PEMODELAN REGRESI RIDGE ROBUST S,M, MM-ESTIMATOR DALAM PENANGANAN MULTIKOLINIERITAS DAN PENCILAN (Studi Kasus : Faktor-Faktor yang Mempengaruhi Kemiskinan di Jawa Tengah Tahun 2020)

The Ordinary Least Squares (OLS) is one of the most commonly used method to estimate linier regression parameters. If there is a violation of assumptions such as multicolliniearity especially coupled with the outliers, then the regression with OLS is no longer used. One method can be used to solved the multicollinearity and outliers problem is Ridge Robust Regression. Ridge Robust Regression is a modification of ridge regression method used to solve the multicolliniearity and using some estimators of robust regression used to solve the outlier, the estimator including : Maximum likelihood estimator (M-estimator), Scale estimator (S-estimator), and Method of moment estimator (MM-estimator). The case study can be used with this method is data with multicollinearity and outlier, the case study in this research is poverty in Central Java 2020 influenced by life expentancy, unemployment number, GRDP rate, dependency ratio, human development index, the precentage of population over 15 years of age with the highest education in primary school, mean years school. The result of estimation using OLS show that there is a multicollinearity and presence an outliers. Applied the ridge robust regression to case study prove that ridge robust regression can improve parameter estimation. The best ridge robust regression model is Ridge Robust Regression S-Estimator. The influence value of predictor variabels to poverty is 73,08% and the MSE value is 0,00791.

The Redescending M estimator For detection and deletion of Outliers in Regression analysis

Outliers in a statistical analysis strongly affect the performance of the ordinary least squares, such outliers need to be detected and extreme outliers deleted. Thisp is aimed at proposing a Redescending M-estimator which is more efficient and robust compared to other existing methods. The results show that the proposed method is effective in detection and deletion of extreme outliers compared to the other existing ones.

A New Efficient Redescending M-Estimator for Robust Fitting of Linear Regression Models in the Presence of Outliers

Robust regression is an important iterative procedure that seeks analyzing data sets that are contaminated with outliers and unusual observations and reducing their impact over regression coefficients. Robust estimation methods have been introduced to deal with the problem of outliers and provide efficient and stable estimates in their presence. Various robust estimators have been developed in the literature to restrict the unbounded influence of the outliers or leverage points on the model estimates. Here, a new redescending M-estimator is proposed using a novel objective function with the prime focus on getting highly robust and efficient estimates that give promising results. It is evident from the results that, for normal and clean data, the proposed estimator is almost as efficient as ordinary least square method and, however, becomes highly resistant to outliers when it is used for contaminated datasets. The simulation study is being carried out to assess the performance of the proposed redescending M-estimator over different data generation scenarios including normal, t-distribution, and double exponential distributions with different levels of outliers’ contamination, and the results are compared with the existing redescending M-estimators, e.g., Huber, Tukey Biweight, Hampel, and Andrew-Sign function. The performance of the proposed estimators was also checked using real-life data applications of the estimators and found that the proposed estimators give promising results as compared to the existing estimators.

