Suppose that the probability density function of the random variable X is if , and 0 otherwise, where is an unknown parameter. Based on a single observation X, the confidence coefficient of the confidence interval [(2/5)X, (5/2)X] for is
Part BCSIR NET December 2024only-one-side-of-the-interval-can-fail
Only one side of the interval can fail
Related counterexample: The MLE is unbiased
- Part B questionDecember 2023
- shifted exponentialDecember 2023
- the components do not overlap so y is observedDecember 2024
- the prior adds one to the exponentDecember 2024
- the parameter space is open so the extremes have no mleDecember 2024
- the maximum tracks the upper endpointDecember 2024
The chapter behind this: Maximum likelihood and the method of moments — free to read