Judul: Metode kuadrat terkecil pada analisis data dengan ulangan dan ukuran subsampling tidak sama
Abstrak: Penelitian ini bersumber dari percobaan yang dilakukan oleh seorang mahasiswa program S3 IPB dalam mempelajari pengaruh pemberian 3 taraf protein dan 3 taraf yodium pada kambing induk, serta diamati pula pengaruhnya pada kambing anak yang dilahirkannya. Pada penelitian ini terutama membahas aspek-aspek statistika yang timbul akibat keadaan struktur data pada percobaan tersebut, dimana banyaknya ulangan dan ukuran subsampling yang tidak sama besar. Permasalahan yang timbul adalah dalam penentuan nilai harapan kuadrat tengah perlakuan, penguraian jumlah kuadrat dalam analisis regresi polinomial ortogonal, dan statistik uji yang digunakan untuk menguji hipotesis linear. Untuk penentuan nilai harapan kuadrat tengah, diperkenalkan metode Doolittle dipersingkat, yang sangat berguna jika unit pengamatan dalam percobaan tidak sama. Kemudian dalam analisis regresi polinomial ortogonal, diperkenalkan metode pengortogonalan matriks dengan metode pengortogonalan Gram-Schmidt yang dapat digunakan secara umum. ...
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Judul: Studi simulasi masalah multikolinear pada regresi linear ganda dengan beberapa metode pendugaan dan penerapannya
Abstrak: Penelitian ini bertujuan membandingkan penggunaan Dode kuadrat terkecil (LS), regresi komponen utama. (PC) dan regresi bubungan (RR) dalam mengatasi masalah multikolinear pada analisis regresi linear ganda. Pene- litian ini memakai data simulasi sebagai tiruan masalah multikolinear, kemudian metode-metode tersebut diperiksa kesesuaiannya dengan menggunakan data ekspor karet alam Indonesia sebagai teladan. Untuk mengetahui derajat multikolinear suatu matriks data dalam analisis regresi linear ganda, dapat diguna- kan konsep Indeks Kondisi (j) perubahan akar ciri. Da- lam pendugaan persamaannya apabila kita hadapi matriks data dengan derajat multikolinear hampir bebas, maka da- pat digunakan metode LS. Untuk derajat multikolinear rendah dapat digunakan metode RR. Sedangkan untuk dera- Jat multikolinear tinggi tidak ada metode pendugaan yang baik, untuk itu perlu dipertimbangkan pembuangan peubah pas yang mempunyai multikolinear tinggi dengan peubah as lainnya atau dapat juga digunakan metode LS untuk...dst
Keyword: Statistical Mathematics

Judul: Thermal Characteristics and Dynamics of Tropical Cyclone over Western North Pacific Ocean: A Case Study of Typhoon Songda (Chedeng) 2011
Abstrak: The frequent occasion of Tropical Cyclone (TC) over Western North Pacific (WNP) Ocean lies from 10˚N to 26˚N and 121˚E to 170˚E. Sources of TC development come from warm ocean temperature where latent heat is released during condensation processes and subsequently concentrated in the boundary layer. Relative humidity at 850-700 hPa is responsible to produce the most intense storm. Meanwhile, weak vertical wind shear between 850-200 hPa is one of the dynamical factors that lead to the development of TC. Pressure level of 850-200 hPa is chosen to minimize the thermodynamic effect in the lower troposphere. Typhoon Songda (Chedeng in the Philippines) or TSC lasted from May 18th to 30th, 2011 and strengthened into powerful Super Typhoon stage between May 24th and 27th. Long curving track and the exhibition of all sequences of TC life cycle, TSC is then considered as an ideal case of TC. The objective of the study with case of TSC is to investigate the role of thermal characteristics and dynamics on TC intensity. The research is carried out by using Advanced Research of Weather Research and Forecasting model (WRF ARW model) version 3.3. Two domains are employed in the model. The first domain situate from 02˚N to 40˚N and 118˚E to 149˚E and cover spatial resolution () of 33.1 km. The second domain situate from 09˚N to 27˚N and 119˚E to 132˚E with of 11 km. Timestep of the model () is 120 seconds. The model is supported by the following physical parameterization, i.e., Yonsei University Scheme (YSU) in the boundary layer, Kain-Fritsch scheme (KF) in the cumulus, and WRF Single-Moment 3-class scheme in the microphysics. Initial meteorological condition prior to the formation of the cyclone is generated using WRF ARW standard-release model. Sensitivity of the model output is obtained from a selected single-parameter change scenarios, namely, 10 % to 20 % decrease and increase of wind shear initial data at 850-200 hPa, and by 10 % to 20 % decrease of relative humidity initial data at 850-700 hPa. The result showed that the negative correlations between wind shear and intensity are found in wind shear scenarios. Wind shears of 10 ms-1 which lead to strengthening of the wind intensity in the early period of Typhoon development are found in wind shear scenarios. The effect of wind shear changes on wind intensity is statistically significant in the 20 % wind shear scenarios. During mature stage, weak wind intensity occurred when wind shear increase as given in the WRF standard-release and the 20 % decreasing scenario. Different situation is found in the 20 % increasing scenario where wind shear tend to weak and lead to strong wind intensity at this stage. Meanwhile, the reduction of moisture supply at 850-700 hPa resulting from 20 % decreasing relative humidity play a major role in the weakening of wind intensity and reduces mechanical energy of the cycle process as much as 300 J kg-1.
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