Multivariate Analysis
44 questions across 3 topics. Also examined in CNET, ISS, GATE ST.
Multivariate Normal Distribution, Wishart Distribution, Quadratic Forms
- 157Likelihood ratio test for a multivariate normal meanMSET June 2025Multivariate Normal Distribution, Wishart Distribution, Quadratic FormsHard
- 161Mahalanobis distance between two normal populationsMSET June 2025Multivariate Normal Distribution, Wishart Distribution, Quadratic FormsHard
- 140Asymptotic normality — independence of bar Xn and Sn^2 under normalityMSET April 2024Multivariate Normal Distribution, Wishart Distribution, Quadratic FormsHard
- 155Multivariate normal — correlation between two linear combinationsMSET April 2024Multivariate Normal Distribution, Wishart Distribution, Quadratic FormsMedium
- 130Cochran's theorem for correlated normals — only the whitened form is chi-squareMSET March 2023Multivariate Normal Distribution, Wishart Distribution, Quadratic FormsHard
- 157The likelihood ratio test for a multivariate mean — flagged against standard Hotelling's T^2/F theoryMSET March 2023Multivariate Normal Distribution, Wishart Distribution, Quadratic FormsHard
- 161A Mahalanobis distance that matches none of the printed optionsMSET March 2023Multivariate Normal Distribution, Wishart Distribution, Quadratic FormsHard
- 112Linear combinations of iid trivariate normal vectorsMSET September 2021Multivariate Normal Distribution, Wishart Distribution, Quadratic FormsHard
- 157When a linear transform of a spherical normal has uncorrelated componentsMSET September 2021Multivariate Normal Distribution, Wishart Distribution, Quadratic FormsMedium
- 158Summing independent Wishart matrices — degrees of freedom addMSET September 2021Multivariate Normal Distribution, Wishart Distribution, Quadratic FormsMedium
- 159Standardising a Wishart matrix by its scale parameterMSET September 2021Multivariate Normal Distribution, Wishart Distribution, Quadratic FormsEasy
- 160The multivariate normal characteristic functionMSET September 2021Multivariate Normal Distribution, Wishart Distribution, Quadratic FormsEasy
- 108A covariance matrix must be symmetric and positive semi-definiteMSET December 2020Multivariate Normal Distribution, Wishart Distribution, Quadratic FormsMedium
- 145Mixed moments of a multivariate normal from derivatives of its characteristic functionMSET December 2020Multivariate Normal Distribution, Wishart Distribution, Quadratic FormsHard
- 156Principal components share independence but not a common varianceMSET December 2020Multivariate Normal Distribution, Wishart Distribution, Quadratic FormsHard
- 158An idempotent-matrix quadratic form in Mahalanobis coordinates gives a chi-square with rank-many degrees of freedomMSET December 2020Multivariate Normal Distribution, Wishart Distribution, Quadratic FormsEasy
- 112The Mahalanobis quadratic form is always chi-square distributedMSET June 2019Multivariate Normal Distribution, Wishart Distribution, Quadratic FormsEasy
- 156Equicorrelated normals: sums of two coordinates share one lawMSET June 2019Multivariate Normal Distribution, Wishart Distribution, Quadratic FormsMedium
- 157Flipping the sign on X1le3 keeps the N(0,1) marginal but makes the pair strongly negatively correlatedMSET June 2019Multivariate Normal Distribution, Wishart Distribution, Quadratic FormsMedium
- 158X1+X3 and X1-X2 are proportional, so their joint law is singularMSET June 2019Multivariate Normal Distribution, Wishart Distribution, Quadratic FormsEasy
- 159S11+S12 can be negative, so it is never a multiple of a chi-squareMSET June 2019Multivariate Normal Distribution, Wishart Distribution, Quadratic FormsHard
