# Chapter 3 ML estimation Flashcards Preview

## Econometrics > Chapter 3 ML estimation > Flashcards

Flashcards in Chapter 3 ML estimation Deck (8)
1
Q

Identification condition in ML estimation

A

There is no set of parameters observationally equivalent to the true set of parameters.

Inconsistency of the ML estimator can arise if the likelihood is flat arount the true value => curvature of the likelihood can be interpreted as a measure of the precision of the ML estimate

2
Q

Asymptotic distribution of ML

A

Random sampling is assumed.

• When the likelihood is well specified the information equality applies, as a result the asymptotic variance is simplified.
• The information matrix just measures the curvature of the likelihood function and as such it is a measure of the precision of the estimates
3
Q

Consistency of ML

A
• Identification condition is required.
• Random sampling also, so that LLN applies.
4
Q

Definition of MLE

A
5
Q

Wald test

A

H0: h(theta)=0

H1: h(theta)<>0

• We use the unrestricted estimator.
• In the case of the ML we replace the estimator of the variance by the -1*hessian of the log-likelihood
• The result is true even for mispecified likelihoods
• Notice we just need to compute the unrestricted model
6
Q

LM test

A

Delta tilde is the maximizer of the log likelihood subject to the restriction

• Under the null, its distribution is given by the one below
• Notice for the LM test we just need to compute the restricted estimator
7
Q

LR test

A

Againt theta tilde is the restricted estimator

• Notice that to perform this test we have to compute both the restricted and unrestricted models
• Asymtotic distribution requires a well specified likelihood
8
Q

Nominal size

A

Supposed size of an asymptotic test different of true size of the thest