What is generalized likelihood ratio test?

The Generalized Likelihood Ratio Test (GLRT) is a statistical test used to compare two statistical models, one of which is nested within the other. It is commonly used in hypothesis testing when we need to test if two models fit a given set of data and identify the better-fitting model. The null hypothesis is that the simpler model is the better fit and the alternative hypothesis is that the more complex model fits the data better. The GLRT compares the maximum likelihoods of both models to calculate a likelihood ratio test statistic. The test statistic is then compared to a known distribution (usually the chi-square distribution) to determine if the difference in fit between the two models is statistically significant. The GLRT is a powerful tool that has wide applications in various fields including engineering, economics, and medicine.