Do you mean "integral from -2+x to infinity of exp(-y+x-2) dy"? I don't get e2x for that.cutesteph said:f_v(y-x) = integral of -2+x to infinity of exp(-y+x-2) dy = exp(2x) but maximizing this would mean x = infinity?
A maximum likelihood estimator is a statistical method used to estimate the parameters of a probability distribution by identifying the values that make the observed data most likely to occur.
A maximum likelihood estimator works by finding the set of parameter values that maximize the likelihood function, which is a measure of how likely the observed data is to occur under a given probability distribution. This is typically done through an iterative process, such as gradient descent, until the optimal parameters are found.
Maximum likelihood and least squares are both methods for estimating parameters, but they differ in the type of data they are used for. Maximum likelihood is used for estimating parameters of a probability distribution based on data that follows that distribution, while least squares is used for estimating parameters of a linear regression model based on data that has a linear relationship.
The main assumption of maximum likelihood estimation is that the data follows a specific probability distribution. Additionally, it assumes that the data is independent and identically distributed, and that any outliers or influential data points have been properly accounted for.
Some advantages of using maximum likelihood estimation include its versatility in handling a wide range of data types and distributions, its ability to produce unbiased estimates, and its robustness to small sample sizes. It also allows for the incorporation of prior knowledge or assumptions into the estimation process.