Estimating the Mahalanobis Distance from Mixed Continuous and Discrete Data

We present a method for estimating the Mahalanobis distance between two multivariate normal populations when a subset of the measurements is observed as ordered categorical responses. Asymptotic properties of the proposed estimator are developed. Two examples are discussed.

[1]  C. Cleland.  Focal-Diffuse Model: An Evolutionary Perspective On the Prehistoric Cultural Adaptations of the Eastern United States , 1976 .

[2]  Jean-Jacques Daudin,et al.  Generalization of the Mahalanobis distance in the mixed case , 1995 .

[3]  J. Blangero,et al.  Population structure analysis using polygenic traits: estimation of migration matrices. , 1990, Human biology.

[4]  Calyampudi Radhakrishna Rao,et al.  Linear Statistical Inference and its Applications , 1967 .

[5]  Wai-Yin Poon,et al.  Maximum likelihood estimation of multivariate polyserial and polychoric correlation coefficients , 1988 .

[6]  Wojtek J. Krzanowski,et al.  Discrimination and Classification Using Both Binary and Continuous Variables , 1975 .

[7]  Stephen Plog,et al.  Evolution of “Tribal” Social Networks: Theory and Prehistoric North American Evidence , 1982, American Antiquity.

[8]  J. Blangero,et al.  Anthropometric variation and the genetic structure of the Jirels of Nepal. , 1989, Human biology.

[9]  Karl G. Jöreskog,et al.  On the estimation of polychoric correlations and their asymptotic covariance matrix , 1994 .

[10]  Richard W. Jefferies.  Middle Archaic Bone Pins: Evidence of Mid-Holocene Regional-Scale Social Groups in the Southern Midwest , 1997, American Antiquity.

[11]  David J. Hand,et al.  Discrimination and Classification , 1982 .

[12]  M. Ivaldi.  Estimation of errors-in-latent-variable models on business survey data , 1992 .

[13]  G Molenberghs,et al.  Multivariate probit analysis: a neglected procedure in medical statistics. , 1991, Statistics in medicine.

[14]  W. Krzanowski.  Distance between populations using mixed continuous and categorical variables , 1983 .

[15]  David G. Anderson,et al.  Early Archaic Settlement in the Southeastern United States: A Case Study from the Savannah River Valley , 1988, American Antiquity.

[16]  S WRIGHT,et al.  Genetical structure of populations. , 1950, Nature.

[17]  Ingram Olkin,et al.  Multivariate Correlation Models with Mixed Discrete and Continuous Variables , 1961 .

[18]  P. Wiessner,et al.  Hxaro: a regional system of reciprocity for reducing risk among the !Kung San , 1977 .

[19]  M. Kimura,et al.  The Stepping Stone Model of Population Structure and the Decrease of Genetic Correlation with Distance. , 1964, Genetics.

[20]  L. Konigsberg.  Analysis of prehistoric biological variation under a model of isolation by geographic and temporal distance. , 1990, Human biology.

[21]  J A Anderson,et al.  The grouped continuous model for multivariate ordered categorical variables and covariate adjustment. , 1985, Biometrics.

[22]  J. Powell.  Dental variation and biological affinity among middle Holocene human populations in North America , 1995 .

[23]  R D Bock,et al.  High-dimensional multivariate probit analysis. , 1996, Biometrics.

[24]  Sik-Yum Lee,et al.  Estimation of polychoric correlation with elliptical latent variables , 1988 .

[25]  J. R. Caldwell.  Trend and tradition in the prehistory of the eastern United States , 1959 .

[26]  J. Relethford,et al.  Craniometric variation, genetic theory, and modern human origins. , 1994, American journal of physical anthropology.