diff --git a/lectures/_config.yml b/lectures/_config.yml index 58c8263f..06cbf120 100644 --- a/lectures/_config.yml +++ b/lectures/_config.yml @@ -147,6 +147,7 @@ sphinx: index_toc.md: intro.md lake_model.md: lake_model_intro.md lln_clt.md: lln_clt_intro.md + mle.md: mle_intro.md # Remote Redirects redirects: ak2: https://python.quantecon.org/ak2.html diff --git a/lectures/_toc.yml b/lectures/_toc.yml index 5c589e6b..5ac39061 100644 --- a/lectures/_toc.yml +++ b/lectures/_toc.yml @@ -25,7 +25,7 @@ parts: numbered: true chapters: - file: simple_linear_regression - - file: mle + - file: mle_intro - file: wealth_tax - file: bayes_intro - caption: Foundations diff --git a/lectures/fitting_distributions.md b/lectures/fitting_distributions.md index 47ea2905..676fd0e6 100644 --- a/lectures/fitting_distributions.md +++ b/lectures/fitting_distributions.md @@ -45,7 +45,7 @@ make the fit as close as possible. This lecture is mainly about the first part. For the second we use just one technique, called the method of moments, leaving -a fuller treatment to {doc}`mle`. +a fuller treatment to {doc}`mle_intro`. Even so, we start with the parameters, since we have to be able to fit a class before we can judge it. @@ -736,7 +736,7 @@ Our estimate of it came from the sample kurtosis, which is a fourth moment, and higher moments are estimated poorly precisely when the tails are heavy. Fitting this distribution by maximum likelihood instead, as we do in -{doc}`mle`, gives $\nu \approx 3.6$ rather than $5.8$, and a smaller KS distance +{doc}`mle_intro`, gives $\nu \approx 3.6$ rather than $5.8$, and a smaller KS distance again. The method of moments is simple and general, but it is not always the best use diff --git a/lectures/mle.md b/lectures/mle_intro.md similarity index 100% rename from lectures/mle.md rename to lectures/mle_intro.md diff --git a/lectures/wealth_tax.md b/lectures/wealth_tax.md index 3f180333..bdff19dd 100644 --- a/lectures/wealth_tax.md +++ b/lectures/wealth_tax.md @@ -40,7 +40,7 @@ survey data. Estimation is challenging because the richest households are under-represented in the data. To fill the gap we model the upper tail of the wealth distribution with a -Pareto distribution, which we fit by {doc}`maximum likelihood `. +Pareto distribution, which we fit by {doc}`maximum likelihood `. We will use the following imports. @@ -282,7 +282,7 @@ which is also where our tax begins. ## Estimating the tail index -In {doc}`mle` we found that the maximum likelihood estimate of the tail index, +In {doc}`mle_intro` we found that the maximum likelihood estimate of the tail index, given observations $x_1, \ldots, x_n$ above a known threshold $u$, is $$ @@ -298,7 +298,7 @@ $$ \ell(\alpha) = \sum_{i: w_i > u} \lambda_i \ln f(w_i; \alpha) $$ -Repeating the calculation in {doc}`mle` with these weights gives +Repeating the calculation in {doc}`mle_intro` with these weights gives $$ \hat \alpha = \frac{\sum_{i: w_i > u} \lambda_i}