### 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 language | English (US) |
---|---|

Pages (from-to) | 217-234 |

Number of pages | 18 |

Journal | Journal of Statistical Computation and Simulation |

Volume | 46 |

Issue number | 3-4 |

DOIs | |

State | Published - 1993 |

Externally published | Yes |

### Fingerprint

### 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

*Journal of Statistical Computation and Simulation*,

*46*(3-4), 217-234. https://doi.org/10.1080/00949659308811504

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

Research output: Contribution to journal › Article

*Journal of Statistical Computation and Simulation*, vol. 46, no. 3-4, pp. 217-234. https://doi.org/10.1080/00949659308811504

}

TY - JOUR

T1 - Minimum mean-square error quadrature

AU - Piegorsch, Walter W

AU - John Bailer, A.

PY - 1993

Y1 - 1993

N2 - 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.

AB - 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.

KW - Area under curve

KW - Exponential models

KW - Mean squared error

KW - Numerical quadrature

KW - Pharmacokinetics

KW - Shrinkage estimators

UR - http://www.scopus.com/inward/record.url?scp=5544249909&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=5544249909&partnerID=8YFLogxK

U2 - 10.1080/00949659308811504

DO - 10.1080/00949659308811504

M3 - Article

VL - 46

SP - 217

EP - 234

JO - Journal of Statistical Computation and Simulation

JF - Journal of Statistical Computation and Simulation

SN - 0094-9655

IS - 3-4

ER -