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dc.contributor.authorJiang, Yizhou
dc.date.accessioned2010-02-09T20:53:27Z
dc.date.available2010-02-09T20:53:27Z
dc.date.issued2010-02-09T20:53:27Z
dc.date.submittedDecember 2009
dc.identifier.urihttp://hdl.handle.net/1928/10299
dc.description.abstractLatent structure techniques have recently found extensive use in regression analysis for high dimensional data. This thesis attempts to examine and expand two of such methods, Partial Least Squares (PLS) regression and Supervised Principal Component Analysis (SPCA). We propose several new algorithms, including a quadratic spline PLS, a cubic spline PLS, two fractional polynomial PLS algorithms and two multivariate SPCA algorithms. These new algorithms were compared to several popular PLS algorithms using real and simulated datasets. Cross validation was used to assess the goodness-of-fit and prediction accuracy of the various models. Strengths and weaknesses of each method were also discussed based on model stability, robustness and parsimony. The linear PLS and the multivariate SPCA methods were found to be the most robust among the methods considered, and usually produced models with good t and prediction. Nonlinear PLS methods are generally more powerful in fitting nonlinear data, but they had the tendency to over-fit, especially with small sample sizes. A forward stepwise predictor pre-screening procedure was proposed for multivariate SPCA and our examples demonstrated its effectiveness in picking a smaller number of predictors than the standard univariate testing procedure.en_US
dc.language.isoen_USen_US
dc.subjectPartial Least Squaresen_US
dc.subjectPLSen_US
dc.subjectSupervised Principal Component Analysisen_US
dc.subjectSPCAen_US
dc.subjectregressionen_US
dc.subjectmodelingen_US
dc.subjectmultivariateen_US
dc.subjectmulticollinearityen_US
dc.subjecthigh dimension dataen_US
dc.subjectmultiple responsesen_US
dc.subjectstatisticalen_US
dc.subjectChemometricsen_US
dc.subjectlatent structureen_US
dc.subjectlatent variableen_US
dc.subjectcross validationen_US
dc.subjectalgorithmen_US
dc.subjectsplineen_US
dc.subjectfractional polynomialen_US
dc.subject.lcshLatent structure analysis.
dc.subject.lcshRegression analysis.
dc.subject.lcshLeast squares.
dc.titleContributions to partial least squares regression and supervised principal component analysis modelingen_US
dc.typeDissertationen_US
dc.description.degreeStatisticsen_US
dc.description.levelDoctoralen_US
dc.description.departmentUniversity of New Mexico. Dept. of Mathematics and Statisticsen_US
dc.description.advisorBedrick, Edward
dc.description.committee-memberGuindani, Michele
dc.description.committee-memberHuerta, Gabriel
dc.description.committee-memberKang, Huining


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