Browsing by Author "Osei-Tutu, Olivia"

Now showing 1 - 1 of 1
  • Thumbnail Image
    Item
    Robustness of the Quadratic Discriminant Function to Correlated and Skewed Training Samples
    (2012-06-13) Osei-Tutu, Olivia
    This study investigates the asymptotic performance of Quadratic Discriminant Function and its robustness when the training samples are correlated normal or skewed. The scenarios considered were correlated normal, uncorrelated normal and skewed distribu- tions. Three populations (Πi, i = 1, 2, 3) with increasing group centroid separator function (δ = 1, 2, 3, 4, 5) were considered. The number of predictor variables were 4, 6, and 8 with sample size ratios 1:1:1, 1:2:2 and 1:2:3. We simulated N (µi, Σi) of sample size 30, 60, 100, 150, 250, 300, 400, 500, 600, 700 and 2000 with MatLabR2009a for p variables in Π1. The sizes of Π2 and Π3 are determined by sample ratios at 1:1:1, 1:2:2 and 1:2:3 for n1 : n2 : n3 and these ratios also determine the prior probabilities considered. The population means were µ1 = (0, 0, 0, . . . , 0), µ2 = (0, 0, 0, . . . , δ) and µ3 = (0, 0, 0, . . . , 2δ) respectively. The covariance matrix Σi has σkl = 0.7 and σ2 = i for k = l, i = 1, 2, 3. Reduction in error rates was more pronounced with increase in Mahalanobis distance than asymptotically. The coefficients of variation for sample size ratio 1:2:3 was more volatile under the three distributions considered. The optimal sample size ratio for the three distributions is 1:1:1. The results show the correlated normal distribution exhibits high coefficient of variation as δ increased. Further results show that the Quadratic Discriminant Function perform poorly when the training samples were skewed therefore, uncorrelated normal distribution was preferred