Hypothesis Testing Flashcards
(13 cards)
1
Q
What is the property of MLE that allows us to peform hypothesis tests
A
- As n tends to infinity, the estimator has mean θ and variance var(θ)
- Asymptotically Normally Distributed
2
Q
What is the formula for the t-statistic
A
- t = θ hat - c / se(θhat)
3
Q
How can we calculate the confidence interval of a t-statistic
A
- θ hat +- t\c * se(θ hat)
4
Q
What is the MLE for a bernoulli
A
- p hat = sum of y / N
- p hat = sample mean
5
Q
What is the variance of a bernoulli in a sample
A
- Var(p hat) = p hat (1 - p hat) / N
- Standard Error p hat se(p hat) = sqrt(var(phat))
6
Q
How to we conclude the result of a t-statistic test
A
- If the |test statistic| is less than the critical value then we cannot reject the H0
7
Q
What does the LR test help with
A
- Deciding which model fits best
- “Likelihood Ratio” test
8
Q
How does the LR-test work
A
- It compares the two likelihoods and tests the hypothesis that there is no difference between the two models
9
Q
- How is the correct model decidied in an LR test
A
- If the null hypothesis is rejected, the model without the restrictions is chosen
10
Q
What does the LR test do analytically
A
- Compares the value of the log likelihood at θ hat with its value at c
- If θ hat and c are close, their difference is close to zero, being in favour of H0, no statistically difference
11
Q
- What is the likelihood ratio test statistic
A
- LR = 2[LnL(θhat) - LnL(c)]
- Asymptotically distributed by chi squared
12
Q
How do we conclude the hypothesis test for a chi squared
A
- If the test statistic is less than the critical value, we cannot reject the H0
13
Q
How does the Wald test work
A
- Takes the sqaure of the distance between θ hat and c
