Transcription of A Tutorial on Multivariate Statistical Analysis
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A Tutorial on Multivariate Statistical Analysis
A Tutorial onMultivariateStatistical AnalysisCraig A. TracyUC DavisSAMSIS eptember 20061 ELEMENTARY STATISTICSC ollection of (real-valued) data from a sequence of experimentsX1,X2,..,XnMight make assumption underlying law isN( , 2) with unknownmean and variance 2. Want to estimate and 2from the Mean & Sample Variance: X=1nXjXj, S=1n 1Xj Xj X 2 Estimators are unbiased E( X) = ,E(S) = 22 Theorem:IfX1,X2,..are independentN( , 2) variables then XandSare independent. We have that XisN( , 2/n) and(n 1)S/ 2is 2(n 1).Recall 2(d) denotes the chi-squared distribution withddegrees offreedom. Its density isf 2(x) =12d/2 (d/2)xd/2 1e x/2, x 0,where (z) =Z 0tz 1e tdt, (z)> GENERALIZATIONSFrom the classic textbook of Anderson[1]: Multivariate Statistical Analysis is concerned with data thatconsists of sets of measurements on a number of individualsor objects. The sample data may be heights and weights ofsome individuals drawn randomly from a population ofschool children in a given city, or the Statistical treatmentmay be made on a collection of measurements, such aslengths and widths of petals and lengths and widths ofsepals of iris plants taken from two species, or one maystudy the scores on batteries of mental tests administeredto a number of # of sets of measurements on a given individual,n= # of observations = sample size4 Remarks: In above examples, one can assume thatp nsince typically
MULTIVARIATE GENERALIZATIONS From the classic textbook of Anderson[1]: Multivariate statistical analysis is concerned with data that consists of sets of measurements on a number of individuals or objects. The sample data may be heights and weights of some individuals drawn randomly from a population of
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