1 / 9

Hypothesis Testing In Less Than Full Rank Model

Hypothesis Testing In Less Than Full Rank Model. Uji hipotesis dalam model ini ada dua cara , yaitu : Uji hipotesis terhadap estimable functions of β . Reparameterisasi ke dalam bentuk full rank model. Definisi:

hinda
Download Presentation

Hypothesis Testing In Less Than Full Rank Model

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Hypothesis TestingIn Less Than Full Rank Model Ujihipotesisdalam model iniadaduacara, yaitu: Ujihipotesisterhadap estimable functions of β. Reparameterisasikedalambentuk full rank model.

  2. Definisi: Sebuahhipotesis Ho disebuttestable jikaterdapatsekumpulanfungsi yang estimable c1΄β, c2΄β, …, cm΄βsehingga Ho benarjikadanhanyajika c1΄β = c2΄β = … = cm΄β = 0 Dengan c1΄, c2΄, …, cm΄adalahbebas linier. Bentukumumdaritestable hypothesis : Ho: Cβ=0 C adalahmatriksnxpdengan rank m ≤r.

  3. Contoh: Model klasifikasisatuarahdenganpengaruhtetapdimana k=3 dan N=n1+n2+n3. yij = μ + τi + εij i=1,2,3 j=1,2,…,n1 Hipotesisnoladalahτ1 = τ2 = τ3. τ1 = τ2 = τ3jikadanhanyajika: τ1 –τ2 = 0 danτ2 – τ3 = 0 Dalambentukmatriks Ho menjadi: Ho: Cβ=0

  4. Statistik yang digunakanuntukujihipotesis di atasadalah:

  5. Theorema: Misalkan y=Xβ+εdimana X adalahmatriksnxpdanεberditribusi normal dengan rata-rata 0 danvariansσ2I. Misalkan Cβ=0 adalah testable dimana C adalahmatriksmxpdengan rank m≤r. Maka mengikutidistribusi chi-square noncentraldenganderajatbebas m dan parameter noncentral:

  6. Theorema: Misalkan y=Xβ+εdimana X adalahmatriksnxpdanεberditribusi normal dengan rata-rata 0 danvariansσ2I. Misalkan Cβ=0 adalah testable dimana C adalahmatriksmxpdengan rank m≤r. MakaCbsalingbebasterhadap s2.

  7. Reparameterization: One-way classification model Less than full rank model Full rank model Transformasi y=Zα+ε* y=Xβ+ε Transformasi

  8. Hipotesissetelahdireparameterisasi: H0: μ1=μ2=… = μk Equivalent dengan : H0: τ1=τ2 =… = τk ANOVA Table

More Related