scholarly journals Response Surface Regression with LTS and MM-Estimator to Overcome Outliers on Red Roselle Flowers

Jurnal Varian ◽  
2021 ◽  
Vol 4 (2) ◽  
pp. 91-98
Author(s):  
Trianingsih Eni Lestari ◽  
Rike Desy Tri Yuansa Yuansa
Keyword(s):  
Response Surface ◽  
Plant Height ◽  
Robust Regression ◽  
Estimation Method ◽  
Breakdown Point ◽  
Fertilizer Application ◽  
Least Square ◽  
Surface Response Method ◽  
Response Surface Regression ◽  
Response Method

The surface response method is similar to the regression analysis method which uses procedures or ways of estimating the response function regression model based on the Ordinary Least Square (OLS) method. Unfortunately, using the quadratic method has no drawbacks because it is easily sensitive to assumption deviations due to outlier cases. One of the solutions to the outlier problem is using robust regression. The method of parameters in the regression is very diverse, but the methods used in this study are the Least Trimmed Square (LTS) and MM-estimator methods because both methods have a high breakdown point of nearly 50%. The variables studied were the response variable consisting of red roselle plant height (Y1) and red roselle flower weight (Y2). While the independent variables were soil moisture factor (X1) and NPK fertilizer application factor (X2). The purpose of this study is to estimate the response surface regression parameters. using the LTS and MM-estimator methods on data that contains outliers. The resulting model in data analysis shows the same result that the best model is using the LTS estimation method. The modeling result of plant height obtained an R-Square value of 98,27% with an error is 1,243. Meanwhile, for the red rosella plant flower weight model, the R-Square value was 97,31% with an error is 0.6632.

scholarly journals Overcoming the Existence of Extreme Outlier Data by Using Robust MM Method Based on The Objective Function of Tukey bisquare

2018 ◽  
Vol 1 (1) ◽  
pp. 022-032
Author(s):  
Science Nature
Keyword(s):  
High Efficiency ◽  
Robust Regression ◽  
Weighting Function ◽  
Estimation Method ◽  
Breakdown Point ◽  
Error Component ◽  
Least Square ◽  
Model Parameters ◽  
Observation Data ◽  
Extreme Outlier

A widely used estimation method in estimating regression model parameters is the ordinary least square (OLS) that minimizes the sum of the error squares. In addition to the ease of computing, OLS is a good unbiased estimator as long as the error component assumption ()  in the given model is met. However, in the application, it is often encountered violations of assumptions. One of the violation types is the violation of distributed error assumption which is caused by the existence of the outlier on observation data. Thus, a solid method is required to overcome the existence of outlier, that is Robust Regression. One of the Robust Regression methods commonly used is robust MM method. Robust MM method is a combination of breakdown point and high efficiency. Results obtained based on simulated data generated using SAS software 9.2, shows that the use of objective weighting function tukey bisquare is able to overcome the existence of extreme outlier. Furthermore, it is determined that the value of tuning constant c with Robust MM method is 4.685 and it is obtained95% of efficiency. Thus, the obtained breakdown point is 50%.    

scholarly journals Overcoming the Existence of Extreme Outlier Data by Using Robust MM Method Based on The Objective Function of Tukey bisquare

2018 ◽  
Vol 1 (1) ◽  
pp. 022-032
Author(s):  
Science Nature
Keyword(s):  
High Efficiency ◽  
Robust Regression ◽  
Weighting Function ◽  
Estimation Method ◽  
Breakdown Point ◽  
Error Component ◽  
Least Square ◽  
Model Parameters ◽  
Observation Data ◽  
Extreme Outlier

A widely used estimation method in estimating regression model parameters is the ordinary least square (OLS) that minimizes the sum of the error squares. In addition to the ease of computing, OLS is a good unbiased estimator as long as the error component assumption ()  in the given model is met. However, in the application, it is often encountered violations of assumptions. One of the violation types is the violation of distributed error assumption which is caused by the existence of the outlier on observation data. Thus, a solid method is required to overcome the existence of outlier, that is Robust Regression. One of the Robust Regression methods commonly used is robust MM method. Robust MM method is a combination of breakdown point and high efficiency. Results obtained based on simulated data generated using SAS software 9.2, shows that the use of objective weighting function tukey bisquare is able to overcome the existence of extreme outlier. Furthermore, it is determined that the value of tuning constant c with Robust MM method is 4.685 and it is obtained95% of efficiency. Thus, the obtained breakdown point is 50%.    

scholarly journals Response Surface Model with Comparison of OLS Estimation and MM Estimation

2021 ◽  
Vol 5 (2) ◽  
pp. 273-283
Author(s):  
Salsabila Basalamah ◽  
Edy Widodo
Keyword(s):  
Response Surface ◽  
Robust Regression ◽  
Estimation Method ◽  
Least Square ◽  
Surface Model ◽  
Method Of Moment ◽  
Optimal Point ◽  
Rsm Model ◽  
Mm Estimation

