update qte notebooks

Author: SvenKlaassen

doc/examples/py_double_ml_pension_qte.ipynb

@@ -17,8 +17,8 @@
    "source": [
     "In this real-data example, we illustrate how the [DoubleML](https://docs.doubleml.org/stable/index.html) package can be used to estimate the effect of 401(k) eligibility and participation on accumulated assets. The 401(k) data set has been analyzed in several studies, among others [Chernozhukov et al. (2018)](https://arxiv.org/abs/1608.00060), see [Kallus et al. (2019)](https://arxiv.org/abs/1912.12945) for quantile effects.\n",
     "\n",
-    "_Remark:_\n",
-    "_This notebook focuses on the evaluation of the treatment effect at different quantiles. For a basic introduction to the [DoubleML](https://docs.doubleml.org/stable/index.html) package and a detailed example of the average treatment effect estimation for the 401(k) data set, we refer to the notebook [Python: Impact of 401(k) on Financial Wealth](https://docs.doubleml.org/stable/examples/py_double_ml_pension.html). The Data sections of both notebooks coincide._\n",
+    "**Remark:**\n",
+    "This notebook focuses on the evaluation of the treatment effect at different quantiles. For a basic introduction to the [DoubleML](https://docs.doubleml.org/stable/index.html) package and a detailed example of the average treatment effect estimation for the 401(k) data set, we refer to the notebook [Python: Impact of 401(k) on Financial Wealth](https://docs.doubleml.org/stable/examples/py_double_ml_pension.html). The Data sections of both notebooks coincide.\n",
     "\n",
     "401(k) plans are pension accounts sponsored by employers. The key problem in determining the effect of participation in 401(k) plans on accumulated assets is saver heterogeneity coupled with the fact that the decision to enroll in a 401(k) is non-random. It is generally recognized that some people have a higher preference for saving than others. It also seems likely that those individuals with high unobserved preference for saving would be most likely to choose to participate in tax-advantaged retirement savings plans and would tend to have otherwise high amounts of accumulated assets. The presence of unobserved savings preferences with these properties then implies that conventional estimates that do not account for saver heterogeneity and endogeneity of participation will be biased upward, tending to overstate the savings effects of 401(k) participation.\n",
     "\n",

doc/examples/py_double_ml_pq.ipynb

@@ -364,7 +364,7 @@
     "collapsed": false
    },
    "source": [
-    "## Quantile Treatment Effects (QTEs)\n",
+    "### Quantile Treatment Effects (QTEs)\n",
     "In most cases, we want to evaluate the quantile treatment effect as the difference between potential quantiles.\n",
     "Here, different quantiles can be estimated in parallel with `n_jobs_models`.\n",
     "\n",
@@ -874,7 +874,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "## Local Potential Quantile Estimation\n",
+    "### Local Potential Quantile Estimation\n",
     "Next, we can initialize our two machine learning algorithms to train the different nuisance elements. As above, we can initialize the `DoubleMLLPQ` objects and call `fit()` to estimate the relevant parameters. To obtain confidence intervals, we can use the `confint()` method."
    ]
   },
@@ -1056,7 +1056,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "## Local Quantile Treatment Effects (LQTEs)\n",
+    "### Local Quantile Treatment Effects (LQTEs)\n",
     "As for quantile treatment effects, we often want to evaluate the (local) treatment effect.\n",
     "To estimate local quantile treatment effects, we can use the `DoubleMLQTE` object and specify `LPQ` as the score. \n",
     "\n",