A Calculus for Factorial Arrangements:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer New York
1989
|
| Schriftenreihe: | Lecture Notes in Statistics
59 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | Factorial designs were introduced and popularized by Fisher (1935). Among the early authors, Yates (1937) considered both symmetric and asymmetric factorial designs. Bose and Kishen (1940) and Bose (1947) developed a mathematical theory for symmetric priIi't&-powered factorials while Nair and Roo (1941, 1942, 1948) introduced and explored balanced confounded designs for the asymmetric case. Since then, over the last four decades, there has been a rapid growth of research in factorial designs and a considerable interest is still continuing. Kurkjian and Zelen (1962, 1963) introduced a tensor calculus for factorial arrangements which, as pointed out by Federer (1980), represents a powerful statistical analytic tool in the context of factorial designs. Kurkjian and Zelen (1963) gave the analysis of block designs using the calculus and Zelen and Federer (1964) applied it to the analysis of designs with two-way elimination of heterogeneity. Zelen and Federer (1965) used the calculus for the analysis of designs having several classifications with unequal replications, no empty cells and with all the interactions present. Federer and Zelen (1966) considered applications of the calculus for factorial experiments when the treatments are not all equally replicated, and Paik and Federer (1974) provided extensions to when some of the treatment combinations are not included in the experiment. The calculus, which involves the use of Kronecker products of matrices, is extremely helpful in deriving characterizations, in a compact form, for various important features like balance and orthogonality in a general multifactor setting |
| Beschreibung: | 1 Online-Ressource (VI, 126p) |
| ISBN: | 9781441987303 9780387971728 |
| ISSN: | 0930-0325 |
| DOI: | 10.1007/978-1-4419-8730-3 |
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| 500 | |a Factorial designs were introduced and popularized by Fisher (1935). Among the early authors, Yates (1937) considered both symmetric and asymmetric factorial designs. Bose and Kishen (1940) and Bose (1947) developed a mathematical theory for symmetric priIi't&-powered factorials while Nair and Roo (1941, 1942, 1948) introduced and explored balanced confounded designs for the asymmetric case. Since then, over the last four decades, there has been a rapid growth of research in factorial designs and a considerable interest is still continuing. Kurkjian and Zelen (1962, 1963) introduced a tensor calculus for factorial arrangements which, as pointed out by Federer (1980), represents a powerful statistical analytic tool in the context of factorial designs. Kurkjian and Zelen (1963) gave the analysis of block designs using the calculus and Zelen and Federer (1964) applied it to the analysis of designs with two-way elimination of heterogeneity. Zelen and Federer (1965) used the calculus for the analysis of designs having several classifications with unequal replications, no empty cells and with all the interactions present. Federer and Zelen (1966) considered applications of the calculus for factorial experiments when the treatments are not all equally replicated, and Paik and Federer (1974) provided extensions to when some of the treatment combinations are not included in the experiment. The calculus, which involves the use of Kronecker products of matrices, is extremely helpful in deriving characterizations, in a compact form, for various important features like balance and orthogonality in a general multifactor setting | ||
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Datensatz im Suchindex
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| author | Gupta, Sudhir |
| author_facet | Gupta, Sudhir |
| author_role | aut |
| author_sort | Gupta, Sudhir |
| author_variant | s g sg |
| building | Verbundindex |
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| dewey-full | 519.5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.5 |
| dewey-search | 519.5 |
| dewey-sort | 3519.5 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4419-8730-3 |
| format | Electronic eBook |
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| institution | BVB |
| isbn | 9781441987303 9780387971728 |
| issn | 0930-0325 |
| language | English |
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| spelling | Gupta, Sudhir Verfasser aut A Calculus for Factorial Arrangements by Sudhir Gupta, Rahul Mukerjee New York, NY Springer New York 1989 1 Online-Ressource (VI, 126p) txt rdacontent c rdamedia cr rdacarrier Lecture Notes in Statistics 59 0930-0325 Factorial designs were introduced and popularized by Fisher (1935). Among the early authors, Yates (1937) considered both symmetric and asymmetric factorial designs. Bose and Kishen (1940) and Bose (1947) developed a mathematical theory for symmetric priIi't&-powered factorials while Nair and Roo (1941, 1942, 1948) introduced and explored balanced confounded designs for the asymmetric case. Since then, over the last four decades, there has been a rapid growth of research in factorial designs and a considerable interest is still continuing. Kurkjian and Zelen (1962, 1963) introduced a tensor calculus for factorial arrangements which, as pointed out by Federer (1980), represents a powerful statistical analytic tool in the context of factorial designs. Kurkjian and Zelen (1963) gave the analysis of block designs using the calculus and Zelen and Federer (1964) applied it to the analysis of designs with two-way elimination of heterogeneity. Zelen and Federer (1965) used the calculus for the analysis of designs having several classifications with unequal replications, no empty cells and with all the interactions present. Federer and Zelen (1966) considered applications of the calculus for factorial experiments when the treatments are not all equally replicated, and Paik and Federer (1974) provided extensions to when some of the treatment combinations are not included in the experiment. The calculus, which involves the use of Kronecker products of matrices, is extremely helpful in deriving characterizations, in a compact form, for various important features like balance and orthogonality in a general multifactor setting Statistics Statistics, general Statistik Matrix Mathematik (DE-588)4037968-1 gnd rswk-swf Kalkül (DE-588)4163108-0 gnd rswk-swf Faktorielle Versuchsplanung (DE-588)4153601-0 gnd rswk-swf Faktorielle Versuchsplanung (DE-588)4153601-0 s Kalkül (DE-588)4163108-0 s 1\p DE-604 Matrix Mathematik (DE-588)4037968-1 s 2\p DE-604 Mukerjee, Rahul Sonstige oth https://doi.org/10.1007/978-1-4419-8730-3 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Gupta, Sudhir A Calculus for Factorial Arrangements Statistics Statistics, general Statistik Matrix Mathematik (DE-588)4037968-1 gnd Kalkül (DE-588)4163108-0 gnd Faktorielle Versuchsplanung (DE-588)4153601-0 gnd |
| subject_GND | (DE-588)4037968-1 (DE-588)4163108-0 (DE-588)4153601-0 |
| title | A Calculus for Factorial Arrangements |
| title_auth | A Calculus for Factorial Arrangements |
| title_exact_search | A Calculus for Factorial Arrangements |
| title_full | A Calculus for Factorial Arrangements by Sudhir Gupta, Rahul Mukerjee |
| title_fullStr | A Calculus for Factorial Arrangements by Sudhir Gupta, Rahul Mukerjee |
| title_full_unstemmed | A Calculus for Factorial Arrangements by Sudhir Gupta, Rahul Mukerjee |
| title_short | A Calculus for Factorial Arrangements |
| title_sort | a calculus for factorial arrangements |
| topic | Statistics Statistics, general Statistik Matrix Mathematik (DE-588)4037968-1 gnd Kalkül (DE-588)4163108-0 gnd Faktorielle Versuchsplanung (DE-588)4153601-0 gnd |
| topic_facet | Statistics Statistics, general Statistik Matrix Mathematik Kalkül Faktorielle Versuchsplanung |
| url | https://doi.org/10.1007/978-1-4419-8730-3 |
| work_keys_str_mv | AT guptasudhir acalculusforfactorialarrangements AT mukerjeerahul acalculusforfactorialarrangements |