Stratified sampling in highly polluted data as an effective and reliable alternative to high breakdown point estimators

Observations on certain real-life cases include units that are incompatible with other data sets. Values that are extreme in nature do influence estimates obtained by conventional estimators. Robust estimators are therefore necessary for efficient estimation of parameters. This paper uses stratification with simple random sampling without replacement to optimize sample allocation in stratum for efficient parameter estimation as an alternative method of handling highly contaminated samples. Our proposed method stratifies the highly contaminated population into two non-overlapping sub-populations, and stratified samples of sizes 50, 200, and 500 was drawn. We estimate the model parameters form the contaminated sampled data using ordinary least squares under the proposed method, and using the two high breakdown point estimators; the Least Median of Squares and Least Trimmed Squares. Our findings shows that the proposed method did not perform well for low contamination levels (⩽ 30%) but outperformed Least Median of Squares and Least Trimmed Squares for higher contamination rates (⩾ 40%). This indicates that our proposed method compares well and compete favorably with the two high breakdown point estimators.

MENGATASI PENCILAN PADA PEMODELAN REGRESI LINEAR BERGANDA DENGAN METODE REGRESI ROBUST PENAKSIR LMS

Ordinary Least Squares (OLS) is frequent used method for estimating parameters. OLS estimator is not a robust regression procedure for the presence of outliers, so the estimate becomes inappropriate. Least Median of Squares (LMS) is one of a robust estimator for the presence of outliers and has a high breakdown value. LMS estimate parameters by minimizing the median of squared residuals. Least Median of Squares (LMS) The purpose of this study is geting a regression equation that better than the regression equation before using OLS for the data that having outlier. For the first step, checking if there is outlier at data and then searching regression equation with LMS method. In this study used data stackloss and from estimation parameter of this data, LMS estimator showed better results compared to the OLS estimator because the regression equation from LMS method have smaller value of Mean Absolute Percentage Error (MAPE).

Penggunaan Metode Momen untuk Mengatasi Data Outlier dalam Rancangan Acak Kelompok (Studi Kasus Hasil Produksi Tandan Buah Segar (TBS) selama 5 bulan (kg/pohon))

Cabang matematika yang membahas bagaimana melakukan pengambilan data, pengolahan data, penyajian data, analisis data, dan melakukan pengambilan keputusan disebut dengan Statistika. Salah satu cara untuk memperoleh data dengan melakukan perancangan percobaan. Ada hal penting yang perlu diperhatikan pada data yang diperoleh dari suatu percobaan yaitu adanya outlier dalam data. Suatu data menjadi outlier apabila terjadi kesalahan dalam pengamatan atau tidak berhasilnya suatu pengamatan pada salah satu unit percobaan. Hal ini dalam rancangan percobaan dikenal dengan istilah data hilang. Salah satunya menggunakan metode Regresi Robust. Regresi Robust memiliki beberapa metode estimasi, diantaranya adalah median (Estimasi-M), Least Median of Squares (LMS), least trimmed Squares (LTS), Scale (Estimasi-S), dan Metode Momen (Estimasi-MM). Pada penelitian ini, penerapan dilakukan untuk data Rancangan Acak Kelompok (RAK). Diilustrasikan terdapat pengamatan yang tidak berhasil sehingga datanya menjadi hilang dan diganti dengan nilai 0 yang sifatnya outlier. Pendugaan data hilang menggunakan metode Momen. Uji analisis variansi kemudian dilakukan pada kedua data, dan diperoleh kesimpulan yang sama untuk masing-masing pengaruh perlakuan dan pengaruh kelompok.