diff --git a/lectures/_config.yml b/lectures/_config.yml index e7ec9b45..58c8263f 100644 --- a/lectures/_config.yml +++ b/lectures/_config.yml @@ -146,6 +146,7 @@ sphinx: rediraffe_redirects: index_toc.md: intro.md lake_model.md: lake_model_intro.md + lln_clt.md: lln_clt_intro.md # Remote Redirects redirects: ak2: https://python.quantecon.org/ak2.html diff --git a/lectures/_toc.yml b/lectures/_toc.yml index 0d898865..5c589e6b 100644 --- a/lectures/_toc.yml +++ b/lectures/_toc.yml @@ -19,7 +19,7 @@ parts: - file: observed_distributions - file: fitting_distributions - file: bivariate_dist - - file: lln_clt + - file: lln_clt_intro - file: heavy_tails - caption: Estimation numbered: true diff --git a/lectures/heavy_tails.md b/lectures/heavy_tails.md index 0aa8a450..f6bb8143 100644 --- a/lectures/heavy_tails.md +++ b/lectures/heavy_tails.md @@ -952,7 +952,7 @@ Averaging tends to eliminate extreme outcomes. One impact of heavy tails is that sample averages can be poor estimators of the underlying mean of the distribution. -To understand this point better, recall {doc}`our earlier discussion ` +To understand this point better, recall {doc}`our earlier discussion ` of the law of large numbers, which considered IID $X_1, \ldots, X_n$ with common distribution $F$ If $\mathbb E |X_i|$ is finite, then diff --git a/lectures/lln_clt.md b/lectures/lln_clt_intro.md similarity index 100% rename from lectures/lln_clt.md rename to lectures/lln_clt_intro.md diff --git a/lectures/markov_chains_II.md b/lectures/markov_chains_II.md index e6da714e..88e62eb9 100644 --- a/lectures/markov_chains_II.md +++ b/lectures/markov_chains_II.md @@ -196,7 +196,7 @@ This gives us another way to interpret the stationary distribution (provided irr Importantly, the result is valid for any choice of $\psi_0$. -The theorem is related to {doc}`the law of large numbers `. +The theorem is related to {doc}`the law of large numbers `. It tells us that, in some settings, the law of large numbers sometimes holds even when the sequence of random variables is [not IID](iid_violation). diff --git a/lectures/monte_carlo.md b/lectures/monte_carlo.md index 0a9ec14e..bc70c2ea 100644 --- a/lectures/monte_carlo.md +++ b/lectures/monte_carlo.md @@ -140,7 +140,7 @@ This is the Monte Carlo method, which runs as follows: This average will be close to the true mean when $n$ is large. -This is due to the law of large numbers, which we discussed in {doc}`lln_clt`. +This is due to the law of large numbers, which we discussed in {doc}`lln_clt_intro`. We use the following values for $p$ and each $\mu_i$ and $\sigma_i$. diff --git a/lectures/observed_distributions.md b/lectures/observed_distributions.md index 88019ea8..05c943e0 100644 --- a/lectures/observed_distributions.md +++ b/lectures/observed_distributions.md @@ -909,7 +909,7 @@ print(f'{"":16}population mean = {u.mean():.4f}') ``` This convergence is a version of the *law of large numbers*, which we discuss -in {doc}`lln_clt`. +in {doc}`lln_clt_intro`. ### The role of independence @@ -973,5 +973,5 @@ What matters is that new observations keep bringing new information, which the example above destroys entirely. The general question of what a sample can tell us about its distribution is -taken up in {doc}`lln_clt`. +taken up in {doc}`lln_clt_intro`. ```