Hypothesis test based on the approximate normal distribution of the maximum likelihood estimator.
Questions tagged [wald-test]
76 questions
8
votes
1 answer
Why use the Wald test in logistic regression?
Some statistical software use the Wald statistic when reporting on the regression coefficients. As examples, R and Stata report Wald by default.
The logistic regression article on Wikipedia says, unfortunately without reference:
“Rather than the…
Single Malt
- 504
- 1
- 5
- 15
8
votes
1 answer
Which variance estimate to use for a Wald test?
I have seen the following justification for the Wald test of the null hypothesis $H_0: \theta = \theta_0$ for a scalar parameter $\theta$. When $\hat{\theta}_n$ is the MLE for $\theta$ estimated from an independent sample of size $n$, under the null…
ravstat
- 81
- 2
7
votes
1 answer
Why need wald test ( a squared version of t test ) when we already have t test?
It seems to me that they are basically calculate the same thing. Since we already have t-test, why do we need a squared version (wald test)? Does wald test have its own advantage? For example in Cox model, why can't we just use t test?
unicorn
- 739
- 4
- 13
6
votes
1 answer
Asymptotic equivalence of Likelihood Ratio Statistic and Wald Statistic?
When we say the likelihood ratio statistic and the Wald statistic of a set of binomial distributions are asymptotically equivalent, do we mean that the sampling distributions of the two statistics will get close as we take larger samples of both…
HDB
- 249
- 1
- 6
6
votes
1 answer
Where are the Wald p-values and where are the LRT ones in the resulf of mixed models?
I read, that there are many methods of determining the degrees of freedom, thus calculating the p-values for fixed effects in mixed models. I read, that the worst is the Wald test and the Log-Likelihood test is a little bit better. So many names.…
Damasco
- 163
- 4
5
votes
0 answers
Standard error of the coefficient in GLM
I'm trying to learn about Wald test.
I know, that its test statistics is
$$
t = \frac{\beta_i}{se\left( \beta_i \right)}
$$
But, how is standard error $se$ computed in GLM? I've found only the case with linear model mentioned here.
I've also found…
Eenoku
- 443
- 8
- 17
4
votes
2 answers
Asymptotic Distribution of the Wald Test Statistic
I am trying to understand the asymptotic distribution of the Wald test statistic, specifically under the alternative hypothesis which I've found little reference to.
For clarity, the binary hypothesis for an unknown parameter vector $\theta$ of size…
pellis
- 41
- 4
3
votes
1 answer
Distribution of the F-statistic of a Wald test
On the Wikipedia page for the Wald test, there is a derivation for the test statistic under multiple hypotheses. The derivation ends in an F-distribution. I am curious about the final step in that derivation, repeated below.
Suppose $\hat{\theta}_n$…
Michael Gmeiner
- 120
- 9
3
votes
0 answers
Wald Test with one-sided alternative hypothesis
it is not clear to me what happens if I want to use the Wald test to test a simple hypothesis vs a one-sided alternative. I know that if I have $H_0: \theta = \theta_0$ vs $H_1: \theta \neq \theta_0$, the statistics $$
W =(\widehat{\theta} -…
John Giorgio
- 145
- 4
3
votes
1 answer
Why should one do Wald test after linear regression
I see that the Wald test can be performed on the model obtained from linear regression as shown here. I understand that it gives information whether a predictor is adding significant value to outcome variable. However, I am not clear why Wald test…
rnso
- 8,893
- 14
- 50
- 94
3
votes
1 answer
How can these two expressions both converge in distribution to N(0, 1)?
In All of Statistics, chapter 11 (pg. 183), Larry Wasserman states in his description of the Wald Test:
We are testing the null hypothesis $ \hat{\theta} = \theta_0 $ versus the alternative hypothesis $ \theta \neq \theta_0 $.
He then says we…
an1lam
- 146
- 10
3
votes
1 answer
Likelihood ratio, Wald, and Score are equivalent?
In Foundations of Linear and Generalized Linear Models, Agresti makes a comment on page 131 about likelihood ratio, Wald, and Score testing of regression parameters.
For the best-known GLM, the normal linear model, the three types of
inference…
Dave
- 28,473
- 4
- 52
- 104
3
votes
1 answer
Difference between Wald test and Chi-squared test
I am aware that both tests assume Chi-square distribution of data. Here are what I know:
Wald test as multi-variable generalization of student's t-test tests the statistical difference of mean between groups. Chi-squared test on the other hand tests…
unicorn
- 739
- 4
- 13
3
votes
2 answers
Is it possible to generate power curves for score-tests, wald-test, LR test?
A power curve is something in the example
Do score-tests, wald-test, LR test have power curves?
What do they look like?
user271077
3
votes
1 answer
Wald test standard error
I want to compute from scratch a Wald test to test significance of one coefficient in a logistic regression model. I've been to so many posts and blogs but couldn't find a clear explanation with sample calculation for a NON-EXPERT like me.
My basic…
aerijman
- 143
- 5