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The unweighted mean estimator in a Growth Curve model
Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, Faculty of Science & Engineering.
2016 (English)Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
Abstract [en]

The field of statistics is becoming increasingly more important as the amount of data in the world grows. This thesis studies the Growth Curve model in multivariate statistics which is a model that is not widely used. One difference compared with the linear model is that the Maximum Likelihood Estimators are more complicated. That makes it more difficult to use and to interpret which may be a reason for its not so widespread use.

From this perspective this thesis will compare the traditional mean estimator for the Growth Curve model with the unweighted mean estimator. The unweighted mean estimator is simpler than the regular MLE. It will be proven that the unweighted estimator is in fact the MLE under certain conditions and examples when this occurs will be discussed. In a more general setting this thesis will present conditions when the un-weighted estimator has a smaller covariance matrix than the MLEs and also present confidence intervals and hypothesis testing based on these inequalities.

Place, publisher, year, edition, pages
2016. , 35 p.
Series
LiTH-MAT-EX, 2016:03
Keyword [en]
Growth Curve model, maximum likelihood, eigenvalue inequality, un-weighted mean estimator, covariance matrix, circular symmetric Toeplitz, intra-class, generalized intraclas
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:liu:diva-131043ISRN: LiTH-MAT-EX--2016/03--SEOAI: oai:DiVA.org:liu-131043DiVA: diva2:958220
Subject / course
Mathematics
Available from: 2016-10-12 Created: 2016-09-06 Last updated: 2017-07-06Bibliographically approved

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CiteExportLink to record
Permanent link

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Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
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