How deeply does Causal Inference for Data Science cover empirical distribution function?

Defines equal 1/n weighting, relates convergence to the generating distribution, and stops short of proving Glivenko–Cantelli.

Empirical distribution function

As explained in Causal Inference for Data Science

An empirical distribution is a probability distribution formed from a finite sample by assigning equal probability weight to each observation.

An empirical distribution turns a finite sample into a probability distribution by assigning every observation weight 1/n. For five coin tosses yielding H, H, T, T, T, heads has probability 2/5 and tails 3/5. Its expectation equals the sample average, while the unobserved data-generating distribution describes the process that produced the sample. section 1.5.1

Use the empirical distribution to:

Represent an observed dataset as a probability distribution when the data-generating distribution is unavailable. section 4.2.1
Apply the adjustment formula by weighting each observed row equally, giving every configuration probability 1/n. section 4.2.1
Handle continuous variables without requiring integrals in practice, because the empirical distribution has at most n observed outcome values. section 4.2.3

Five coin tosses

Encode heads as 1 and tails as 0. The sample (1, 1, 0, 0, 0) assigns probability 1/5 to each toss, producing an empirical probability of 2/5 for heads and a sample average of 2/5. section 1.5.1

Table 4.4 Empirical distribution in a case with multiple confounders

Y	X	Z ₁	…	Z _p	Empirical probability
y ¹	x ¹	z ¹ ₁	…	z ¹ _p	1/ n
y ²	x ²	z ² ₁	…	z ² _p	…
y ³	x ³	z ³ ₁	…	z ³ _p	1/ n

Inspect how equal 1/n weights represent rows containing outcomes, treatments, and multiple confounders. section 4.2.1

How Causal Inference for Data Science covers it

Cover of Causal Inference for Data Science

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Related concepts

data-generating processequivalent to · A data-generating process is the underlying mechanism, procedure, or probability distribution that produces observed data and their relationships.
probability distributionuses · A probability distribution is a mathematical specification assigning probabilities to the possible values or outcomes of a random variable, with total probability one.
causal adjustmentused by · Causal adjustment estimates a causal effect by conditioning on variables that block noncausal pathways and averaging over their target-population distribution.
sample sizeconfigured by · The number of observations or other units included in a sample, study, or analysis.
statistical sampleproduced by · A statistical sample is one or more observations selected or generated from a population or probability process for analysis.

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