10.1 Identification versus estimation

10.1 Identification versus estimation

• An estimator is consistent for an estimand if the estimates get closer to the to the patameter as the sample size increases
• If the sample size size is small consistent estimators may produce estimates that are far from the super population value (estimand)

10.1 Identification versus estimation

• 95% confidence interval is calibrated if it contains the estimand in more than 95% of random samples
• 95% confidence interval is conservative if it contains the estimand in more than 95% of samples
• 95% confidence interval is anticonservative if it does not contain the estimand in more than 95% of samples
• 95% confidence interval is valid if for any value of the true parameter the confodence interval is either calibrated or conservative (covers the true parameter at least 95% of the time)
• 95% confidence interval is frequentist

Estimation of causal effects

• Due to random variability, we cannot expect that exchangeability will always precisely hold in the sample
• "Because of the presence of random sampling variability, we do not expect that exchangeability will exactly hold in our sample"

10.3 The myth of the super population

• Scenario 1: Infinite super population (source or target population)
  • Convenient fictions --> simpler statistical methods & ease of generalization
• Scenario 2: Each sampled individual has a non-deterministic (stochastic) probability of a potential outcome

10.4 The conditionality “principle”

• Random non-exchangeability
• Random observed A-L associations are ancillary statistic for the causal risk difference
• "The conditionality principle states that inference on a parameter should be performed conditional on ancillary statistics"

10.5 The curse of dimensionality

• 100 pre-treatment binary variables produce $2^{100}$ strata

References

Hernán MA, Robins JM (2020). Causal Inference: What If. Boca Raton: Chapman & Hall/CRC (v. 31jan21)