Abstract
Different forms of discriminant functions and the essence of their appearances were considered in this study. Various forms of classification problems were also considered, and in each of the cases mentioned, classification from simple functions of the observational vector rather than complicated regions in the higher-dimensional space of the original vector were made. Ever since the emergence of the Linear Discriminant Function (LDF) by Fisher, several other classification statistics have emerged and violation of condition of equal variance covariance matrix for Linear Discriminant Function (LDF) results to Quadratic Discriminant Function (QDF). While the Best Linear Discriminant Function (BLDF) is referred to Best Sample Discriminant Function (BSDF) when the parameters are estimated from a sample and also optimal in the same sense as Quadratic Discriminant Function (QDF), Rao statistic is best for discriminating between options that are close each other. The relationships among the classification statistics examined were established: Among the methods of classification statistics considered, Anderson’s (W) and Rao’s (R) statistics are equivalent when the two sample sizes n<sub>1</sub> and n<sub>2</sub> are equal, and when a constant is equal to 1, W, R and John-Kudo’s (Z) classification statistics are asymptotically comparable. A linear relationship is also established between W and Z classification.
Highlights
Discriminant analysis is a statistical method used for classification of objects into mutually exclusive and exhaustive groups on the basis of a set of independent variables
( ) ( ) C X,; μ, μ ; Σ = μ − μ 1 Σ−1 X. It assigns p-dimensional observation vector, X, into one of the two populations, π i (i = 1, 2), and it is employed as an assignment rule when the following assumptions are satisfied: The density functions of observations from populations π1 and π2 are multivariate normal; (πi ∼ N p, i = 1, 2) ; the variance-covariance matrix (Σ1) in population, π1 is the same as (Σ2 ) in population π2 ; the prior probabilities of observations coming from populations π1 and π2 are known; the parameters of the density functions are known
Suppose that n1 = n2 = n, α = 1, there is a linear relationship between Z and W statistics expressed as focus of research since the introduction of Fisher’s Linear Discriminant Function (FLDF)
Summary
Discriminant analysis is a statistical method used for classification of objects into mutually exclusive and exhaustive groups on the basis of a set of independent variables. The method handles two or multiple group problems It derives linear combinations of the independent variables that discriminate between the a priori defined groups, such that the error rates misclassification are minimized as much as possible [20]. (vi) In a hospital, a patient is admitted with a diagnosis of myocardial infarction, and systolic blood pressure, heart rate, stroke index and mean arterial pressure are obtained by the Doctor. Is it possible to predict whether the patient will survive? It is assumed that historic data are readily available to assist in determining an assignment rule [20]
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