Bias correction of cross-validation criterion based on Kullback–Leibler information under a general condition

Yanagihara, Hirokazu; Tonda, Tetsuji; Matsumoto, Chieko

doi:10.1016/j.jmva.2005.10.009

Cited by 18 publications

(21 citation statements)

References 18 publications

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“…In this paper, two bias-corrected versions of K-fold crossvalidation are derived. The results can be seen as a generalization of the results of Yanagihara et al (2006).…”

Section: Introductionsupporting

confidence: 57%

“…Yanagihara et al (2006) considered bias correction of leave-one-out cross-validation when Ψ (z; θ) = − log p(z; θ). They showed that (1) and (2) are bias-corrected leave-one-out cross-validation estimates of the prediction error when λ = (2N) −1 + O(N −2 ).…”

Section: Problem Formulationmentioning

confidence: 99%

“…However, the bias of K-fold cross-validation may become a problem in real data analysis when K is small (Davison and T. Fushiki ( ) The Institute of Statistical Mathematics, 10-3 Midori-cho, Tachikawa,, Japan e-mail: fushiki@ism.ac.jp Hinkley 1997). Bias-corrected versions of cross-validation have been proposed by Burman (1989) and Yanagihara et al (2006). Burman (1989) considered bias correction of K-fold cross-validation, but Yanagihara et al (2006) only considered bias correction of leave-one-out cross-validation.…”

Section: Introductionmentioning

confidence: 99%

“…Bias-corrected versions of cross-validation have been proposed by Burman (1989) and Yanagihara et al (2006). Burman (1989) considered bias correction of K-fold cross-validation, but Yanagihara et al (2006) only considered bias correction of leave-one-out cross-validation. In this paper, two bias-corrected versions of K-fold crossvalidation are derived.…”

Section: Introductionmentioning

confidence: 99%

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Estimation of prediction error by using K-fold cross-validation

2009

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Estimation of prediction accuracy is important when our aim is prediction. The training error is an easy estimate of prediction error, but it has a downward bias. On the other hand, K-fold cross-validation has an upward bias. The upward bias may be negligible in leave-one-out crossvalidation, but it sometimes cannot be neglected in 5-fold or 10-fold cross-validation, which are favored from a computational standpoint. Since the training error has a downward bias and K-fold cross-validation has an upward bias, there will be an appropriate estimate in a family that connects the two estimates. In this paper, we investigate two families that connect the training error and K-fold crossvalidation.

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“…In this paper, two bias-corrected versions of K-fold crossvalidation are derived. The results can be seen as a generalization of the results of Yanagihara et al (2006).…”

Section: Introductionsupporting

confidence: 57%

Section: Problem Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Estimation of prediction error by using K-fold cross-validation

2009

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“…Since the distribution of u i is the same as that of y i and since Y and U are independent of each other, the following commutative equation, as in Yanagihara et al (2006), holds:…”

Section: A2 Decomposition Of E * [Press]mentioning

confidence: 99%

Second-order bias-corrected AIC in multivariate normal linear models under non-normality

2011

Self Cite

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This paper deals with correcting a bias of Akaike's information criterion (AIC) for selecting variables in multivariate normal linear regression models when the true distribution of observation is an unknown nonnormal distribution. It is well known that the bias of AIC is O(1), and there are several information criteria which improve the bias to O(n −1 ), where n is the sample size. By slightly adjusting the first-order bias-corrected AIC, we propose a new information criterion. Although the adjustment merely uses constant coefficients, the bias of the new criterion is reduced to O(n −2 ). Through numerical experiments, we verify that our criterion is superior to others.

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Monitoring multivariate coefficient of variation for high‐dimensional processes

Adegoke

Dawod

Sanusi

2022

Quality & Reliability Eng

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Multivariate coefficient of variation (MCV) charts are effective tools for monitoring process relative variability. They are developed on the assumption that the process subgroup size available for monitoring the MCV parameter is larger than the number of process characteristics. In such a case, the unbiased estimates of the in‐control mean vector and covariance matrix are used to calculate the chart monitoring statistic. Here, we study the performance of MCV control charts when only a small subgroup size is available for estimating the in‐control mean vector and covariance matrix. We examine the use of a shrinkage estimate of the covariance matrix and propose two one‐sided upward and downward least absolute shrinkage and selection operator (LASSO)‐based MCV charts for detecting upward and downward shifts in the process MCV parameter, respectively. Our simulation study shows that the LASSO‐based MCV charts outperform the classical two one‐sided MCV charts when small subgroup sizes are available for monitoring. The improved performance of the proposed LASSO‐based MCV charts in monitoring shifts in the MCV parameter is demonstrated via an illustrative case study of carbon fiber tube application, where changes are detected earlier than the classical two one‐sided MCV charts.

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Bias correction of cross-validation criterion based on Kullback–Leibler information under a general condition

Cited by 18 publications

References 18 publications

Estimation of prediction error by using K-fold cross-validation

Estimation of prediction error by using K-fold cross-validation

Second-order bias-corrected AIC in multivariate normal linear models under non-normality

Monitoring multivariate coefficient of variation for high‐dimensional processes

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