A New and Efficient Approach for Estimating Probabilities of Misclassification and Discrimination

This study proposed a new and efficient approach for estimating probabilities of misclassification and discrimination.The study explores the estimation of apparent and optimum probabilities of misclassification for three populations using reallife anthropometric data. It also compares the effectiveness of Linear Discriminant Analysis (LDA) and Quadratic Discriminant Analysis (QDA) in classifying data from three distinct populations, assessing their accuracy and reliability. Real life anthropometric datasets were utilized, and both stratified random and simple random sampling techniques were employed, comprising three populations of school students with four variables.A computer programming language codes were written via R-Studio package to solve the numerical problems posed in the study. The model misclassified around 4.86% of observations for Linear Discriminant Analysis (LDA) and approximately 3.71% for Quadratic Discriminant Analysis (QDA). QDA showed higher accuracy (98.76% vs. 98.38%) and lower error rate (1.24% vs. 1.62%) compared to LDA. Additionally, QDA demonstrated excellent discriminatory power with a perfect AUC-ROC score.The study shown that QDA outperformed LDA in terms of accuracy and error rates, demonstrating superior discriminatory power. This study provided valuable insights for those working with datasets involving multiple populations and variables with potential applications in various fields such as multivariate methods, data science, machine learning, business, healthcare and finance. Furthermore, the study offers a practical approach to classifying observations into distinct populations using LDA and QDA, achieving high accuracy rates for real-life data scenarios. It establishes a foundation for future research endeavours andpresents a comprehensive framework for comparing LDA and QDA performance in ESD data, highlighting the effectiveness of QDA in handling skewed data for multiple populations .The research recommended further exploration into developing a generalized model for estimating probabilities of misclassification via ESD with flexible distribution assumptions and robust estimation methods.