Bandwidth parameter

As explained in Causal Inference for Data Science

A bandwidth is a positive radius that determines the neighborhood of observations receiving nonzero or substantial weight in a local regression.

In local linear regression, the bandwidth h sets how much nearby data influences a prediction at t0. A positive h includes observations in [t0 − h, t0 + h], while kernel weights can give closer observations greater influence. section 11.2.5

Changing the bandwidth changes the local estimate:

• A smaller window focuses on observations very near the target timepoint. section 11.2.5
• A larger window uses more observations but may include points less representative of the target neighborhood. section 11.2.5
• Uniform kernels give included observations equal weight; triangular kernels decrease weight with distance. section 11.2.5

Varying the time window

RDD estimates can be recomputed across time windows, such as 10 down to 4. Comparing estimates and confidence intervals shows how sensitive the estimated effect is to the bandwidth.

Figure 11.11 Triangular kernel

Compare uniform and triangular kernel shapes to see how bandwidth and distance determine observation weights. section 11.2.5

How Causal Inference for Data Science covers it

How deep it goes

Defines interval selection and kernel weighting, then compares estimates across windows without deriving bandwidth selection.

Examples

Demonstrates uniform and triangular kernels and regression estimates across time windows from 10 down to 4.

What it assumes

Builds on ordinary least squares and assumes familiarity with regression discontinuity designs and residual minimization.

What you can do after

Apply it via local regression and compare effect estimates and confidence intervals across candidate windows.

How it connects

Connects local linear regression, ordinary least squares, kernels, regression discontinuity designs, and confidence intervals.

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Related concepts

• kernel density estimateconfigures · A kernel density estimate is a nonparametric probability-density estimate formed by combining localized kernel functions centered on observed data points.
• local linear regressionconfigures · Local linear regression estimates a locally linear relationship by fitting weighted linear models around each prediction point.

This explainer was generated by Manning's knowledge graph from the text of Causal Inference for Data Science. The section links point to the parts of the book it draws on.