Theory of Point Estimation¶
Lehmann, E. L., & Casella, G. (1998). Theory of Point Estimation. Springer.
Cited by¶
3 citations across 3 artifacts.
Each citation links to the sentence it supports in the citing article.
Primes¶
- Distributional Assumption
- It separates unbounded possibility space from a constrained-but-tractable family of distributions, trading expressiveness for computational and inferential power, a structure Lehmann and Casella (1998) develop rigorously in their treatment of parametric estimation theory.
This sourceCanonical rigorous treatment of parametric estimation theory: develops maximum-likelihood, sufficiency, the Cramér–Rao bound, and efficiency within an assumed distributional family — the formal machinery that converts the infinite-dimensional inference problem into finite-dimensional estimation once a shape family is committed.
Supported in partVerified against the publisher's abstract
Shows only that Lehmann & Casella's Theory of Point Estimation is a technical monograph on estimation theory; the abstract we hold never states the claim's separation of an unbounded possibility space from a tractable family.
“Other major additions deal with new developments concerning the information in equality and simultaneous and shrinkage estimation.”
- It separates unbounded possibility space from a constrained-but-tractable family of distributions, trading expressiveness for computational and inferential power, a structure Lehmann and Casella (1998) develop rigorously in their treatment of parametric estimation theory.
- Impartiality
- Where statistics formalized this as the unbiased estimator — an estimator whose expectation equals the true parameter, independent of the sampling identity, a property Lehmann and Casella (1998) develop as the canonical formal definition of an unbiased statistical procedure — ethics formalized it as the impartial standpoint, and law formalized it as the impartial tribunal.
This sourceCanonical formal treatment of unbiased estimation: an estimator's expectation equals the true parameter regardless of which sample drew it; the Cramér–Rao bound and the broader theory of unbiased estimators are developed as the statistical realization of identity-invariance.
- Where statistics formalized this as the unbiased estimator — an estimator whose expectation equals the true parameter, independent of the sampling identity, a property Lehmann and Casella (1998) develop as the canonical formal definition of an unbiased statistical procedure — ethics formalized it as the impartial standpoint, and law formalized it as the impartial tribunal.
- Statistical Inference
- Statistical inference, as Lehmann and Casella (1998) develop in their canonical theory of point estimation, converts vague questions like "Do we have enough evidence?" or "What is the true effect?" into formal problems: specify a probability model (e.g., Bernoulli, normal, logistic), choose an estimation method (maximum likelihood, Bayesian, method-of-moments), derive or approximate the sampling distribution of the estimator, and report a point estimate with an uncertainty bound.
This sourceCanonical formal treatment of unbiased estimation: an estimator's expectation equals the true parameter regardless of which sample drew it; the Cramér–Rao bound and the broader theory of unbiased estimators are developed as the statistical realization of identity-invariance.
- Statistical inference, as Lehmann and Casella (1998) develop in their canonical theory of point estimation, converts vague questions like "Do we have enough evidence?" or "What is the true effect?" into formal problems: specify a probability model (e.g., Bernoulli, normal, logistic), choose an estimation method (maximum likelihood, Bayesian, method-of-moments), derive or approximate the sampling distribution of the estimator, and report a point estimate with an uncertainty bound.
Verification¶
Does it exist? Confirmed. This work's DOI resolves to a registered record, which fixes its identity. That is all it fixes.
Does it back the claim? Read against the text for 1 of 3 citations: 1 supported in part. Each verdict is shown under its citation below, with what in the work backs the sentence.
Support is checked per citation rather than per work — the same source can be cited soundly in one article and wrongly in another. Per-citation recording began recently, so a citation with no recorded check is a gap in the record rather than evidence it went unchecked.
See how references were verified.
Registry ID ref:8a3d557da646 · see in the full table