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Variance Laplacian: Quadratic Forms in Statistics

EasyChair Preprint no. 821, version 9

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40 pagesDate: November 16, 2021


In  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: eigenvalues, Eigenvectors, Laplacian matrix, quadratic form, variance

BibTeX entry
BibTeX does not have the right entry for preprints. This is a hack for producing the correct reference:
  author = {Rama Murthy Garimella},
  title = {Variance  Laplacian:  Quadratic  Forms  in  Statistics},
  howpublished = {EasyChair Preprint no. 821},

  year = {EasyChair, 2021}}
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