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Results tagged with mathematical-statistics
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user 357055
Mathematical theory of statistics, concerned with formal definitions and general results.
7
votes
2
answers
214
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Does the likelihood ratio test violate the likelihood principle?
I've been going over Berger's famous example of negative binomial vs binomial sampling leading to two different p-values conditional on the same observed data. To summarize, suppose we observe 9 tails …
- 161
1
vote
Are there possibilities to determine 95% confidence interval for right skewed data?
Usually integer data, like days, is modeled using a Poisson (or Negative Binomial) regression model, both instances of what is called a generalized linear model (GLM).
$$Y \sim Poisson(\lambda)$$
$$lo …
- 161
7
votes
1
answer
93
views
Why not always use CI's from LRT since they don't require symmetry?
I'm confused on why anyone would appeal to asymptotic normality of mle,
$$\hat{\theta} - \theta_0 \rightarrow^D N(0,I^{-1}(\theta))$$
When we can simply invert the likelihood ratio test
$$L(\hat{\thet …
- 161