selection in the composite materials industry. For this study, experts in composite materials were asked to comment on the findings of the survey and their value to the industry. The results presented may assist companies in the composite materials industry with technology selection decision-making processes.     

天然真石漆饰面喷涂在昆山下穿通道应用初探

在公路建设工程中,搞好施工材料的选用与管理对于加快施工进度、保证工程质量、降低工程成本、提高经济效益,具有十分重要的意义。结合昆山市东城大道规三路下穿通道敞开段的真石漆喷涂饰面工程施工实践,阐述了真石漆产品的特性、施工要求、控制要点及产品应用前景,为施工中的材料选择积累了经验,提出了相应思考。     

Robust likelihood inferences for multivariate correlated data

Multivariate normal, due to its well-established theories, is commonly utilized to analyze correlated data of various types. However, the validity of the resultant inference is, more often than not, erroneous if the model assumption fails. We present a modification for making the multivariate normal likelihood acclimatize itself to general correlated data. The modified likelihood is asymptotically legitimate for any true underlying joint distributions so long as they have finite second moments. One can, hence, acquire full likelihood inference without knowing the true random mechanisms underlying the data. Simulations and real data analysis are provided to demonstrate the merit of our proposed parametric robust method.     

The Loss Rank Criterion for Variable Selection in Linear Regression Analysis

Abstract. Lasso and other regularization procedures are attractive methods for variable selection, subject to a proper choice of shrinkage parameter. Given a set of potential subsets produced by a regularization algorithm, a consistent model selection criterion is proposed to select the best one among this preselected set. The approach leads to a fast and efficient procedure for variable selection, especially in high‐dimensional settings. Model selection consistency of the suggested criterion is proven when the number of covariates d is fixed. Simulation studies suggest that the criterion still enjoys model selection consistency when d is much larger than the sample size. The simulations also show that our approach for variable selection works surprisingly well in comparison with existing competitors. The method is also applied to a real data set.     

Shared gamma frailty models based on reversed hazard rate for modeling Australian twin data

In this paper, we consider shared gamma frailty model with the reversed hazard rate (RHR) with two different baseline distributions, namely the generalized inverse Rayleigh and the exponentiated Gumbel distributions. With these two baseline distributions we propose two different shared frailty models. We develop the Bayesian estimation procedure using Markov Chain Monte Carlo technique to estimate the parameters involved in these models. We present a simulation study to compare the true values of the parameters with the estimated values. A search of the literature suggests that currently no work has been done for these two baseline distributions with a shared gamma frailty with the RHR so far. We also apply these two models by using a real life bivariate survival data set of Australian twin data given by Duffy et a1. (1990) and a better model is suggested for the data.     

Causal inferences from many experiments

The underlying statistical concept that animates empirical strategies for extracting causal inferences from observational data is that observational data may be adjusted to resemble data that might have originated from a randomized experiment. This idea has driven the literature on matching methods. We explore an un-mined idea for making causal inferences with observational data – that any given observational study may contain a large number of indistinguishably balanced matched designs. We demonstrate how the absence of a unique best solution presents an opportunity for greater information retrieval in causal inference analysis based on the principle that many solutions teach us more about a given scientific hypothesis than a single study and improves our discernment with observational studies. The implementation can be achieved by integrating the statistical theories and models within a computational optimization framework that embodies the statistical foundations and reasoning.     

Variable selection for varying dispersion beta regression model

The beta regression models are commonly used by practitioners to model variables that assume values in the standard unit interval (0, 1). In this paper, we consider the issue of variable selection for beta regression models with varying dispersion (VBRM), in which both the mean and the dispersion depend upon predictor variables. Based on a penalized likelihood method, the consistency and the oracle property of the penalized estimators are established. Following the coordinate descent algorithm idea of generalized linear models, we develop new variable selection procedure for the VBRM, which can efficiently simultaneously estimate and select important variables in both mean model and dispersion model. Simulation studies and body fat data analysis are presented to illustrate the proposed methods.     

考虑随机利率和通货膨胀的连续时间资产组合选择

通过随机控制技术、Bellman最优性原理和HJB方程研究了通货膨胀、随机利率和交易成本等因素影响下的连续时间投资组合选择的最优化问题，将利率假定为服从Vasicek利率模型的随机过程，应用连续时间的动态均值-方差方法得到符合实际意义的HJB方程，通过多重网格的数值逼近方法求解相应的HJB方程得到双目标优化问题的最优投资策略。用实证方法与国内证券市场上代表性指数基金进行对比研究，发现通货膨胀和利率变动以及经济环境和投资者的异质信念等因素均会对最优策略产生影响，有效前沿会随之发生变化，债券与股票之间的投资比例并不是简单维持固定比例就可以保证总资产最优，拓展了基金分离定理。考虑通货膨胀和交易成本等因素的资产组合选择模型可以实实在在为机构投资者提供客观的实践指导和科学的理论依据。