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Edgeworth-corrected small-sample confidence intervals for ratio parameters in linear regression
Dissertation (PhD)--Stellenbosch University, 2002.
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| Format: | Thesis |
| Language: | en_ZA |
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Stellenbosch : Stellenbosch University
2012
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| _version_ | 1867614136081317888 |
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| access_status_str | Open Access |
| author | Binyavanga, Kamanzi-wa |
| author2 | Maritz, J. S. |
| author_browse | Binyavanga, Kamanzi-wa Maritz, J. S. |
| author_facet | Maritz, J. S. Binyavanga, Kamanzi-wa |
| author_sort | Binyavanga, Kamanzi-wa |
| collection | Thesis |
| dc_rights_str_mv | Stellenbosch University |
| description | Dissertation (PhD)--Stellenbosch University, 2002. |
| format | Thesis |
| id | oai:scholar.sun.ac.za:10019.1/52814 |
| institution | Stellenbosch University (South Africa) |
| language | en_ZA |
| last_indexed | 2026-06-10T12:47:14.419Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from SUNScholar — Stellenbosch University Repository |
| publishDate | 2012 |
| publishDateRange | 2012 |
| publishDateSort | 2012 |
| publisher | Stellenbosch : Stellenbosch University |
| publisherStr | Stellenbosch : Stellenbosch University |
| record_format | dspace |
| source_str | SUNScholar — Stellenbosch University Repository |
| spelling | oai:scholar.sun.ac.za:10019.1/52814 Edgeworth-corrected small-sample confidence intervals for ratio parameters in linear regression Binyavanga, Kamanzi-wa Maritz, J. S. Steel, S. J. Stellenbosch University. Faculty of Economic and Management Sciences. Dept. of Statistical and Actuarial Science. Confidence intervals Regression analysis Edgeworth expansions Dissertations -- Statistics and actuarial science Theses -- Statistics and actuarial science Dissertation (PhD)--Stellenbosch University, 2002. ENGLISH ABSTRACT: In this thesis we construct a central confidence interval for a smooth scalar non-linear function of parameter vector f3 in a single general linear regression model Y = X f3 + c. We do this by first developing an Edgeworth expansion for the distribution function of a standardised point estimator. The confidence interval is then constructed in the manner discussed. Simulation studies reported at the end of the thesis show the interval to perform well in many small-sample situations. Central to the development of the Edgeworth expansion is our use of the index notation which, in statistics, has been popularised by McCullagh (1984, 1987). The contributions made in this thesis are of two kinds. We revisit the complex McCullagh Index Notation, modify and extend it in certain respects as well as repackage it in the manner that is more accessible to other researchers. On the new contributions, in addition to the introduction of a new small-sample confidence interval, we extend the theory of stochastic polynomials (SP) in three respects. A method, which we believe to be the simplest and most transparent to date, is proposed for deriving cumulants for these. Secondly, the theory of the cumulants of the SP is developed both in the context of Edgeworth expansion as well as in the regression setting. Thirdly, our new method enables us to propose a natural alternative to the method of Hall (1992a, 1992b) regarding skewness-reduction in Edgeworth expansions. AFRIKAANSE OPSOMMING: In hierdie proefskrif word daar aandag gegee aan die konstruksie van 'n sentrale vertrouensinterval vir 'n gladde skalare nie-lineêre funksie van die parametervektor (3 in 'n enkele algemene lineêre regressiemodel y = X (3 + e.. Dit behels eerstens die ontwikkeling van 'n Edgeworth uitbreiding vir die verdelingsfunksie van 'n gestandaardiseerde puntberamer. Die vertrouensinterval word dan op grond van hierdie uitbreiding gekonstrueer. Simulasiestudies wat aan die einde van die proefskrif gerapporteer word, toon dat die voorgestelde interval goed vertoon in verskeie klein-steekproef gevalle. Die gebruik van indeksnotasie, wat in die statistiek deur McCullagh (1984, 1987) bekendgestel is, speel 'n sentrale rol in die ontwikkeling van die Edgeworth uitbreiding. Die bydrae wat in hierdie proefskrif gemaak word, is van 'n tweërlei aard. Die ingewikkelde Indeksnotasie van McCullagh word ondersoek, aangepas en ten opsigte van sekere aspekte uitgebrei. Die notasie word ook aangebied in 'n vorm wat dit hopelik meer toeganklik sal maak vir ander navorsers. Betreffende die bydrae wat gemaak word, word 'n nuwe klein-steekproef vertrouensinterval voorgestel, en word die teorie van stogastiese polinome (SP) ook in drie opsigte uitgebrei. 'n Metode word voorgestelom die kumulante van SP'e af te lei. Ons glo dat hierdie metode die duidelikste en eenvoudigste metode is wat tot dusver hiervoor voorgestel is. Tweedens word die teorie van die kumulante van SP'e ontwikkel binne die konteks van Edgeworth uitbreidings, sowel as die konteks van regressie. Derdens stelons nuwe metode ons in staat om 'n natuurlike alternatief voor te stel vir die metode van Hall (1992a, 1992b) vir die vermindering van skeefheid in Edgeworth uitbreidings. Doctoral 2012-08-27T11:35:10Z 2012-08-27T11:35:10Z 2002-03 Thesis http://hdl.handle.net/10019.1/52814 en_ZA Stellenbosch University 147 p. application/pdf Stellenbosch : Stellenbosch University |
| spellingShingle | Confidence intervals Regression analysis Edgeworth expansions Dissertations -- Statistics and actuarial science Theses -- Statistics and actuarial science Binyavanga, Kamanzi-wa Edgeworth-corrected small-sample confidence intervals for ratio parameters in linear regression |
| title | Edgeworth-corrected small-sample confidence intervals for ratio parameters in linear regression |
| title_full | Edgeworth-corrected small-sample confidence intervals for ratio parameters in linear regression |
| title_fullStr | Edgeworth-corrected small-sample confidence intervals for ratio parameters in linear regression |
| title_full_unstemmed | Edgeworth-corrected small-sample confidence intervals for ratio parameters in linear regression |
| title_short | Edgeworth-corrected small-sample confidence intervals for ratio parameters in linear regression |
| title_sort | edgeworth corrected small sample confidence intervals for ratio parameters in linear regression |
| topic | Confidence intervals Regression analysis Edgeworth expansions Dissertations -- Statistics and actuarial science Theses -- Statistics and actuarial science |
| url | http://hdl.handle.net/10019.1/52814 |
| work_keys_str_mv | AT binyavangakamanziwa edgeworthcorrectedsmallsampleconfidenceintervalsforratioparametersinlinearregression |