Minimum mean-square error quadrature

Walter W Piegorsch, A. John Bailer

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

Minimum mean squared error linear estimators of the area under a curve are considered for cases when the observations are observed with error. The underlying functional form giving rise to the observations is left unspecified, leading to use of quadrature estimators for the true area. The optimal estimator is calculated as a shrinkage of some preliminary estimator (based on, e.g., the trapezoidal rule). Applications to selected exponential functions demonstrate that savings in mean squared error varies with the level of underlying variance. For cases where variance at each time point is large, the proposed rule can bring about savings in mean squared error of as much as 30%. For experiments with small underlying variance at each time point, squared bias is of greater importance than variance in contributing to mean squared error, and the value of higher-order quadrature routines that focus on minimizing approximation error is noted.

Original languageEnglish (US)
Pages (from-to)217-234
Number of pages18
JournalJournal of Statistical Computation and Simulation
Volume46
Issue number3-4
DOIs
StatePublished - 1993
Externally publishedYes

Fingerprint

Minimum Mean Square Error
Mean Squared Error
Quadrature
Mean square error
Estimator
Trapezoidal Rule
Linear Estimator
Error Estimator
Approximation Error
Shrinkage
Exponential functions
Vary
Higher Order
Curve
Mean squared error
Demonstrate
Experiment
Observation
Savings
Experiments

Keywords

  • Area under curve
  • Exponential models
  • Mean squared error
  • Numerical quadrature
  • Pharmacokinetics
  • Shrinkage estimators

ASJC Scopus subject areas

  • Statistics, Probability and Uncertainty
  • Modeling and Simulation
  • Statistics and Probability
  • Applied Mathematics

Cite this

Minimum mean-square error quadrature. / Piegorsch, Walter W; John Bailer, A.

In: Journal of Statistical Computation and Simulation, Vol. 46, No. 3-4, 1993, p. 217-234.

Research output: Contribution to journalArticle

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