Linear Regression Analysis: Seber/Linear

By George A. F. Seber, Alan Lee. 2003

712 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/3e0f03223e3fc677bf1c27f5468c85ff044e7df8

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In Statistics and Probability

Citations in the corpus

An EZ-diffusion model for response time and accuracy (2007, neutral): “This fitting procedure requires that the lack of fit for MRT, VRT, and Pc be weighted, for instance by the precision with which these quantities are estimated (i.e., weighted least squares; Seber & Lee, 2003).”
On model selection criteria in multimodel analysis (2007, methodology): “One can then estimate s2 a posteriori by setting 2@ln[L(q̂k, s2jz*)]/@s2 = 0, yielding the ML estimate [Seber and Wild, 1989; Seber and Lee, 2003; Carrera and Neuman, 1986a] ŝ2ML ¼ eTwe Nz qk¼ q̂k : ðB3Þ As this ML estimate is biased, it is sometimes replaced by the unbiased LS estimator [Seber…”
New Confidence Intervals and Bias Comparisons Show That Maximum Likelihood Can Beat Multiple Imputation in Small Samples (2013, methodology): “Breaking this into components, we see that the first component is a quadratic form whose expectation can be calculated using a standard matrix identity (Seber & Lee, 2003, pp. 9–12), Δ .”
Is unequal weighting significantly better than equal weighting for multi‐model forecasting? (2013, methodology): “This review is selective in the sense that only material relevant to our particular procedure is discussed; more extensive coverage of hypothesis testing in regression models can be found in Graybill (1961), Neter and Wasserman (1974), Mardia et al. (1979), and Seber and Lee (2003).”
Is the ML Chi-Square Ever Robust to Nonnormality? A Cautionary Note With Missing Data (2008, background): “In particular, Q, and therefore TML, is asymptotically chi-square distributed if and only if U U D U; (13) or in other words, if and only if the matrix U is idempotent.4 When this condition is not met, the distribution of Q is a weighted mixture of chi-square variates (e.g., Seber & Lee, 2003).”
Understanding Robust Corrections in Structural Equation Modeling (2014, background): “The mathematical developments presented in this section assume that the reader is familiar with regression presented in matrix form (e.g., Christensen, 2002; Neter et al., 1996; Seber & Lee, 2003).”
Small Sample Statistics for Incomplete Nonnormal Data: Extensions of Complete Data Formulae and a Monte Carlo Comparison (2010, background): “…a variety of studied conditions, whereas 1% to 15% of models failed to converge under ADF for larger samples, and as many as 20% to 40% in smaller samples. where P¢? is an orthogonal complement to the matrix of model derivatives (for working with projection operators, see, e.g., Seber & Lee, 2003).”
Analysis of regression confidence intervals and Bayesian credible intervals for uncertainty quantification (2012, background): “When s2 is known, the distribution of estimates b of the unknown true parameters b is multivariate Gaussian, i.e., [Draper and Smith, 1998, p. 94; Seber and Lee, 2003, p. 47], b Np b; XTC 1ɛ X 1 ∝ exp 1 2 b b TXTC 1ɛ X b b : ð8Þ Ideally X in (8) is the same as in (6), but in reality alternative…”
Skill improvement from increased ensemble size and model diversity (2014, background): “If the noise terms 𝜖1 and 𝜖12 are Gaussian, then under the null hypothesis 𝛽2 = 0 the statistic F = SSES − SSEC SSEC N − 3 1 (32) has an F distribution with 1 and N − 3 degrees of freedom [Seber and Lee, 2003], where N is the number of samples.”
Model-free model-fitting and predictive distributions (2010, background): “(10.12) of Seber and Lee (2003) further implies 1/n ≤ hi ≤ 1 from which it follows that |z̃i| ≥ |zi| for all i. Noting that the fitted residuals have variance depending on hi, Stine (1985) sug- gested resampling the studentized residuals ẑi = zi/ √ 1 − hi in his construction of bootstrap…”