Identification in Parametric Models¶
Rothenberg, T. J. (1971). Identification in Parametric Models. Econometrica, 39(3), 577-591.
Cited by¶
3 citations across 3 artifacts.
Each citation links to the sentence it supports in the citing article.
Primes¶
- Observational Equivalence
- The prime therefore separates sameness for an observer under stated access conditions from sameness in all respects.
This sourceDefines observationally equivalent structures by exact equality of their observable probability distributions.
- The prime therefore separates sameness for an observer under stated access conditions from sameness in all respects.
Domain-specific¶
- Kernel
- Linear algebra — the null space: ker(T) as a subspace, paired with the image by rank–nullity (dim im + dim ker = dim V) and reconstructed by the first isomorphism theorem V/ker T ≅ im T. Group theory — the normal subgroup: the kernel of a homomorphism, with G/ker φ ≅ im φ, the data quotiented out to expose the faithful part. Ring and module theory — the ideal (or submodule): the kernel of a ring or module homomorphism, the same triviality criterion and quotient reconstruction porting verbatim. Statistics — parameter identifiability: the kernel of the likelihood-to-parameter map, a non-trivial kernel marking exactly which parameter directions the data cannot distinguish
This sourceEstablishes that local identifiability of a parameter vector is equivalent to nonsingularity of the information matrix.
Supported in partVerified against the publisher's abstract
“It is shown under weak regularity conditions that local identifiability of the unknown parameter vector is equivalent to nonsingularity of the information matrix.”
- Linear algebra — the null space: ker(T) as a subspace, paired with the image by rank–nullity (dim im + dim ker = dim V) and reconstructed by the first isomorphism theorem V/ker T ≅ im T. Group theory — the normal subgroup: the kernel of a homomorphism, with G/ker φ ≅ im φ, the data quotiented out to expose the faithful part. Ring and module theory — the ideal (or submodule): the kernel of a ring or module homomorphism, the same triviality criterion and quotient reconstruction porting verbatim. Statistics — parameter identifiability: the kernel of the likelihood-to-parameter map, a non-trivial kernel marking exactly which parameter directions the data cannot distinguish
Mechanisms¶
- Redundant-Variable Elimination
- Its failure mode is eliminating a direction that is not actually redundant — a parameter that is weakly but genuinely identifiable, or one the current data misses but a richer design would resolve — thereby baking a false constraint into the model.
This sourceLocal parameter identifiability depends on whether the observations contain enough information to distinguish nearby parameter values.
- Its failure mode is eliminating a direction that is not actually redundant — a parameter that is weakly but genuinely identifiable, or one the current data misses but a richer design would resolve — thereby baking a false constraint into the model.
Verification¶
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