%Gra: an SAS macro for generalized redundancy analysis

In the framework of redundancy analysis and reduced rank regression, the extended redundancy analysis model managed to account for more than two blocks of manifest variables in its specification. A further extension, the generalized redundancy analysis (GRA), has been recently proposed in literature, with the aim of incorporating external covariates into the model, thanks to a new estimation algorithm that manages to separate all the contributions of the exogenous and external covariates in the formation of the latent composites. At present, software to estimate GRA models is not available. In this paper, we provide an SAS macro, %GRA, to specify and fit structural relationships, with an application to illustrate the use of the macro.     

Statistical analysis for rounded data

When random variables do not take discrete values, observed data are often the rounded values of continuous random variables. Errors caused by rounding of data are often neglected by classical statistical theories. While some pioneers have identified and made suggestions to rectify the problem, few suitable approaches were proposed. In this paper, we propose an approximate MLE (AMLE) procedure to estimate the parameters and discuss the consistency and asymptotic normality of the estimates. For our illustration, we shall consider the estimates of the parameters in AR(p)$\mathit{AR}(p)$ and MA(q)$\mathit{MA}(q)$ models for rounded data.     

Sensitivity analysis for ranked data

Sensitivity analysis is to study the influence of a small change in the input data on the output of the analysis. Han and Huh (1995) developed a quantification method for the ranked data. However, the question of stability in the analysis of ranked data has not been considered. Here, we propose a method of sensitivity analysis for ranked data. Our aim is to evaluate perturbations by using a graphical approach suggested by Han and Huh (1995). It extends the results obtained by Tanaka (1984) and Huh (1989) for the sensitivity analysis in Hayashi’s third method of quantification and those by Huh and Park (1990) for the principal component reduction of the case influence derivatives in regression. A numerical example is provided to explain how to conduct sensitivity analysis based on the proposed approach.     

An exploratory data analysis in scale-space for interval-valued data

We propose an exploratory data analysis approach when data are observed as intervals in a nonparametric regression setting. The interval-valued data contain richer information than single-valued data in the sense that they provide both center and range information of the underlying structure. Conventionally, these two attributes have been studied separately as traditional tools can be readily used for single-valued data analysis. We propose a unified data analysis tool that attempts to capture the relationship between response and covariate by simultaneously accounting for variability present in the data. It utilizes a kernel smoothing approach, which is conducted in scale-space so that it considers a wide range of smoothing parameters rather than selecting an optimal value. It also visually summarizes the significance of trends in the data as a color map across multiple locations and scales. We demonstrate its effectiveness as an exploratory data analysis tool for interval-valued data using simulated and real examples.     

Factor analysis as a tool for data analysis

The use of factor analysis in analyzing real data is influenced not only by mathematical models but also by the objectives of the research at hand, the amount of data to be analyzed and the departures of the data from the model. Factor analysis is a process performed in several steps, including data screening and assessment of assumptions necessary for the model as well as the actual computations—the new analyst may need assistance in deter-mining the initial method of extraction, how many factors to request, the method of rotation and how to interpret the factors— these steps are discussed with reference to figures containing computer output for a real problem. The importance of auxiliary information and graphical displays to aid the statistician during the factor analysis process is stressed.     

Linear discriminant analysis for multiple functional data analysis

In multivariate data analysis, Fisher linear discriminant analysis is useful to optimally separate two classes of observations by finding a linear combination of p variables. Functional data analysis deals with the analysis of continuous functions and thus can be seen as a generalisation of multivariate analysis where the dimension of the analysis space p strives to infinity. Several authors propose methods to perform discriminant analysis in this infinite dimensional space. Here, the methodology is introduced to perform discriminant analysis, not on single infinite dimensional functions, but to find a linear combination of p infinite dimensional continuous functions, providing a set of continuous canonical functions which are optimally separated in the canonical space.KEYWORDS: Functional data analysis, linear discriminant analysis, classification