Scootertaj said:
Homework Equations
[tex]L(x,p) = \prod_{i=1}^npdf[/tex]
[tex]l= \sum_{i=1}^nlog(pdf)[/tex]
Then solve [tex]\frac{dl}{dp}=0[/tex] for p (parameter we are seeking to estimate)
The Attempt at a Solution
I know how to do this when we are given a pdf, but I'm confused how to do this when we have a sample.
A Maximum Likelihood Estimator (MLE) is a statistical method used to estimate the values of unknown parameters in a probability distribution. It is based on the principle of choosing the parameter values that make the observed data most likely to occur.
The Maximum Likelihood Estimator is calculated by finding the parameter values that maximize the likelihood function. This is typically done using calculus and optimization techniques such as gradient descent.
The main assumptions made in Maximum Likelihood Estimation are that the data follows a specific probability distribution and that the observations are independent and identically distributed.
Maximum Likelihood Estimators have several advantages, including being consistent, efficient, and asymptotically normal. They also have a strong theoretical foundation and can be used in a wide range of statistical models.
Maximum Likelihood Estimators are commonly used in statistical modeling and inference, such as in linear regression, logistic regression, and time series analysis. They are also used in machine learning algorithms, such as in neural networks and hidden Markov models.