Generalized Least Squares

Kariya, Takeaki; Kurata, Hiroshi

doi:10.1002/0470866993

Cited by 224 publications

(151 citation statements)

References 91 publications

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“…From the noise vectorε, one can directly compute the expanded noise covariance matrixΨ usingΨ = E εε † , where E[·] denotes the expectation value of a random variable and " †" denotes conjugate transpose. The GLS solution 14 to Eq. (3) with Tikhonov regularization is given by…”

Section: A Regularization Of Splash Reconstructionmentioning

confidence: 99%

Image‐guided spatial localization of heterogeneous compartments for magnetic resonance

Liu

Shen

2015

Medical Physics

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Purpose: Image-guided localization SPectral Localization Achieved by Sensitivity Heterogeneity (SPLASH) allows rapid measurement of signals from irregularly shaped anatomical compartments without using phase encoding gradients. Here, the authors propose a novel method to address the issue of heterogeneous signal distribution within the localized compartments. Methods: Each compartment was subdivided into multiple subcompartments and their spectra were solved by Tikhonov regularization to enforce smoothness within each compartment. The spectrum of a given compartment was generated by combining the spectra of the components of that compartment.The proposed method was first tested using Monte Carlo simulations and then applied to reconstructing in vivo spectra from irregularly shaped ischemic stroke and normal tissue compartments. Results: Monte Carlo simulations demonstrate that the proposed regularized SPLASH method significantly reduces localization and metabolite quantification errors. In vivo results show that the intracompartment regularization results in ∼40% reduction of error in metabolite quantification. Conclusions: The proposed method significantly reduces localization errors and metabolite quantification errors caused by intracompartment heterogeneous signal distribution.

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Section: A Regularization Of Splash Reconstructionmentioning

confidence: 99%

Image‐guided spatial localization of heterogeneous compartments for magnetic resonance

Liu

Shen

2015

Medical Physics

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“…It is also a two-step approach where the first step estimates population parameters measuring sample structure and tests the significance of these parameters to the phenotypic variance once, and the second step uses an F-test (generalized least square (GLS)) [49] or a score test [50] for each SNP with population parameters as dependent variable. The practicability of this approach is based on one assumption that the effect of each marker on the trait is small for a large GWAS data, and then it is not necessary to estimate random variances for each marker in the second step which greatly reduces the computing time from years to hours.…”

Section: The Development Of Lmm-based Approachesmentioning

confidence: 99%

Genetic Studies: The Linear Mixed Models in Genome-wide Association Studies

Zhu

2013

TOBIOIJ

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Abstract:With the availability of high-density genomic data containing millions of single nucleotide polymorphisms and tens or hundreds of thousands of individuals, genetic association study is likely to identify the variants contributing to complex traits in a genome-wide scale. However, genome-wide association studies are confounded by some spurious associations due to not properly interpreting sample structure (containing population structure, family structure and cryptic relatedness). The absence of complete genealogy of population in the genome-wide association studies model greatly motivates the development of new methods to correct the inflation of false positive. In this process, linear mixed model based approaches with the advantage of capturing multilevel relatedness have gained large ground. We summarize current literatures dealing with sample structure, and our review focuses on the following four areas: (i) The approaches handling population structure in genome-wide association studies; (ii) The linear mixed model based approaches in genome-wide association studies; (iii) The performance of linear mixed model based approaches in genome-wide association studies and (iv) The unsolved issues and future work of linear mixed model based approaches.

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“…whereβ is estimated from equation (5), and equation (7) is the best linear unbiased predictor (BLUP) for y|x j (Kariya and Kurata 2004). Given this unbiased estimator for y|x j and again that the variance and covariance parameters are known, the prediction mean-squared error (MSE) can be computed as Jeske 1992, Zimmerman andCressie 1992):…”

Section: Corrected Prediction Intervals For Change Detectionmentioning

confidence: 99%