Nugraheni, Listia (2013) Pendugaan Komponen Ragam Model Acak Klasifikasi Satu Arah Dengan Metode Kemungkinan Maksimum Terbatas (REML). Sarjana thesis, Universitas Brawijaya.
Abstract
Analisis ragam untuk model acak klasifikasi satu arah jika keragaman total hanya diuraikan ke dalam keragaman antar kelas dan keragaman dalam kelas (keragaman tak terjelaskan), di mana tingkat faktor dipilih secara acak dari himpunan tak hingga tingkat faktor. Prosedur pendugaan komponen ragam yakni (1) Metode ANOVA, menyamakan jumlah kuadrat dengan nilai harapan (2) Metode kemungkinan maksimum (MKM), memaksimumkan persamaan kemungkinan, (3) Metode REML mewakili kemungkinan maksimum bersifat sisa (Residual Maximum Likelihood) atau kemungkinan maksimum terbatas (Restricted maximum likelihood), dengan memaksimumkan persamaan kemungkinan yang tidak mengandung parameter Data sekunder mengenai bobot kering total tebu (kg/m2), bobot segar total tebu (kg/m2), dan bobot kering gulma (g/m2) di 10 lokasi (kecamatan) di Kabupaten Malang. Di setiap lokasi terdapat 4 petak contoh sebagai ulangan. Berdasarkan hasil analisis yang diterapkan pada 3 data, disimpulkan penduga adalah tidak negatif. Pada data seimbang penduga komponen ragam metode REML sama dengan metode ANOVA, yang memiliki ragam minimum. Penduga bagi untuk ketiga metode adalah sama, yaitu Penduga tak bias terhadap dan penyelesaian MKM, berbias terhadap
English Abstract
Analysis of variance for the one-way random classification model if the total variability described into the intra-class variability and the inter-class variability (random variability), in which the level of factor is choosen randomly from infinite set of levels of a factor. The procedure to estimate variance components (1) Method of ANOVA, equalizing sums of square to their expected value, (2) Maximum likelihood estimation (MLE), maximizing of the likelihood equations. (3) The method of REML known as residual maximum likelihood or restricted maximum likelihood, considered of maximizing that part of the likelihood which parameters of the model. The secondary data about the total dry weight of sugarcane (kg/m2), total fresh weight of sugarcane (kg/m2), and dry weight of weeds (g/m2) at 10 locations (subdistricts) in Malang. At each location, there are 4 units of sample as replicates. Based on the analysis of result applied from three data, can be concluded that the estimate of are non-negative. For all cases of balance data, solution of the REML equations are the ANOVA estimators, which have minimum varian. The estimate of for third method are the same, The estimate of is unbiased estimator of and the solution of MLE, is a biased estimator of
| Item Type: | Thesis (Sarjana) |
|---|---|
| Identification Number: | SKR/MIPA/2013/160/051307140 |
| Subjects: | 500 Natural sciences and mathematics > 519 Probabilities and applied mathematics > 519.5 Statistical mathematics |
| Divisions: | Fakultas Matematika dan Ilmu Pengetahuan Alam > Statistika |
| Depositing User: | Hasbi |
| Date Deposited: | 28 Aug 2013 15:26 |
| Last Modified: | 25 Oct 2021 01:58 |
| URI: | http://repository.ub.ac.id/id/eprint/153419 |
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