Response Surface Method (RSM) is a collection of statistical techniques in the form of experiments and regression, as well as mathematics that is useful for developing, improving, and optimizing processes. In general, the determination of models in RSM is estimated by linear regression with Ordinary Least Square (OLS) estimation. However, OLS estimation is very weak in the presence of data identified as outliers, so in determining the RSM model a strong and resistant estimation is needed namely robust regression. One estimation method in robust regression is the Method of Moment (MM) estimation. This study aims to compare the OLS estimation and MM estimation method to get the optimal point of response in this case study. Comparison of the best estimation models using the parameters MSE and R^2 adj. The results of MM estimation give better results to the optimal response results in this case study.

scholarly journals Robust Regression with Density Power Divergence: Theory, Comparisons, and Data Analysis

Entropy ◽  
2020 ◽  
Vol 22 (4) ◽  
pp. 399 ◽  
Author(s):  
Marco Riani ◽  
Anthony C. Atkinson ◽  
Aldo Corbellini ◽  
Domenico Perrotta
Keyword(s):  
Robust Regression ◽  
Robust Statistics ◽  
Estimation Method ◽  
Estimation Procedure ◽  
Breakdown Point ◽  
Parameter Estimates ◽  
Normal Density ◽  
Density Power Divergence ◽  
Numerical Minimization ◽  
Power Divergence

Minimum density power divergence estimation provides a general framework for robust statistics, depending on a parameter α , which determines the robustness properties of the method. The usual estimation method is numerical minimization of the power divergence. The paper considers the special case of linear regression. We developed an alternative estimation procedure using the methods of S-estimation. The rho function so obtained is proportional to one minus a suitably scaled normal density raised to the power α . We used the theory of S-estimation to determine the asymptotic efficiency and breakdown point for this new form of S-estimation. Two sets of comparisons were made. In one, S power divergence is compared with other S-estimators using four distinct rho functions. Plots of efficiency against breakdown point show that the properties of S power divergence are close to those of Tukey’s biweight. The second set of comparisons is between S power divergence estimation and numerical minimization. Monitoring these two procedures in terms of breakdown point shows that the numerical minimization yields a procedure with larger robust residuals and a lower empirical breakdown point, thus providing an estimate of α leading to more efficient parameter estimates.

scholarly journals Comparison of M Estimation, S Estimation, with MM Estimation to Get the Best Estimation of Robust Regression in Criminal Cases in Indonesia

2022 ◽  
Vol 18 (2) ◽  
pp. 251-260
Author(s):  
Malecita Nur Atala Singgih ◽  
Achmad Fauzan
Keyword(s):  
Regression Analysis ◽  
Robust Regression ◽  
Estimation Method ◽  
Least Square Method ◽  
Influential Factors ◽  
Least Square ◽  
Method Of Moment ◽  
Best Estimate ◽  
M Estimation ◽  
Mm Estimation

Crime incidents that occurred in Indonesia in 2019 based on Survey Based Data on criminal data sourced from the National Socio-Economic Survey and Village Potential Data Collection produced by the Central Statistics Agency recorded 269,324 cases. The high crime rate is caused by several factors, including poverty and population density. Determination of the most influential factors in criminal acts in Indonesia can be done with Regression Analysis. One method of Regression Analysis that is very commonly used is the Least Square Method. However, Regression Analysis can be used if the assumption test is met. If outliers are found, then the assumption test is not completed. The outlier problem can be overcome by using a robust estimation method. This study aims to determine the best estimation method between Maximum Likelihood Type (M) estimation, Scale (S) estimation, and Method of Moment (MM) estimation on Robust Regression. The best estimate of Robust Regression is the smallest Residual Standard Error (RSE) value and the largest Adjusted R-square. The analysis of case studies of criminal acts in Indonesia in 2019 showed that the best estimate was the S estimate with an RSE value of 4226 and an Adjusted R-square of 0.98  

scholarly journals Interactions of Xanthan Gum and Carboxymethyl Cellulose on Physical and Sensory of Cloudy Asparagus Juice using Response Surface Methodology

2019 ◽  
Vol 31 (10) ◽  
pp. 2345-2350 ◽  
Author(s):  
Nguyen Thi Van Linh ◽  
Vuong Thi Ngoc Mai ◽  
Tran Thi Yen Nhi ◽  
Tri Duc Lam
Keyword(s):  
Response Surface Methodology ◽  
Response Surface ◽  
Carboxymethyl Cellulose ◽  
Xanthan Gum ◽  
Product State ◽  
Concentration Effects ◽  
Surface Response Method ◽  
Response Method ◽  
Physical And Chemical ◽  
Green Asparagus

