In many multivariate statistical techniques, a set of linear functions of the original p variables is produced. One of the more dif cult aspects of these techniques is the interpretation of the linear functions, as these functions usually have nonzero coef cients on all p variables. A common approach is to effectively ignore (treat as zero) any coef cients less than some threshold value, so that the function becomes simple and the interpretation becomes easier for the users. Such a procedure can be misleading. There are alternatives to principal component analysis which restrict the coef cients to a smaller number of possible values in the derivationof the linear functions,or replace the principalcomponentsby "principal variables." This article introduces a new technique, borrowing an idea proposed by Tibshirani in the context of multiple regression where similar problems arise in interpreting regression equations. This approach is the so-called LASSO, the "least absolute shrinkage and selection operator," in which a bound is introduced on the sum of the absolute values of the coef cients, and in which some coef cients consequently become zero. We explore some of the propertiesof the new technique,both theoreticallyand using simulation studies, and apply it to an example.

It is fairly common, following a principal component analysis, to rotate components in order to simplify their structure. Here, we propose an alternative to this two-stage procedure which involves only one stage and combines the objectives of variance maximization and simplification. It is shown, using examples, that the new technique can provide alternative ways of interpreting a dataset. Some properties of the technique are investigated using a simulation study.

Principal component analysis (PCA) is widely used in atmospheric science, and the resulting empirical orthogonal functions (EOFs) are often rotated to aid interpretation. In this paper 3 methods are described which provide alternatives to the standard 2-stage procedure of PCA followed by rotation. The techniques are illustrated on a small example involving sea-surface temperatures in the Mediterranean. Each method is shown to give different simplified interpretations for the major sources of variation in the data set. All 3 techniques have advantages over standard rotation.

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The risk of flood prevention and to make the management and planning of hydrological resources effective, it is required to analyse and measure the flow of water continuously at a number of barrages and dams. The flow variation over a certain time period can graphically be represented through hydrograph for any barrage considered. The hydrograph provides information which is vital to determine the frequencies and severity regarding extreme events. Approaches for analysis of functional data (AFD) are introduced with an intention to concentrate on the visualization of data and detection of outliers using graphical methods in the context of both functional and multivariate study. These methods are illustrated on real-world flood data of Sukkur barrage on the River Indus, in Sindh province, Pakistan.