Bias Corrections of some Criteria for Selecting Multivariate Linear Models in a General Nonnormal Case

Fujikoshi, Yasunori; Yanagihara, Hirokazu; Wakaki, Hirofumi

doi:10.1080/01966324.2005.10737651

Cited by 11 publications

(18 citation statements)

References 10 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Since there is no assumption of a concrete distribution in the definition of C p , using C p may be more suitable for selecting variables in nonnormal data. However, Fujikoshi and Satoh (1997) and Fujikoshi et al (2003Fujikoshi et al ( , 2005 reported that the selectionprobability of a bias-corrected C p is lower than that of a bias-corrected AIC. In summary,…”

Section: Resultsmentioning

confidence: 99%

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

2011

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Section: Resultsmentioning

confidence: 99%

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

2011

Self Cite

View full text Add to dashboard Cite

show abstract

“…From the result in Fujikoshi et al [5], if the candidate model is the overspecified model, the risk R KL in (3) is expanded as…”

Section: Theorem 32 Let Be a Noncentrality Parameter Matrix Defined Bymentioning

confidence: 99%

“…By using the same calculation as in Fujikoshi et al [5], which is an asymptotic expansion with respect to the expectations of Z and V having asymptotic normality, where…”

Section: Theorem 32 Let Be a Noncentrality Parameter Matrix Defined Bymentioning

confidence: 99%

See 1 more Smart Citation

Corrected version of AIC for selecting multivariate normal linear regression models in a general nonnormal case

Yanagihara

2006

Journal of Multivariate Analysis

Self Cite

View full text Add to dashboard Cite

This paper deals with the bias reduction of Akaike information criterion (AIC) for selecting variables in multivariate normal linear regression models when the true distribution of observation is an unknown nonnormal distribution. We propose a corrected version of AIC which is partially constructed by the jackknife method and is adjusted to the exact unbiased estimator of the risk when the candidate model includes the true model. It is pointed out that the influence of nonnormality in the bias of our criterion is smaller than the ones in AIC and TIC. We verify that our criterion is better than the AIC, TIC and EIC by conducting numerical experiments.

show abstract

“…Although we will consider primarily the above five criteria, the family also includes information criteria for which the penalty terms are random variables, e.g., the modified AIC (MAIC) proposed by Fujikoshi and Satoh (1997), Takeuchi's information criterion (TIC) proposed by Takeuchi (1976), the extended information criterion (EIC) proposed by Ishiguro et al (1997), the cross-validation (CV) criterion proposed by Stone (1974Stone ( , 1977, and other bias-corrected AICs, such as those proposed by Fujikoshi et al (2005), Yanagihara (2006), and Yanagihara et al (2011) (for the details of those criteria, see Yanagihara et al (2013)). The best subset of ω, which is chosen by minimizing IC m (j), is written aŝ…”

Section: Notation and Assumptionsmentioning

confidence: 99%

Conditions for Consistency of a Log-Likelihood-Based Information Criterion in Normal Multivariate Linear Regression Models under the Violation of the Normality Assumption

Yanagihara

2015

JJSS

Self Cite

View full text Add to dashboard Cite

In this paper, we clarify conditions for consistency of a log-likelihood-based information criterion in multivariate linear regression models with a normality assumption. Although normality is assumed for the distribution of the candidate model, we frame the situation so that the assumption of normality may be violated. The conditions for consistency are derived from two types of asymptotic theory; one is based on a large-sample asymptotic framework in which only the sample size approaches ∞, and the other is based on a high-dimensional asymptotic framework in which the sample size and the dimension of the vector of response variables simultaneously approach infinity. In both cases, our results are independent of any indicator measuring a discrepancy between the true distribution and the normal distribution, e.g., skewness, kurtosis and other higher-order cumulants of the true distribution.

show abstract

Bias Corrections of some Criteria for Selecting Multivariate Linear Models in a General Nonnormal Case

Cited by 11 publications

References 10 publications

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

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

Corrected version of AIC for selecting multivariate normal linear regression models in a general nonnormal case

Conditions for Consistency of a Log-Likelihood-Based Information Criterion in Normal Multivariate Linear Regression Models under the Violation of the Normality Assumption

Contact Info

Product

Resources

About