In this paper we present a sensitivity analysis for drawing inferences about parameters that are not estimable from observed data without additional assumptions. We present the methodology using two different examples: a causal parameter that is not identifiable due to violations of the randomization assumption, and a parameter that is not estimable in the nonparametric model due to measurement error. Existing methods for tackling these problems assume a parametric model for the type of violation to the identifiability assumption, and require the development of new estimators and inference for every new model. The method we present can be used in conjunction with any existing asymptotically linear estimator of an observed data parameter that approximates the unidentifiable full data parameter, and does not require the study of additional models.
Díaz, Iván and van der Laan, Mark J., "Sensitivity Analysis for Causal Inference Under Unmeasured Confounding and Measurement Error Problems" (December 2012). U.C. Berkeley Division of Biostatistics Working Paper Series. Working Paper 303.