Lineer modellerde kestirilebilir fonksiyonlar ve sınanabilir varsayımlar
Estimable function and testable hypotheses in linear models
- Tez No: 52028
- Danışmanlar: PROF.DR. MERİH İPEK
- Tez Türü: Yüksek Lisans
- Konular: Ekonomi, Economics
- Anahtar Kelimeler: Genelleştirilmiş ters matrisler, Kestirilebilir fonksiyonlar, Varyans analizi, Generalized reverse matrices, Estimable functions, Variance analysis
- Yıl: 1995
- Dil: Türkçe
- Üniversite: İstanbul Üniversitesi
- Enstitü: Sosyal Bilimler Enstitüsü
- Ana Bilim Dalı: Belirtilmemiş.
- Bilim Dalı: Belirtilmemiş.
- Sayfa Sayısı: Belirtilmemiş.
Özet
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Özet (Çeviri)
SUMMARY The application of the generalized inverse matrices to the linear statistical models is of relatively recent occurrence. As a mathematical tool such aid in understanding certain aspects of the analysis procedures associated with linear models, especially the analysis of unbalanced data, a topic to which considerable attention is given in this thesis. An approximate starting point is therefore a summary of the features of generalized inverse matrices that are important to linear models. A generalized inverse of a matrix A is defined as any matrix G that satisfies the equation in Chapter 0 A GA =A Regression analysis is designed for situations where available is thought to be related to one or more other measurements, made usually on the same object. A purpose of the analysis is to use data (observed values of the variables) to estimate the form of this relationship. The equation of the general linear model is Y = X0 + e identical that used for regression analysis but are not given here. Therefore, the normal equation for estimating j8 can be written as X'X0=X'Y When Ş is the estimator of j3. This thesis illustrates how the same equation can apply to linear models generally when X does not have full column rank. Estimation and hypothesis testing for this case are now considered. The underlying idea of estimable function was introduced in Section 1.2. Basically, it is a linear function of the parameters for which an estimator can be found from @0 that is invariant to whatever solution of the normal equations is used for Ş0. We now discuss such fractions in detail, confining ourselves to linear functions of the form k' j3, where k' is a row vector. The equation to summarize the main results of Chapter 1 that are used in this and next chapters. The equation of the mode is Y=X0 + e with normal equations X'XŞ0 = X'Y whose solution is PQ = GX'Ywhere G is a generalized inverse of X' X, meaning that it satisfies X' X G X X' = X' X. In the first chapter a suitable equation of linear model is y9 = n + oil + e9 where y9 is the observations, fi is a mean, a, is the effect of the rth row and e& is an error term. Chapter 2 with 2 way crossed classification (with and without interactions). A suitable equation of the model of 2 way classification without interactions y9 = n + or,- + jj + e& where yv is the observation in the /th row and/th column, /* is a mean, a, is the effect of the /th row, y is the effect of they'th column, and e^ is an error term. The equation of a suitable linear model of 2 way classification with iteration is ?«,= M + a, + yj + 8{j + eijk where y&k is the observation in the /th row andyth column, fi is a mean, or, is the effect of the ith row, 7,- is the effect of the y'th column, S? is the effect of the rth row and y'th column, and evk is an error term. -VI-
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