Linear Models, Least Squares and Alternatives

By D. Borowiak. Technometrics, 2001

505 citations recorded by the source corpus.

Subfields: Applied Mathematics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/5bf9d740734cae8846f7ddfe39d12215272be821

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In Applied Mathematics

In Statistics and Probability

Citations in the corpus

Statistical analysis of fNIRS data: A comprehensive review (2014, unknown): “Furthermore, for such contrast L, we have L ^ α ¼ L X′V −1 X − X ′V −1 y, and the corresponding error covariance is given by (Rao and Toutenburg (1999)) C V ¼ E ^ α−α ð Þ ^ α−α ð Þ′ f g ¼ L X′V −1 X − L′∈R p1Âp1 : Accordingly, we have the following test statistic (SAS Institute, 1985): ^ z ¼ C −1 V…”
Hidden Multiplicity in Multiway ANOVA: Prevalence, Consequences, and Remedies (2014, unknown): “The situation becomes even more troublesome for designs with unequal numbers of participants per condition: in such unbalanced designs, the three tests in our hypothetical 2× 3 experiment are no longer independent and this further increases the probability of a Type I error (Rao & Toutenburg, 1999).”
The Restricted and Unrestricted Two-Parameter Estimators (2007, methodology): “Since k 1+ d S−1 + 2I is n.n.d., using basic properties of positive definite (p.d.) matrices (see, for example, Farebrother, 1976, 1978; Rao and Toutenburg, 1995), we have the following theorem.”
COMPARATIVE METHODS FOR THE ANALYSIS OF CONTINUOUS VARIABLES: GEOMETRIC INTERPRETATIONS (2001, unknown): “The usual generalized least-square estimate (see section 4.2 of Rao and Toutenburg 1999) of the parameters is t 21 21 t 21b̂ 5 (X S X) X S y. (9) Note that the s2 term canceled out.”
Prediction of spatial soil property information from ancillary sensor data using ordinary linear regression: Model derivations, residual assumptions and model validation tests (2008, background): “…the statistic t1 ¼ r= s1 ffiffiffi h p where h ¼ 1=n2ð Þ þ qTX2 XT1X1 −1 XT2q h i : ð33Þ Note that t1 follows a central t distribution (with n1−p degrees of freedom) under the null hypothesis, where s1 represents the square root of the calibration model MSE estimate (Rao and Toutenburg, 1999).”
Mean Squared Error Matrix Comparisons of Some Biased Estimators in Linear Regression (2003, unknown): “…ð ~ 1, ~ 2Þ ¼ Mðe 1, Þ Mðe 2, Þ is positive definite (p.d.) we may confine ourselves the following case: D ¼ Covð ~ 1Þ Covð ~ 2Þ > 0 ðp:d:Þ: ð2:16Þ As d1d 0 1 ¼ Biasðe 1ÞBiasðe 1Þ0 0, it is easy to see that D>0 implies Dþ d1d 01 > 0 (see Trenkler and Toutenburg, 1990; Rao and Toutenburg, 1995).”
Bayesian generalized least squares regression with application to log Pearson type 3 regional skew estimation (2005, methodology): “In practice the matrix 6 is rarely known and must be estimated, which usually causes a loss of efficiency in the estimators of B and d 2 [ Rao and Toutenburg, 1999 ].”