biblio.bib

@inreference{2022ProofsInvolvingOrdinary,
  title = {Proofs Involving Ordinary Least Squares},
  booktitle = {Wikipedia},
  date = {2022-01-18T21:25:58Z},
  url = {https://en.wikipedia.org/w/index.php?title=Proofs_involving_ordinary_least_squares&oldid=1066540290},
  urldate = {2023-08-01},
  abstract = {The purpose of this page is to provide supplementary materials for the ordinary least squares article, reducing the load of the main article with mathematics and improving its accessibility, while at the same time retaining the completeness of exposition.},
  langid = {english},
  annotation = {Page Version ID: 1066540290}
}

@book{bates2018Lme4MixedeffectsModeling,
  title = {Lme4: {{Mixed-effects}} Modeling with {{R}}},
  author = {Bates, Douglas},
  date = {2018},
  url = {https://stat.ethz.ch/~maechler/MEMo-pages/lMMwR.pdf},
  urldate = {2023-07-25}
}

@article{cholesky2005ResolutionNumeriqueSystemes,
  title = {Sur la résolution numérique des systèmes d’équations linéaires},
  author = {Cholesky, André-Louis},
  date = {2005-12-01},
  journaltitle = {Bulletin de la Sabix. Société des amis de la Bibliothèque et de l’Histoire de l'École polytechnique},
  number = {39},
  pages = {81--95},
  publisher = {SABIX},
  issn = {0989-3059},
  doi = {10.4000/sabix.529},
  url = {https://journals.openedition.org/sabix/529},
  urldate = {2023-08-01},
  abstract = {La solution des problèmes dépendant de données expérimentales, qui peuvent dans certains cas être soumises à des conditions, et auxquelles on applique la methode des moindres carrés, est toujours subordonnée au calcul numérique des racines d’un système d’équations linéaires. C’est le cas de la recherche des lois physiques~; c’est aussi le cas de la compensation des réseaux géodésiques. Il est donc interessant de rechercher un moyen sur et aussi simple que possible d’effectuer la résolution nu...},
  issue = {39},
  langid = {french}
}

@book{davis2006DirectMethodsSparse,
  title = {Direct {{Methods}} for {{Sparse Linear Systems}}},
  author = {Davis, Timothy A.},
  date = {2006-01},
  series = {Fundamentals of {{Algorithms}}},
  publisher = {{Society for Industrial and Applied Mathematics}},
  doi = {10.1137/1.9780898718881},
  url = {https://epubs.siam.org/doi/book/10.1137/1.9780898718881},
  urldate = {2023-08-01},
  isbn = {978-0-89871-613-9},
  pagetotal = {228},
  keywords = {algorithms,linear algebra,matrix,software,sparse}
}

@article{didonato1992Algorithm708Significant,
  title = {Algorithm 708: {{Significant}} Digit Computation of the Incomplete Beta Function Ratios},
  shorttitle = {Algorithm 708},
  author = {Didonato, Armido R. and Morris, Alfred H.},
  date = {1992-09-01},
  journaltitle = {ACM Transactions on Mathematical Software},
  shortjournal = {ACM Trans. Math. Softw.},
  volume = {18},
  number = {3},
  pages = {360--373},
  issn = {0098-3500},
  doi = {10.1145/131766.131776},
  url = {https://dl.acm.org/doi/10.1145/131766.131776},
  urldate = {2024-01-01},
  abstract = {An algorithm is given for evaluating the incomplete beta function ratio Ix(a,b) and its complement 1 - Ix(a,b). A new continued fraction and a new asymptotic series are used with classical results. A transportable Fortran subroutine based on this algorithm is currently in use. It is accurate to 14 significant digits when precision is not restricted by inherent error.},
  keywords = {continued fractions,F-distribution,minimax approximations}
}

@online{ingram2006MinimumDegreeReordering,
  title = {Minimum {{Degree Reordering Algorithms}}: {{A Tutorial}}},
  author = {Ingram, Stephen},
  date = {2006},
  url = {http://sfingram.net/cs517_final.pdf},
  langid = {english},
  pubstate = {preprint},
  keywords = {⛔ No DOI found}
}

@book{klenke2020ProbabilityTheoryComprehensive,
  title = {Probability {{Theory}}: {{A Comprehensive Course}}},
  shorttitle = {Probability {{Theory}}},
  author = {Klenke, Achim},
  date = {2020},
  series = {Universitext},
  publisher = {Springer International Publishing},
  location = {Cham},
  doi = {10.1007/978-3-030-56402-5},
  url = {https://link.springer.com/10.1007/978-3-030-56402-5},
  urldate = {2023-07-18},
  isbn = {978-3-030-56401-8 978-3-030-56402-5},
  langid = {english}
}

@book{press1995NumericalRecipes2nd,
  title = {Numerical Recipes in {{C}} (2nd Ed.): The Art of Scientific Computing},
  shorttitle = {Numerical Recipes in {{C}} (2nd Ed.)},
  author = {Press, William H. and Teukolsky, Saul A. and Vetterling, William T. and Flannery, Brian P.},
  date = {1995},
  edition = {2},
  publisher = {Cambridge University Press},
  location = {USA},
  isbn = {978-0-521-43108-8},
  pagetotal = {994}
}

@book{rao2007LinearModelsGeneralizations,
  title = {Linear {{Models}} and {{Generalizations}}: {{Least Squares}} and {{Alternatives}}},
  shorttitle = {Linear {{Models}} and {{Generalizations}}},
  author = {Rao, C. Radhakrishna and Toutenburg, Helge and Shalabh and Heumann, Christian},
  date = {2007-10-15},
  series = {Springer {{Series}} in {{Statistics}}},
  edition = {3},
  eprint = {3LK9JoGEyN4C},
  eprinttype = {googlebooks},
  publisher = {Springer Berlin, Heidelberg},
  abstract = {Thebookisbasedonseveralyearsofexperienceofbothauthorsinteaching linear models at various levels. It gives an up-to-date account of the theory and applications of linear models. The book can be used as a text for courses in statistics at the graduate level and as an accompanying text for courses in other areas. Some of the highlights in this book are as follows. A relatively extensive chapter on matrix theory (Appendix A) provides the necessary tools for proving theorems discussed in the text and o?ers a selectionofclassicalandmodernalgebraicresultsthatareusefulinresearch work in econometrics, engineering, and optimization theory. The matrix theory of the last ten years has produced a series of fundamental results aboutthe de?niteness ofmatrices,especially forthe di?erences ofmatrices, which enable superiority comparisons of two biased estimates to be made for the ?rst time. We have attempted to provide a uni?ed theory of inference from linear models with minimal assumptions. Besides the usual least-squares theory, alternative methods of estimation and testing based on convex loss fu- tions and general estimating equations are discussed. Special emphasis is given to sensitivity analysis and model selection. A special chapter is devoted to the analysis of categorical data based on logit, loglinear, and logistic regression models. The material covered, theoretical discussion, and a variety of practical applications will be useful not only to students but also to researchers and consultants in statistics.},
  isbn = {978-3-540-74226-5},
  langid = {english},
  pagetotal = {583},
  keywords = {Business & Economics / Economics / Theory,Business & Economics / Operations Research,Computers / Mathematical & Statistical Software,Mathematics / Discrete Mathematics,Mathematics / Probability & Statistics / General,Mathematics / Probability & Statistics / Stochastic Processes}
}