Maximum Likelihood Estimates (MLE) refer to the statistical method used to estimate the parameters of a statistical model that maximizes the likelihood function. It is based on the principle that the most likely set of parameter values is the one that maximizes the probability of observing the given data.
In a statistical model, MLE calculates the values of the parameters that make the observed data most probable under the assumed distribution. It assumes that the data points are independent and identically distributed (i.i.d).
To find these estimates, MLE uses an iterative process called optimization, such as the method of gradient descent, to iteratively adjust the parameter values until the likelihood function is maximized or the convergence criterion is met.
MLE has several desirable properties, including consistency, asymptotic efficiency, and asymptotic normality. Consistency ensures that as the sample size increases, the estimated parameters converge to the true values. Asymptotic efficiency implies that MLE provides the most efficient estimates among all consistent estimators. Asymptotic normality states that the distribution of the MLE approaches a normal distribution as the sample size grows, enabling the estimation of confidence intervals and hypothesis testing.
MLE is widely used in various fields, including probability theory, statistics, econometrics, and machine learning. It serves as a powerful tool for estimating parameters in complex models.
