Effects of Mahalanobis Distance and Prior Probabilities

Effects of Mahalanobis Distance and Prior Probabilities

On the Performance of the Linear and Quadratic Discriminant Functions: A Monte Carlo Approach

LAP Lambert Academic Publishing ( 2011-11-09 )

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In Discriminant analysis, one requires a relatively large training sample to construct a discriminant function and evaluate its performance. This is often unattainable in practice and so numerous Monte Carlo studies have been undertaken in an attempt to shed light on the asymptotic properties of classification functions. This empirical study examines the asymptotic performance of normal-based Linear and Quadratic discriminant functions for observations from two multivariate normal populations with different prior probabilities and varying between group distances. The sensitivity of these functions to increase in sample size, prior probability and Mahalanobis distance is investigated. Four sample size ratios of group1 to group2 (n1:n2) considered are: (1:1), (1:2), (1:3), and (1:4). Sample sizes ranging from 25 to 3,000 were considered for values 1 to 7 of group centroid separator. Multivariate normal observations were generated for two P-variate populations with p=4, p=6, and p=8 (LDF(4), LDF(6) , LDF(8), QDF(4), QDF(6) and QDF(8)) models. The respective sample size-ratio combinations were repeated for each level of with 100 replications for each scenario.

Book Details:

ISBN-13:

978-3-8465-2416-9

ISBN-10:

3846524166

EAN:

9783846524169

Book language:

English

By (author) :

Atinuke Adebanji
Sagary Nokoe

Number of pages:

144

Published on:

2011-11-09

Category:

Other