- 160Mixed moments from the c.f.: divide the derivative at underline0 by i^4=1MSET June 2019Multivariate Normal Distribution, Wishart Distribution, Quadratic FormsEasy
- 110The scaled T^2 is F-distributed — central only under H0MSET January 2018 Paper IIIMultivariate Normal Distribution, Wishart Distribution, Quadratic FormsMedium
- 111(n-1)Ssim Wp(n-1,Sigma), so Ssim Wp(n-1,Sigma/(n-1))MSET January 2018 Paper IIIMultivariate Normal Distribution, Wishart Distribution, Quadratic FormsEasy
- 112The Mahalanobis form of bar X is chi^2pMSET January 2018 Paper IIIMultivariate Normal Distribution, Wishart Distribution, Quadratic FormsEasy
- 113Conditional covariance: the Schur complement Sigma11-Sigma12Sigma22^-1Sigma21MSET January 2018 Paper IIIMultivariate Normal Distribution, Wishart Distribution, Quadratic FormsEasy
- 114Ymid X=5 has mean 10 and s.d. 5sqrt1-rho^2; the sign of rho is not identifiedMSET January 2018 Paper IIIMultivariate Normal Distribution, Wishart Distribution, Quadratic FormsMedium
- 92The options are statistics, not distributions; the conditional law is N(T/3,1/6)MSET April 2017 Paper IIIMultivariate Normal Distribution, Wishart Distribution, Quadratic FormsMedium
- 108u'Sigma^-1u/u'A^-1usimchi^2n-p for Wishart A with n-1 d.f.MSET April 2017 Paper IIIMultivariate Normal Distribution, Wishart Distribution, Quadratic FormsHard
- 109l'Alsim(l'Sigma l)chi^2n-1MSET April 2017 Paper IIIMultivariate Normal Distribution, Wishart Distribution, Quadratic FormsEasy
- 110The Mahalanobis form is chi^2p, with MGF (1-2t)^-p/2MSET April 2017 Paper IIIMultivariate Normal Distribution, Wishart Distribution, Quadratic FormsEasy
- 111Read off sigma1^2=4, sigma2^2=1, rho=0.8 from the bivariate normal densityMSET April 2017 Paper IIIMultivariate Normal Distribution, Wishart Distribution, Quadratic FormsMedium
- 112The regression of X^(1) on X^(2) is the conditional meanMSET April 2017 Paper IIIMultivariate Normal Distribution, Wishart Distribution, Quadratic FormsEasy
Partial and Multiple Correlation Coefficients
- 160Partial correlation — the residual-correlation identityMSET April 2024Partial and Multiple Correlation CoefficientsMedium
- 160Computing a partial correlation from three simple correlationsMSET March 2023Partial and Multiple Correlation CoefficientsEasy
- 120Partial correlation — what it shares with, and how it differs from, ordinary correlationMSET September 2021Partial and Multiple Correlation CoefficientsHard
- 120A multiple correlation coefficient can never be negativeMSET June 2019Partial and Multiple Correlation CoefficientsEasy
- 69Three standard facts about the partial correlation r12.3MSET January 2018 Paper IIPartial and Multiple Correlation CoefficientsMedium
Data Reduction: PCA, Discriminant, Cluster Analysis
- 162Choosing the number of principal componentsMSET June 2025Data Reduction: PCA, Discriminant, Cluster AnalysisHard
- 161Euclidean distance to a cluster centreMSET April 2024Data Reduction: PCA, Discriminant, Cluster AnalysisEasy
- 162What PCA actually reducesMSET April 2024Data Reduction: PCA, Discriminant, Cluster AnalysisMedium
- 162The standard dimension-reduction techniqueMSET March 2023Data Reduction: PCA, Discriminant, Cluster AnalysisEasy
- 109Squared canonical correlations are the eigenvalues of Sigma11^-1Sigma12Sigma22^-1Sigma21MSET January 2018 Paper IIIData Reduction: PCA, Discriminant, Cluster AnalysisMedium
- 107Principal components redistribute, but preserve, the total varianceMSET April 2017 Paper IIIData Reduction: PCA, Discriminant, Cluster AnalysisEasy