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The article deals with certain quantile regression methods for vector responses. In particular, it describes weighted and locally polynomial extensions to the projectional quantile regression, discusses their properties, addresses their computational side, compares their outcome with recent analogous generalizations of the competing multiple-output directional quantile regression, demonstrates a link between the two competing methodologies, complements the results already available in the literature, illustrates the concepts with a few simulated and insightful examples illustrating some of their features, and shows their application to a real financial data set, namely to Forex 1M exchange rates. The real-data example strongly indicates that the presented methods might have a huge impact on the analysis of multivariate time series consisting of two to four dimensional observations. [ABSTRACT FROM AUTHOR]

Statistical graphics play an important role in exploratory data analysis, model checking and diagnosis. With high dimensional data, this often means plotting low-dimensional projections, for example, in classification tasks projection pursuit is used to find low-dimensional projections that reveal differences between labelled groups. In many contemporary data sets the number of observations is relatively small compared to the number of variables, which is known as a high dimension low sample size (HDLSS) problem. This paper explores the use of visual inference on understanding low-dimensional pictures of HDLSS data. Visual inference helps to quantify the significance of findings made from graphics. This approach may be helpful to broaden the understanding of issues related to HDLSS data in the data analysis community. Methods are illustrated using data from a published paper, which erroneously found real separation in microarray data, and with a simulation study conducted using Amazon's Mechanical Turk. [ABSTRACT FROM AUTHOR]

Using a modification of the Hinich, J Time Ser Anal 3(3):169-176, (1982) bispectrum test for nonlinearity and Gaussianity, the residuals of the Tiao and Box, J Am Stat Assoc 76:802-816, (1981) constrained and unconstrained VAR models for the gas furnace data reject the assumption of Gaussianity and linearity over a grid of bandwidths for estimating the bispectrum. These findings call into question the specification of the linear VAR and VARMA models assumed by Tiao and Box, J Am Stat Assoc 76:802-816, (1981). Utilizing the alternative Hinich J Nonparametr Stat 6:205-221, (1996) nonlinearity test, the residuals of the VAR model were shown to exhibit episodic nonlinearity. The sensitivity of the findings to outliers is investigated by estimating and testing the residuals of L1 and MINIMAX models from 1-6 lags. Building on the linear dynamic specification, a multivariate adaptive regression splines (MARS) model is estimated, using two software implementations, and shown to remove the nonlinearity in the residuals. Leverage plots were used to illustrate the 'cost' of imposing a linearity assumption. Out-of-sample forecasting tests from 1-6 periods ahead found that using the sum-of-squared errors criteria, the MARS model out performed ACE, GAM and projection pursuit models. [ABSTRACT FROM AUTHOR]

Several approaches for robust canonical correlation analysis will be presented and discussed. A first method is based on the definition of canonical correlation analysis as looking for linear combinations of two sets of variables having maximal (robust) correlation. A second method is based on alternating robust regressions. These methods are discussed in detail and compared with the more traditional approach to robust canonical correlation via covariance matrix estimates. A simulation study compares the performance of the different estimators under several kinds of sampling schemes. Robustness is studied as well by breakdown plots. [ABSTRACT FROM AUTHOR]

In this study a projection pursuit method is used to explore c (square) contingency table data. The method operates on projection matrices constructed from the contingency tables using affine geometry and creates projections (or marginals) using a Radon transform. The projection matrices and the projections can be used to find the 'interesting' (nonuniform structure), and to cluster and to order the, cases. This projection pursuit method is implemented with graph visualization of projection. It is similar to the discrete version of Andrews' curve. We demonstrate how this approach compares to association rules commonly used in data mining using a market basket data set and compare the PP results with the analysis of a data set from Wishart and Leach) (1970). [ABSTRACT FROM AUTHOR]

Summary: We address the problem of generalizing Principal Component Analysis (PCA) from the approximation point of view. Given a data set in a high dimensional space, PCA proposes approximations by linear subspaces. These linear models can show some limits when the data distribution is not Gaussian. To overcome these limits, we present Auto-Associative Composite (AAC) models based on manifold approximation. AAC models benefit from interesting theoretical properties, generalizing PCA ones. We take profit of these properties to propose an iterative algorithm to compute the manifold, and prove its convergence in a finite number of steps. PCA models and AAC models are first compared on a theoretical point of view. As a result, we show that PCA is the unique additive AAC model. Then a practical comparison of AAC and PCA models is presented on a data set made of curves. [ABSTRACT FROM AUTHOR]