How to visualize convergence in probability and the weak law of large numbers directly and honestly
Convergence in probability is fundamental to statistical inference. It underpins most large-sample approximations, while consistency is a basic requirement for any sensible estimator. While the formal definition is simple, building an intuitive understanding is a bit challenging. This post explores two “honest” ways to visualize convergence in probability, using the law of large numbers as an example.
Posted in Statistics / Inference on Python, Simulations, Inference
Why simultaneous hypothesis tests are better — but not always — than adjusted multiple tests
When testing multiple hypotheses in a regression, why do we use simultaneous (joint) tests instead of just adjusting the \(p\)-values from separate \(t\)-tests? The usual answer is a vague statement that simultaneous tests are more powerful. This post quantifies that statement and also finds that the story is more nuanced than that.
Posted in Statistics / Heterogeneity on Python, Simulations, Heterogeneity
Why adding (more) fixed effects is not a silver bullet for the problem of unobserved heterogeneity and 3 things you can do about it.
A common approach to controlling for unobserved heterogeneity is to run a linear regression with fixed effects. This post shows that this strategy may lead to strong bias in more realistic settings, even if you specify the fixed effects correctly. It is also about some things you can do about it.
Posted in Simulations / Tools on Matlab, Simulations
An easy way to track progress in parallel for loops in Matlab
Running parallelized Monte Carlo simulations in Matlab is easy with parfor loops. But there’s a catch: how can you know how much of the work is done and how much is left?
This post is about an efficient and easy visual way to keep track of progress in parfor loop (and some less obvious Matlab features I learned about when trying to figure it out).
