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

Yanagihara, Hirokazu; Kamo, Ken-ichi; Tonda, Tetsuji

doi:10.1002/cjs.10090

Cited by 10 publications

(7 citation statements)

References 22 publications

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“…Recent developments in estimating bias in multivariate regression, which is equivalent to ICA/PCA with all sources being Gaussian, offer some hope that this problem might nonetheless be tractable. By adjusting the formula for the optimized log-likelihood itself, Yanagihara, Kamo and Tonda [ 47 ] were able to eliminate the bias term involving the multivariate kurtosis of the underlying distribution even though the underlying distribution is unknown. Unfortunately, the derivation of this adjusted formula involves equalities that do not generalize to the broader context of ICA, but future work might identify an alternative formula that does.…”

Section: Discussionmentioning

confidence: 99%

How Many Separable Sources? Model Selection In Independent Components Analysis

2015

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Unlike mixtures consisting solely of non-Gaussian sources, mixtures including two or more Gaussian components cannot be separated using standard independent components analysis methods that are based on higher order statistics and independent observations. The mixed Independent Components Analysis/Principal Components Analysis (mixed ICA/PCA) model described here accommodates one or more Gaussian components in the independent components analysis model and uses principal components analysis to characterize contributions from this inseparable Gaussian subspace. Information theory can then be used to select from among potential model categories with differing numbers of Gaussian components. Based on simulation studies, the assumptions and approximations underlying the Akaike Information Criterion do not hold in this setting, even with a very large number of observations. Cross-validation is a suitable, though computationally intensive alternative for model selection. Application of the algorithm is illustrated using Fisher's iris data set and Howells' craniometric data set. Mixed ICA/PCA is of potential interest in any field of scientific investigation where the authenticity of blindly separated non-Gaussian sources might otherwise be questionable. Failure of the Akaike Information Criterion in model selection also has relevance in traditional independent components analysis where all sources are assumed non-Gaussian.

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Section: Discussionmentioning

confidence: 99%

How Many Separable Sources? Model Selection In Independent Components Analysis

2015

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“…In the multivariate linear regression model, Yanagihara (2006) proposed an information criterion made from the CV method. Yanagihara et al. (2011) corrected a bias of this criterion and gave the theoretical proof that the standard deviation of the bias‐corrected criterion becomes smaller than that of the original criterion by neglecting the higher order term.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Iterative Bias Correction of the Cross‐Validation Criterion

Yanagihara

Fujisawa

2011

Scandinavian J Statistics

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Abstract. The cross‐validation (CV) criterion is known to be asecond‐order unbiased estimator of the risk function measuring the discrepancy between the candidate model and the true model, as well as the generalized information criterion (GIC) and the extended information criterion (EIC). In the present article, we show that the 2kth‐order unbiased estimator can be obtained using a linear combination from the leave‐one‐out CV criterion to the leave‐k‐out CV criterion. The proposed scheme is unique in that a bias smaller than that of a jackknife method can be obtained without any analytic calculation, that is, it is not necessary to obtain the explicit form of several terms in an asymptotic expansion of the bias. Furthermore, the proposed criterion can be regarded as a finite correction of a bias‐corrected CV criterion by using scalar coefficients in a bias‐corrected EIC obtained by the bootstrap iteration.

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“…DISTLM were carried out as described in (Yap et al 2015) Briefly, the parameters showing the most consistent responses to the corresponding overall profiles (NMR, TRFLP or cytokines) was selected using stepwise selection under the second-order bias-corrected AIC (Yanagihara et al 2011).…”

Section: Methodsmentioning

confidence: 99%

Systems biology analyses of the dynamic host response to Toxoplasma gondii infection in a murine model

et al. 2016

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SUMMARYToxoplasmosis affects a third of the global population and is of particular concern for immunologically compromised individuals. Toxoplasmosis induces host physiological events ranging from immunological to metabolic responses across multiple biological compartments. To understand the sequence of host responses during acute and chronicToxoplasma gondiiinfection, eight male BALB/c mice were infected with 2000T. gondiiME49 tachyzoites with a further eight uninfected mice used as controls. Plasma cytokines status, urinary metabolic profiling and fecal microbial profiles were characterized to monitor temporal variation related toT. gondiiinfection. The results showed elevated serum interferon-γ(IFN-γ), interleukin-12p40 and necrosis factor-αduring acute phase of infection with concomitant perturbation in host energy metabolism and host-gut microbiome co-metabolism of phenolics and a shift in microbial composition. However, the differences were less pronounced during the putative chronic phase of infection with elevated IFN-γ, differences in urinaryN-acetyls andO-acetyls of glycoproteins with no shift in gut microbial composition. Structural equation modelling on the current data showed host immune responses as the main driver for changes observed in urinary metabolites and gut microbial composition. Such an approach can be applied to other models of infectious diseases to aid understanding of host–pathogen interactions and potential biomarker discovery.

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

Cited by 10 publications

References 22 publications

How Many Separable Sources? Model Selection In Independent Components Analysis

How Many Separable Sources? Model Selection In Independent Components Analysis

Iterative Bias Correction of the Cross‐Validation Criterion

Systems biology analyses of the dynamic host response to Toxoplasma gondii infection in a murine model

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