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100 1 Sengupta, Debasis.
245 10 Linear models :|ban integrated approach /|cDebasis
Sengupta, Sreenivasa Rao Jammalamadaka.
264 1 River Edge, N.J. :|bWorld Scientific,|c[2003]
264 4 |c©2003
300 1 online resource (xxi, 622 pages) :|billustrations.
336 text|btxt|2rdacontent
337 computer|bc|2rdamedia
338 online resource|bcr|2rdacarrier
340 |gpolychrome|2rdacc
347 text file|2rdaft
490 1 Series on multivariate analysis ;|vvol. 6
504 Includes bibliographical references (pages 587-606) and
index.
505 0 Ch. 1. Introduction. 1.1. The linear model. 1.2. Why a
linear model? 1.3. Description of the linear model and
notations. 1.4. Scope of the linear model. 1.5. Related
models. 1.6. Uses of the linear model. 1.7. A tour through
the rest of the book. 1.8. Exercises -- ch. 2. Review of
linear algebra. 2.1. Matrices and vectors. 2.2. Inverses
and generalized inverses. 2.3. Vector space and
projection. 2.4. Column space. 2.5. Matrix decompositions.
2.6. Löwner order. 2.7. Solution of linear equations. 2.8.
Optimization of quadratic forms and functions. 2.9
Exercises -- ch. 3. Review of statistical results. 3.1.
Covariance adjustment. 3.2. Basic distributions. 3.3.
Distribution of quadratic forms. 3.4. Regression. 3.5.
Basic concepts of inference. 3.6. Point estimation. 3.7.
Bayesian estimation. 3.8. Tests of hypotheses. 3.9.
Confidence region. 3.10. Exercises -- ch. 4. Estimation in
the linear model. 4.1. Linear estimation: some basic
facts. 4.2. Least squares estimation. 4.3. Best linear
unbiased estimation. 4.4. Maximum likelihood estimation.
4.5. Fitted value, residual and leverage. 4.6.
Dispersions. 4.7. Estimation of error variance and
canonical decompositions. 4.8. Reparametrization. 4.9.
Linear restrictions. 4.10. Nuisance parameters. 4.11.
Information matrix and Cramer-Rao bound. 4.12.
Collinearity in the linear model. 4.13. Exercises -- ch.
5. Further inference in the linear model. 5.1.
Distribution of the estimators. 5.2. Confidence regions.
5.3. Tests of linear hypotheses. 5.4. Prediction in the
linear model. 5.5. Consequences of collinearity. 5.6.
Exercises -- ch. 6. Analysis of variance in basic designs.
6.1. Optimal design. 6.2. One-way classified data. 6.3.
Two-way classified data. 6.4. Multiple treatment/block
factors. 6.5. Nested models. 6.6. Analysis of covariance.
6.7. Exercises.
505 8 Ch. 7. General linear model. 7.1. Why study the singular
model? 7.2. Special considerations with singular models.
7.3. Best linear unbiased estimation. 7.4. Estimation of
error variance. 7.5. Maximum likelihood estimation. 7.6.
Weighted least squares estimation. 7.7. Some recipes for
obtaining the BLUE. 7.8. Information matrix and Cramer-Rao
bound. 7.9. Effect of linear restrictions. 7.10. Model
with nuisance parameters. 7.11. Tests of hypotheses. 7.12.
Confidence regions. 7.13. Prediction. 7.14. Exercises --
ch. 8. Misspecified or unknown dispersion. 8.1.
Misspecified dispersion matrix. 8.2. Unknown dispersion:
the general case. 8.3. Mixed effects and variance
components. 8.4. Other special cases with correlated
error. 8.5. Special cases with uncorrelated error. 8.6.
Some problems of signal processing. 8.7. Exercises -- ch.
9. Updates in the general linear model. 9.1. Inclusion of
observations. 9.2. Exclusion of observations. 9.3.
Exclusion of explanatory variables. 9.4. Inclusion of
explanatory variables. 9.5. Data exclusion and variable
inclusion. 9.6. Exercises -- ch. 10. Multivariate linear
model. 10.1. Description of the multivariate linear model.
10.2. Best linear unbiased estimation. 10.3. Unbiased
estimation of error dispersion. 10.4. Maximum likelihood
estimation. 10.5. Effect of linear restrictions. 10.6.
Tests of linear hypotheses. 10.7. Linear prediction and
confidence regions. 10.8. Applications. 10.9. Exercises --
ch. 11. Linear inference -- other perspectives. 11.1.
Foundations of linear inference. 11.2. Admissible, Bayes
and minimax linear estimators. 11.3. Biased estimators
with smaller dispersion. 11.4. Other linear estimators.
11.5. A geometric view of BLUE in the linear model. 11.6.
Large sample properties of estimators. 11.7. Exercises.
520 Linear Models: An Integrated Approach aims to provide a
clearand deep understanding of the general linear model
using simplestatistical ideas. Elegant geometric arguments
are also invoked asneeded and a review of vector spaces
and matrices is provided to makethe treatment self-
contained.
588 0 Print version record.
590 eBooks on EBSCOhost|bEBSCO eBook Subscription Academic
Collection - North America
650 0 Linear models (Statistics)|0https://id.loc.gov/authorities
/subjects/sh85077177
650 0 Analysis of covariance.|0https://id.loc.gov/authorities/
subjects/sh85004781
650 0 Regression analysis.|0https://id.loc.gov/authorities/
subjects/sh85112392
650 7 Linear models (Statistics)|2fast|0https://id.worldcat.org/
fast/999084
650 7 Analysis of covariance.|2fast|0https://id.worldcat.org/
fast/808327
650 7 Regression analysis.|2fast|0https://id.worldcat.org/fast/
1432090
655 4 Electronic books.
700 1 Jammalamadaka, S. Rao.|0https://id.loc.gov/authorities/
names/n2001000317
776 08 |iPrint version:|aSengupta, Debasis.|tLinear models.
|dRiver Edge, N.J. : World Scientific, ©2003|w(DLC)
2005297683
830 0 Series on multivariate analysis ;|0https://id.loc.gov/
authorities/names/n95093809|vv. 6.
856 40 |uhttps://rider.idm.oclc.org/login?url=http://
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db=nlebk&AN=135173|zOnline eBook. Access restricted to
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856 42 |3Instructions for reading/downloading this eBook|uhttp://
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901 MARCIVE 20231220
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