Statistical Inference

Casella, G., & Berger, R. L. (2002). Statistical Inference. Duxbury Press.

Type

Book chapter

Intellectual base

Review or monograph

Year

2002

ISBN

9780534243128

Link

https://www.cengage.com/c/statistical-inference-2e-casella-berger/9780534243128/

Cited from

mathematics, statistics_experimental_design

Cited by

9 citations across 9 artifacts.

Each citation links to the sentence it supports in the citing article.

Primes

• Bias
  • Calling a single surprising result "biased" confuses an instance with a tendency.

    This sourceStandard graduate text on point estimation: defines bias as a property of an estimator's expectation (visible only across repeated application, never in one draw), and develops the downward-biased sample variance, the n−1 (Bessel) correction, and the finite-sample bias of maximum-likelihood estimators.

• Central Limit Theorem
  • Statistics and inference — confidence intervals, hypothesis tests, and standard errors rest on the CLT-driven asymptotic normality of estimators, even when the underlying data are non-normal.

    This sourceGrounds confidence intervals, hypothesis tests, and standard errors on the CLT-driven asymptotic normality of estimators and the 1/√n shrinkage of the standard error.

• Correlation
  • The defining commitment is statistical association as a self-standing fact: knowing the value of one variable updates the probability distribution over the other, yet the association is silent about which (if either) drives which, leaving open common-cause, reverse-cause, mediated, or coincidental explanations.

    This sourceStandard graduate text; Chapter 4 (Multiple Random Variables) develops joint and marginal distributions, conditional distributions and independence, and covariance and correlation — including that the joint distribution of dependent variables does not factor into the product of its marginals, and that zero (linear) correlation does not imply independence.

• Statistical Independence
  • Probability and statistics: the factorization is the foundational license for IID sampling, naive Bayes, bootstrap resampling, and product-form likelihoods.

    This sourceEstablishes IID sampling, product-form likelihoods, and the role of independence as a premise across statistical methods.

• Statistical Inference
  • The structural insight is robust, as Casella and Berger (2002) emphasize in their canonical treatment: whether estimating a treatment effect in a clinical trial, validating a machine-learning model on unseen data, inferring a disease prevalence from a sample survey, or detecting contamination in a manufacturing process, the template remains: specify a model, estimate parameters with uncertainty, and reason about what the data support.

    This sourceStandard graduate text on point estimation: defines bias as a property of an estimator's expectation (visible only across repeated application, never in one draw), and develops the downward-biased sample variance, the n−1 (Bessel) correction, and the finite-sample bias of maximum-likelihood estimators.

Domain-specific

• Continuous Uniform Distribution
  • Sample minimum and maximum then carry direct endpoint information, and familiar likelihood regularity shortcuts may fail.
• Method of Moments
  • Karl Pearson’s early distribution fitting used moment equations to recover parameters, making the approach foundational in mathematical statistics. Modern texts treat it as a general point-estimation principle and analyze consistency through convergence of sample moments plus identifiability.
• Random Variable
  • The random variable is the foundational technical object of probability theory: estimators, test statistics, p-values, likelihood ratios, and posterior distributions are all random variables, as are portfolio returns, queue lengths, service times, and quantum observables (in the classical sense of their measurement outcomes)

    This sourceEstablishes the statistical half of the list -- estimators, test statistics, likelihood ratios and p-values as random variables with sampling distributions; the finance, queueing and quantum instances are elsewhere.

• Statistic
  • Casella and Berger emphasize the parameter-free sample-function requirement because an expression containing an unknown \(\theta\) cannot be calculated from the data alone and is not a statistic in that model.

Verification

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Links previously used in the corpus

Before the registry existed this work was also linked 2 other ways.

• https://www.cengage.com/c/statistical-inference-2e-casella/9780534243128/ ×1
• https://www.routledge.com/Statistical-Inference/Casella-Berger/p/book/9781032593036 ×1

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