Variance Component Estimation in Linear Inverse Ill-posed Models

By Peiliang Xu, Yunzhong Shen, Y. Fukuda, Yumei Liu. 2006

154 citations recorded by the source corpus.

Subfields: Applied Mathematics, Civil and Structural Engineering, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/d90daa7498dd8bc4f573a8e97aca8a679610f4e7

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Citations in the corpus

Total least squares adjustment in partial errors-in-variables models: algorithm and statistical analysis (2012, methodology): “…accuracy, confidence region and bias of the TLS estimate; (iii) following the bias-correction techniques of Xu (2009) (see also Xu and Shimada 2000; Xu et al. 2006), we will use the biases of the TLS-estimated parameters to remove the biases of residuals, and as a result, use the bias-corrected…”
Bias-corrected regularized solution to inverse ill-posed models (2012, methodology): “Actually, Xu et al. (2006b) and Xu (2009) extended the inverse ill-posed model (1) to combine different types of data with a number of unknown variance components.”
Least-squares variance component estimation: theory and GPS applications (2007, methodology): “, 2004) • estimation of variance components for weighting data of different types in gravity field models (Koch and Kusche, 2002; Kusche, 2003b) • assessment of the stochastic model of CHAMP data using the energy balance in an iterative VCE method (Kusche and van Loon, 2005; van Loon and Kusche, 200”
Non-negative least-squares variance component estimation with application to GPS time series (2016, background): “…best invariant quadratic unbiased estimator (BIQUE) (see Koch 1978, 1999; Schaffrin 1983; Caspary 1987), minimum norm quadratic unbiased estimator (MINQUE) (see Rao 1971; Rao and Kleffe 1988; Sjöberg 1983; Xu et al. 2006, 2007), and restricted maximum likelihood (REML) estimator (see Koch 1986).”
Noise in multivariate GPS position time-series (2009, methodology): “For applications of VCE-methods to GPS and geodetic data we refer to Chen et al. (1990), Kusche (2003a,b),Wangetal.(1998),Teunissenetal.(1998),Barnes (2002),Satirapodetal.(2002),TiberiusandKenselaar(2000), Bona(2000),Bischoffetal.(2005,2006),Fotopoulos(2005), Xu et al. (2006) , Amiri-Simkooei (2007”
Iterative generalized cross-validation for fusing heteroscedastic data of inverse ill-posed problems (2009, background): “The importance of correlation among the same type of data in geophysical inversion was demonstrated by Yagi & Fukahata (2008).”
Variance components in errors-in-variables models: estimability, stability and bias analysis (2014, background): “…component estimation, the reader is referred to Helmert (1907), Rao and Kleffe (1988), Searle et al. (1992) and Koch (1999) in the case of linear models, and Xu et al. (2006) (see also Koch and Kusche 2007; Xu et al. 2007b), Xu (2009) and Eshagh (2010, 2011) in the case of ill-posed linear models.”