AN ALGORITHM OF TREATMENT OF THE RESULTS OF MULTIPLE MEASUREMENTS OF COMPOSITION AND PROPERTIES OF PETROLEUM PRODUCTS

Разработаны новые робастные алгоритмы обработки результатов многократных измерений состава и свойств нефтепродуктов, учитывающие тот факт, что эмпирическая функция распределения результатов измерений состава и свойств нефтепродуктов представляет собой смесь двух нормальных распределений с разными значениями параметров положения и масштаба. В случае измерений состава и свойств нефтепродуктов в качестве робастных оценок параметра положения и параметра масштаба выборки предложено использовать М-оценки с предварительным масштабированием на основе модифицированной функции Хампеля. Для нахождения М-оценки предложены два итеративных способа вычисления на основе средневзвешенного метода наименьших квадратов, отличающиеся процедурами расчета начальных оценок параметров положения и масштаба выборки. При числе результатов в выборке более двадцати в качестве начальных значений параметров положения и масштаба целесообразно использовать α‑урезанное среднее и α‑урезанное стандартное отклонение с долей усечения 0,05. При числе результатов в выборке менее двадцати в качестве начальных значений параметра положения и параметра масштаба обоснованно использование робастных оценок, не требующих удаления части данных. В качестве начальной оценки параметра положения предложено использовать оценку Ходжеса – Лемана; в качестве параметра масштаба – медианы абсолютных разностей. Предложенные робастные алгоритмы могут быть использованы при обработке результатов эксперимента по определению показателей прецизионности, правильности и точности методик измерений состава и свойств нефтепродуктов, итогов межлабораторных сравнительных испытаний нефтепродуктов, расчете аттестованного значения стандартных образцов состава и свойств нефтепродуктов, а также в других случаях многократных наблюдений. New robust algorithms of treatment of the results of multiple measurements of composition and properties of petroleum products were developed in respect that empirical distribution function of the results of measurements of composition and properties of petroleum products are the mixture of two normal distributions with different values of position and scale parameters. In case of measurements of composition and properties of petroleum products it has been proposed to use M-estimator with pre-scaling based on modified Hampel function as robust estimators of position and scale parameters. To calculation M-estimator two iterative methods based on weighted average method of least squares were suggested which differs by procedures of initial estimators of position and scale parameters of sample. In case of more than twenty results in sample, it is expedient to apply α-truncated mean and α-truncated standard deviation with 0,05 truncation share as initial values of position and scale parameters. In case of less than twenty results in sample, it is reasonable to apply robust estimators as initial values of position and scale parameters, which don’t require removal of some part of the data. It was proposed to use Hodges-Lehmann estimator as an initial value of position parameter and median of absolute differences as a scale parameter. The proposed robust algorithms can be used in treatment of experiment results on determination of indexes of precision, trueness and accuracy of the methods of measurement of composition and properties of petroleum products; results of interlaboratory comparison tests of petroleum products; calculation of certified value of standard samples of composition and properties of petroleum products and in other cases of multiple observations.

Sample Size determination for Censored Data

This study aims to describe sample size determination procedure in survival analysis using a real-world example. In this method simulation is used for sample size and precision calculations with censored data that concentrates on various sample sizes involved in carrying out the estimates and precision calculation. The Kaplan-Meier (K-M) estimator is chosen as a point estimator, and the precision measurement focuses on the mean square error, standard error, and confidence limits. Information obtained on the recovery time, in days, of patients from the population are compared with results taken from the sample group. Results showed a cutoff point of sample of size 675 on the basis of mean square error, standard error and confidence limit.

Analisis Hubungan Kepadatan Penduduk dengan Pola Penyebaran COVID-19 Provinsi DKI Jakarta menggunakan Regresi Robust

COVID-19 pandemic have been spread around the world since the first outbreak on Desember 2019 in Wuhan, China. DKI Jakarta as one of the highest population density among 34 provinces in Indonesia, has become an endemic area of COVID-19 with the rate of new cases show some fluctuation for each month along 2020. This is a secondary data research which drawn from Health Ministry of Indonesia as well as Center of Statistics for DKI Jakarta. Focus and the scope of this paper is on analyzing the relation between new cases of COVID-19 with population density of Jakarta’s districts. Descriptive and inferential analysis that combined with Robust Regression Test are conducted due to some outliers data. This unbiased method shows a good regression model of spreading new positive cases. M-Estimator Robust Regression with Tukey Bisquare function, shows the best result with the least Residual Standar Error (RSE), that is 0.411. Analysis on statistical test for the chosen model shows that population density has significant impacts on outbreak pattern of COVID-19 in Jakarta. But mobilities and interactions betweeen citizens has also give a great impact.