### Abstract

The consistency and asymptotic normality of a linear least squares estimate of the form (X'X)^{-}X'Y when the mean is not Xβ is investigated in this paper. The least squares estimate is a consistent estimate of the best linear approximation of the true mean function for the design chosen. The asymptotic normality of the least squares estimate depends on the design and the asymptotic mean may not be the best linear approximation of the true mean function. Choices of designs which allow large sample inferences to be made about the best linear approximation of the true mean function are discussed.

Original language | English (US) |
---|---|

Pages (from-to) | 277-288 |

Number of pages | 12 |

Journal | Journal of Statistical Planning and Inference |

Volume | 10 |

Issue number | 3 |

DOIs | |

State | Published - 1984 |

Externally published | Yes |

### Fingerprint

### Keywords

- Asymptotic normality
- Best linear approximation
- Consistency
- Model robustness

### ASJC Scopus subject areas

- Statistics, Probability and Uncertainty
- Applied Mathematics
- Statistics and Probability

### Cite this

*Journal of Statistical Planning and Inference*,

*10*(3), 277-288. https://doi.org/10.1016/0378-3758(84)90054-5

**Linear least squares estimates and nonlinear means.** / Berger, Roger L.; Langberg, Naftali A.

Research output: Contribution to journal › Article

*Journal of Statistical Planning and Inference*, vol. 10, no. 3, pp. 277-288. https://doi.org/10.1016/0378-3758(84)90054-5

}

TY - JOUR

T1 - Linear least squares estimates and nonlinear means

AU - Berger, Roger L.

AU - Langberg, Naftali A.

PY - 1984

Y1 - 1984

N2 - The consistency and asymptotic normality of a linear least squares estimate of the form (X'X)-X'Y when the mean is not Xβ is investigated in this paper. The least squares estimate is a consistent estimate of the best linear approximation of the true mean function for the design chosen. The asymptotic normality of the least squares estimate depends on the design and the asymptotic mean may not be the best linear approximation of the true mean function. Choices of designs which allow large sample inferences to be made about the best linear approximation of the true mean function are discussed.

AB - The consistency and asymptotic normality of a linear least squares estimate of the form (X'X)-X'Y when the mean is not Xβ is investigated in this paper. The least squares estimate is a consistent estimate of the best linear approximation of the true mean function for the design chosen. The asymptotic normality of the least squares estimate depends on the design and the asymptotic mean may not be the best linear approximation of the true mean function. Choices of designs which allow large sample inferences to be made about the best linear approximation of the true mean function are discussed.

KW - Asymptotic normality

KW - Best linear approximation

KW - Consistency

KW - Model robustness

UR - http://www.scopus.com/inward/record.url?scp=48549111173&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=48549111173&partnerID=8YFLogxK

U2 - 10.1016/0378-3758(84)90054-5

DO - 10.1016/0378-3758(84)90054-5

M3 - Article

AN - SCOPUS:48549111173

VL - 10

SP - 277

EP - 288

JO - Journal of Statistical Planning and Inference

JF - Journal of Statistical Planning and Inference

SN - 0378-3758

IS - 3

ER -