Abstract
Error estimation is a problem of high current interest in many areas of application. This paper concerns the classical problem of determining the performance of error estimators in small-sample settings under a Gaussianity parametric assumption. We provide here for the first time the exact sampling distribution of the resubstitution and leave-one-out error estimators for linear discriminant analysis (LDA) in the univariate case, which is valid for any sample size and combination of parameters (including unequal variances and sample sizes for each class). In the multivariate case, we provide a quasi-binomial approximation to the distribution of both the resubstitution and leave-one-out error estimators for LDA, under a common but otherwise arbitrary class covariance matrix, which is assumed to be known in the design of the LDA discriminant. We provide numerical examples, using both synthetic and real data, that indicate that these approximations are accurate, provided that LDA classification error is not too large.
| Original language | English |
|---|---|
| Pages (from-to) | 2705-2723 |
| Number of pages | 19 |
| Journal | Pattern Recognition |
| Volume | 42 |
| Issue number | 11 |
| DOIs | |
| Publication status | Published - Nov 2009 |
| Externally published | Yes |
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Keywords
- Error estimation
- Leave-one-out
- Linear discriminant analysis
- Parametric classification
- Resubstitution
- Sampling distribution
ASJC Scopus subject areas
- Software
- Artificial Intelligence
- Computer Vision and Pattern Recognition
- Signal Processing
Cite this
On the sampling distribution of resubstitution and leave-one-out error estimators for linear classifiers. / Zollanvari, Amin; Braga-Neto, Ulisses M.; Dougherty, Edward R.
In: Pattern Recognition, Vol. 42, No. 11, 11.2009, p. 2705-2723.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - On the sampling distribution of resubstitution and leave-one-out error estimators for linear classifiers
AU - Zollanvari, Amin
AU - Braga-Neto, Ulisses M.
AU - Dougherty, Edward R.
PY - 2009/11
Y1 - 2009/11
N2 - Error estimation is a problem of high current interest in many areas of application. This paper concerns the classical problem of determining the performance of error estimators in small-sample settings under a Gaussianity parametric assumption. We provide here for the first time the exact sampling distribution of the resubstitution and leave-one-out error estimators for linear discriminant analysis (LDA) in the univariate case, which is valid for any sample size and combination of parameters (including unequal variances and sample sizes for each class). In the multivariate case, we provide a quasi-binomial approximation to the distribution of both the resubstitution and leave-one-out error estimators for LDA, under a common but otherwise arbitrary class covariance matrix, which is assumed to be known in the design of the LDA discriminant. We provide numerical examples, using both synthetic and real data, that indicate that these approximations are accurate, provided that LDA classification error is not too large.
AB - Error estimation is a problem of high current interest in many areas of application. This paper concerns the classical problem of determining the performance of error estimators in small-sample settings under a Gaussianity parametric assumption. We provide here for the first time the exact sampling distribution of the resubstitution and leave-one-out error estimators for linear discriminant analysis (LDA) in the univariate case, which is valid for any sample size and combination of parameters (including unequal variances and sample sizes for each class). In the multivariate case, we provide a quasi-binomial approximation to the distribution of both the resubstitution and leave-one-out error estimators for LDA, under a common but otherwise arbitrary class covariance matrix, which is assumed to be known in the design of the LDA discriminant. We provide numerical examples, using both synthetic and real data, that indicate that these approximations are accurate, provided that LDA classification error is not too large.
KW - Error estimation
KW - Leave-one-out
KW - Linear discriminant analysis
KW - Parametric classification
KW - Resubstitution
KW - Sampling distribution
UR - http://www.scopus.com/inward/record.url?scp=67649390743&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=67649390743&partnerID=8YFLogxK
U2 - 10.1016/j.patcog.2009.05.003
DO - 10.1016/j.patcog.2009.05.003
M3 - Article
AN - SCOPUS:67649390743
VL - 42
SP - 2705
EP - 2723
JO - Pattern Recognition
JF - Pattern Recognition
SN - 0031-3203
IS - 11
ER -