Download PDFOpen PDF in browserVariance Laplacian: Quadratic Forms in StatisticsEasyChair Preprint 821, version 940 pages•Date: November 16, 2021AbstractIn this research paper, it is proved [RRN] that the variance of a discrete random variable, Z can be expressed as a quadratic form associated with a Laplacian matrix i.e. Variance Z= X transpose G X, where X is the vector of values assumed by the discrte random variable and G is the Laplacian matrix whose elements are expressed in terms of probabilities. We formally state and prove the properties of Variance Laplacian matrix, G. Some implications of the properties of such matrix to statistics are discussed. It is reasoned that several interesting quadratic forms can be naturally associated with statistical measures such as the covariance of two random variables. It is hoped that VARIANCE LAPLACIAN MATRIX G will be of significant interest in statistical applications. The results are generalized to continuous random variables also. Keyphrases: Eigenvectors, Laplacian matrix, eigenvalues, quadratic form, variance
|