Research and Analysis of MLE Based on Maximum Likelihood Estimation

This paper presents an in-depth exploration of Maximum Likelihood Estimation (MLE), a paramount method in the domains of statistics and machine learning for parameter estimation. MLE's theoretical underpinnings are discussed, detailing both likelihood and log-likelihood functions and their integral mathematical properties. The estimation process is outlined, emphasizing MLE's applications across various fields such as biostatistics and machine learning through concrete examples. Noteworthy is MLE's dual role in both parameter estimation and model validation, supported by its consistency and asymptotic normality which enhances its applicability in analytical scenarios. However, the study also addresses MLE's limitations, particularly the challenges posed by computational complexity and small sample sizes. Solutions to mitigate these issues are proposed, enhancing MLE's robustness and utility in practical applications. This comprehensive analysis not only clarifies MLE's operational mechanics but also underscores its versatility and pivotal role in advancing empirical research across multiple scientific disciplines.