Theory of Point Estimation¶
Lehmann, E. L., & Casella, G. (1998). Theory of Point Estimation. Springer.
Cited by¶
3 citations across 3 artifacts.
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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.
- 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.
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