Linear discrimination with equicorrelated training vectors

Fisher's linear discrimination rule requires uncorrelated training vectors. In this paper a linear discrimination method is developed to be used when the training vectors are equicorrelated. Also, maximum likelihood ratio tests are proposed to decide whether the training samples are uncorrelated or equicorrelated.

[1]  Muni S. Srivastava,et al.  On Tukey's Confidence Intervals for the Contrasts in the Means of the Intraclass Correlation Model , 1973 .

[2]  A. Donner,et al.  Inferences concerning a common intraclass correlation coefficient. , 1983, Biometrics.

[3]  Myriam Herrera,et al.  Generalización de la distancia de mahalanobis para el análisis discriminante lineal en poblaciones con matrices de covarianza desiguales , 1999 .

[4]  Allan Donner,et al.  Testing the equality of dependent intraclass correlation coefficients , 2002 .

[5]  M. Bartlett.  An Inverse Matrix Adjustment Arising in Discriminant Analysis , 1951 .

[6]  Selecting variables for discrimination when covariance matrices are unequal , 1994 .

[7]  P. Mahalanobis.  On the generalized distance in statistics , 1936 .

[8]  T. O. Lewis,et al.  Determining the effects of intraclass correlation on factorial experiments , 1980 .

[9]  Madhusudhan Bhadary,et al.  Test for the equality of interclass correlation cofefficients under unequal family sizes for several populations , 2000 .

[10]  G. McLachlan.  Discriminant Analysis and Statistical Pattern Recognition , 1992 .

[11]  D. Harville.  Matrix Algebra From a Statistician's Perspective , 1998 .

[12]  John A. Richards,et al.  Remote Sensing Digital Image Analysis: An Introduction , 1999 .

[13]  Arjun K. Gupta,et al.  Nonnull distribution of the likelihood ratio criterion for testing equality of covariance matrices under intraclass correlation model , 1987 .

[14]  R. Fisher.  THE USE OF MULTIPLE MEASUREMENTS IN TAXONOMIC PROBLEMS , 1936 .

[15]  D. J. Young,et al.  Test for equality of intraclass correlation coefficients under unequal family sizes. , 1998, Biometrics.

[16]  C. Radhakrishna Rao,et al.  DISCRIMINATION OF GAUSSIAN PROCESSES , 1965 .

[17]  D. Goldgar,et al.  Comparison of intracalss correlation coefficients with the ratio of two independent f-statistics , 1980 .

[18]  R. K. Barnwal,et al.  Maximum likelihood estimation and a C(α) test for a common intraclass correlation , 1990 .

[19]  M. Okamoto.  An Asymptotic Expansion for the Distribution of the Linear Discriminant Function , 1963 .

[20]  A. Kshirsagar,et al.  Distances between normal populations when covariance matrices are unequal , 1994 .

[21]  LIKELIHOOD RATIO TEST OF EQUALITY OF SEVERAL VARIANCES IN THE INTRACLASS CORRELATION MODEL , 2001 .

[22]  Arjun K. Gupta,et al.  Testing the equality of several intraclass correlation coefficients , 1989 .

[23]  S. Paul.  Maximum likelihood estimation of intraclass correlation in the analysis of familial data : estimating equation approach , 1990 .

[24]  Patrick L. Odell,et al.  Effect of intraclass correlation among training samples on the misclassification probabilities of bayes procedure , 1974, Pattern Recognit..

[25]  Shahjahan Khan,et al.  Predictive inference on equicorrelated linear regression models , 1998, Appl. Math. Comput..

[26]  M. Shoukri,et al.  On the estimation of the intraclass correlation , 1984 .

[27]  T. W. Anderson,et al.  An Introduction to Multivariate Statistical Analysis , 1959 .

[28]  Combined estimators for the correlation coefficient , 1982 .

[29]  T. W. Anderson.  An Introduction to Multivariate Statistical Analysis , 1959 .

[30]  G. Chaudhuri,et al.  Bhattacharyya distance based linear discriminant function for stationary time series , 1991 .

[31]  Calyampudi R. Rao,et al.  Testing intraclass correlation coefficients , 1989 .

[32]  M. Viana.  Combined maximum likelihood estimates for the equicorrelation coefficient. , 1994, Biometrics.