15,376 research outputs found
An Alternative Approach to Functional Linear Partial Quantile Regression
We have previously proposed the partial quantile regression (PQR) prediction
procedure for functional linear model by using partial quantile covariance
techniques and developed the simple partial quantile regression (SIMPQR)
algorithm to efficiently extract PQR basis for estimating functional
coefficients. However, although the PQR approach is considered as an attractive
alternative to projections onto the principal component basis, there are
certain limitations to uncovering the corresponding asymptotic properties
mainly because of its iterative nature and the non-differentiability of the
quantile loss function. In this article, we propose and implement an
alternative formulation of partial quantile regression (APQR) for functional
linear model by using block relaxation method and finite smoothing techniques.
The proposed reformulation leads to insightful results and motivates new
theory, demonstrating consistency and establishing convergence rates by
applying advanced techniques from empirical process theory. Two simulations and
two real data from ADHD-200 sample and ADNI are investigated to show the
superiority of our proposed methods
Methodology and theory for partial least squares applied to functional data
The partial least squares procedure was originally developed to estimate the
slope parameter in multivariate parametric models. More recently it has gained
popularity in the functional data literature. There, the partial least squares
estimator of slope is either used to construct linear predictive models, or as
a tool to project the data onto a one-dimensional quantity that is employed for
further statistical analysis. Although the partial least squares approach is
often viewed as an attractive alternative to projections onto the principal
component basis, its properties are less well known than those of the latter,
mainly because of its iterative nature. We develop an explicit formulation of
partial least squares for functional data, which leads to insightful results
and motivates new theory, demonstrating consistency and establishing
convergence rates.Comment: Published in at http://dx.doi.org/10.1214/11-AOS958 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
PLS dimension reduction for classification of microarray data
PLS dimension reduction is known to give good prediction accuracy in the context of classification with high-dimensional microarray data. In this paper, PLS is compared with some of the best state-of-the-art classification methods. In addition, a simple procedure to choose the number of components is suggested. The connection between PLS dimension reduction and gene selection is examined and a property of the first PLS component for binary classification is proven. PLS can also be used as a visualization tool for high-dimensional data in the classification framework. The whole study is based on 9 real microarray cancer data sets
Partial Least Squares: A Versatile Tool for the Analysis of High-Dimensional Genomic Data
Partial Least Squares (PLS) is a highly efficient statistical regression technique that is well suited for the analysis of high-dimensional genomic data. In this paper we review the theory and applications of PLS both under methodological and biological points of view. Focusing on microarray expression data we provide a systematic comparison of the PLS approaches currently employed, and discuss problems as different as tumor classification, identification of relevant genes, survival analysis and modeling of gene networks
Data-driven Soft Sensors in the Process Industry
In the last two decades Soft Sensors established themselves as a valuable alternative to the traditional means for the acquisition of critical process variables, process monitoring and other tasks which are related to process control. This paper discusses characteristics of the process industry data which are critical for the development of data-driven Soft Sensors. These characteristics are common to a large number of process industry fields, like the chemical industry, bioprocess industry, steel industry, etc. The focus of this work is put on the data-driven Soft Sensors because of their growing popularity, already demonstrated usefulness and huge, though yet not completely realised, potential. A comprehensive selection of case studies covering the three most important Soft Sensor application fields, a general introduction to the most popular Soft Sensor modelling techniques as well as a discussion of some open issues in the Soft Sensor development and maintenance and their possible solutions are the main contributions of this work
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