Additional Simulations

Additional Simulations

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The chapter discusses the performance of causal forests in simulations, focusing on the bias-variance trade-off and the impact of the number of samples $s$ and features $n$. It is observed that causal forests are more biased when $s$ is small relative to $n$, and more variable when $s$ is large. The confidence intervals obtained from the infinitesimal jackknife method show close-to-nominal coverage when the mean-squared error matches the average variance estimate. The chapter also examines the performance of causal forests when the signal is spread over a larger number of features, finding that they do not improve significantly over $k$-NN in such settings. Additionally, it explores the necessity of honesty in causal forests for consistency, demonstrating that while honesty is crucial for unbiased results, adaptive forests can perform poorly due to bias, especially in high-dimensional spaces. The chapter concludes with a comparison of the mean-squared error between honest and adaptive forests, showing that honest forests generally outperform adaptive forests, particularly in terms of bias and root-mean-squared error.The chapter discusses the performance of causal forests in simulations, focusing on the bias-variance trade-off and the impact of the number of samples $s$ and features $n$. It is observed that causal forests are more biased when $s$ is small relative to $n$, and more variable when $s$ is large. The confidence intervals obtained from the infinitesimal jackknife method show close-to-nominal coverage when the mean-squared error matches the average variance estimate. The chapter also examines the performance of causal forests when the signal is spread over a larger number of features, finding that they do not improve significantly over $k$-NN in such settings. Additionally, it explores the necessity of honesty in causal forests for consistency, demonstrating that while honesty is crucial for unbiased results, adaptive forests can perform poorly due to bias, especially in high-dimensional spaces. The chapter concludes with a comparison of the mean-squared error between honest and adaptive forests, showing that honest forests generally outperform adaptive forests, particularly in terms of bias and root-mean-squared error.
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[slides and audio] Estimation and Inference of Heterogeneous Treatment Effects using Random Forests