### Abstract

A classifier is epistemologically vacuous without an accurate estimate of its true error rate. In situations where the number of sample points is of the same order of magnitude as the dimension of observations, serious issues arise with respect to the performance of error estimators. In this paper, we place the problem of synthesizing an error rate estimator of a common linear classifier in an asymptotic setting in which the number of sample points is kept comparable in magnitude to the dimension of observations (double asymptotic). We construct a generalized consistent estimator of the true error rate for linear discriminant analysis in the multivariate Gaussian model under the assumption of a common covariance matrix. In other words, the estimator converges to true error rate in the double asymptotic sense. We employ simulations using both synthetic and real data to compare the performance of the new estimator to the classical consistent estimator of the true error (plug-in estimator) as well as other well-known estimators. We observe that the constructed estimator can outperform other estimators of the true error in many situations in terms of bias and root-mean-square (RMS) error.

Original language | English |
---|---|

Article number | 7078850 |

Pages (from-to) | 2804-2814 |

Number of pages | 11 |

Journal | IEEE Transactions on Signal Processing |

Volume | 63 |

Issue number | 11 |

DOIs | |

Publication status | Published - Jun 1 2015 |

Externally published | Yes |

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### Keywords

- Double asymptotics
- error estimation
- generalized consistent estimation
- linear discriminant analysis
- true error

### ASJC Scopus subject areas

- Electrical and Electronic Engineering
- Signal Processing

### Cite this

*IEEE Transactions on Signal Processing*,

*63*(11), 2804-2814. [7078850]. https://doi.org/10.1109/TSP.2015.2419190

**Generalized consistent error estimator of linear discriminant analysis.** / Zollanvari, Amin; Dougherty, Edward R.

Research output: Contribution to journal › Article

*IEEE Transactions on Signal Processing*, vol. 63, no. 11, 7078850, pp. 2804-2814. https://doi.org/10.1109/TSP.2015.2419190

}

TY - JOUR

T1 - Generalized consistent error estimator of linear discriminant analysis

AU - Zollanvari, Amin

AU - Dougherty, Edward R.

PY - 2015/6/1

Y1 - 2015/6/1

N2 - A classifier is epistemologically vacuous without an accurate estimate of its true error rate. In situations where the number of sample points is of the same order of magnitude as the dimension of observations, serious issues arise with respect to the performance of error estimators. In this paper, we place the problem of synthesizing an error rate estimator of a common linear classifier in an asymptotic setting in which the number of sample points is kept comparable in magnitude to the dimension of observations (double asymptotic). We construct a generalized consistent estimator of the true error rate for linear discriminant analysis in the multivariate Gaussian model under the assumption of a common covariance matrix. In other words, the estimator converges to true error rate in the double asymptotic sense. We employ simulations using both synthetic and real data to compare the performance of the new estimator to the classical consistent estimator of the true error (plug-in estimator) as well as other well-known estimators. We observe that the constructed estimator can outperform other estimators of the true error in many situations in terms of bias and root-mean-square (RMS) error.

AB - A classifier is epistemologically vacuous without an accurate estimate of its true error rate. In situations where the number of sample points is of the same order of magnitude as the dimension of observations, serious issues arise with respect to the performance of error estimators. In this paper, we place the problem of synthesizing an error rate estimator of a common linear classifier in an asymptotic setting in which the number of sample points is kept comparable in magnitude to the dimension of observations (double asymptotic). We construct a generalized consistent estimator of the true error rate for linear discriminant analysis in the multivariate Gaussian model under the assumption of a common covariance matrix. In other words, the estimator converges to true error rate in the double asymptotic sense. We employ simulations using both synthetic and real data to compare the performance of the new estimator to the classical consistent estimator of the true error (plug-in estimator) as well as other well-known estimators. We observe that the constructed estimator can outperform other estimators of the true error in many situations in terms of bias and root-mean-square (RMS) error.

KW - Double asymptotics

KW - error estimation

KW - generalized consistent estimation

KW - linear discriminant analysis

KW - true error

UR - http://www.scopus.com/inward/record.url?scp=84929118622&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84929118622&partnerID=8YFLogxK

U2 - 10.1109/TSP.2015.2419190

DO - 10.1109/TSP.2015.2419190

M3 - Article

AN - SCOPUS:84929118622

VL - 63

SP - 2804

EP - 2814

JO - IEEE Transactions on Signal Processing

JF - IEEE Transactions on Signal Processing

SN - 1053-587X

IS - 11

M1 - 7078850

ER -