This study aims to investigate the effect of xanthan gum and carboxymethylcellulose on physical and chemical qualities of green asparagus juice. We adopted the surface-response method and the CCD experiment design with respect to three response variables including stability, viscosity and colour of the product. It was revealed that both xanthan gum and carboxymethylcellulose concentrations are both positively correlated with viscosity and stability of the product. In addition, the coefficient of the interaction of xanthan gum and carboxymethylcellulose was not significant (p < 0.05). In sensory evaluation, both carboxymethylcellulose and xanthan gum were found to be influential on product state. However, hydrocolloid concentration effects were not profound on perceived product colour and odour

scholarly journals Formulasi Breakfast Meal Flakes dari Tepung Suweg dan Stabilized Rice Bran Menggunakan Metode Respon Permukaan

2019 ◽  
Vol 8 (2) ◽  
Author(s):  
Adha Nuriana ◽  
Nur Aini ◽  
Karseno Karseno
Keyword(s):  
Response Surface ◽  
Rice Bran ◽  
Skim Milk ◽  
Ash Content ◽  
Breakfast Meal ◽  
Physical Chemical ◽  
Organoleptic Characteristics ◽  
Surface Response Method ◽  
Response Method ◽  
Central Composite

Penelitian bertujuan untuk mengetahui jumlah tepung suweg dan stabilized rice bran (SRB) yang harus ditambahkan dalam formula breakfast meal flakes (BMF) yang optimal serta mengetahui karakter fisik, kimia, dan organoleptik BMF yang dihasilkan. Penelitian menggunakan metode respon permukaan dengan model Central Composit Design. Faktor yang diteliti yaitu proporsi tepung suweg dan SRB. Pembuatan BMF dilakukan dengan cara pencampuran tepung suweg (proporsi 70-85%) dan SRB (proporsi 15-30%) dengan bahan lainnya yaitu tapioka 10%, susu skim 15%, garam 1,5 %, margarin 5%, baking powder 3 %, vanili 1% (seluruh persentase terhadap berat tepung suweg dan SRB) dan air 100 ml, hingga membentuk adonan, kemudian dilakukan steam blanching, dicetak dan dipanggang. Penelitian ini berhasil untuk menentukan formula optimum untuk pembuatan BMF yaitu sebesar 22,5% untuk SRB dan 77,5% untuk tepung suweg. Produk BMF dari formula terbaik ini mempunyai hardness sebesar 29,44 N, dan serat pangan, antioksidan, protein, kadar lemak, kadar air, kadar abu dan karbohidrat masing-masing sebesar 15,93, 75,10, 11,7, 9,51, 2,4, 2,16, dan 64,21 %. Warna produk akhir adalah coklat keabuan dengan tekstur yang renyah serta aroma yang netral. Rasa pada produk akhir adalah dinilai tidak pahit dengan nilai kesukaan adalah disukai panelis. Kesimpulannya, formula optimal BMF dari tepung suweg dan SRB berhasil ditentukan dengan menggunakan metode respon permukaan.Formulation of Breakfast Meal Flakes Based on Suweg Flours and Stabilized Rice Bran using Response Surface MethodologyAbstractThe purpose of this research was to study the amount of suweg flour and stabilized rice bran (SRB) which must be added in the optimal breakfast meal flakes (BMF) formula and to study the physical, chemical, and organoleptic characteristics of BMF was produced. The study used Response Surface Methodology with the Central Composite Design model examined the proportion of suweg flour and SRB. Making BMF is done by mixing suweg flour (70-85%) and SB flour (15-30%) with other ingredients namely 10% tapioca starch, 15% skim milk, 1.5% salt, 5% margarine, 3% baking powder, 1% vanilla (all percentages of the weight of suweg flour and SRB), and 100 ml of water, to form a mixture, then steam blanching, molded and baked. The best formula for BMF is the proportion of 22.5 % of SRB and 77.5% of flour suweg. Breakfast meal flakes have a hardness value of 29.44 N, dietary fiber 15.93%,  antioxidant of 75.97%,  protein content of 11.7%, fat of 9.51%, moisture of 2.4%, ash content of 2.16%,  the carbohydrate content of 64.21%, color of 2.3 (grayish brown), texture of 3.3 (crispy), flavor 2.5 (neutral), taste of 2.9 (not bitter), and preference 2.9 (likes). As conclusion, surface response method successfully determined the optimal BMF formula from flour suweg and SRB.

scholarly journals Calibration Method of Array Errors for Wideband MIMO Imaging Radar Based on Multiple Prominent Targets

2021 ◽  
Vol 13 (15) ◽  
pp. 2997
Author(s):  
Zheng Zhao ◽  
Weiming Tian ◽  
Yunkai Deng ◽  
Cheng Hu ◽  
Tao Zeng
Keyword(s):  
Multiple Input Multiple Output ◽  
Estimation Method ◽  
Target Position ◽  
Position Estimation ◽  
Least Square ◽  
Antenna Structure ◽  
Imaging Radar ◽  
Position Errors ◽  
Calibration Methods ◽  
Array Errors

Wideband multiple-input-multiple-output (MIMO) imaging radar can achieve high-resolution imaging with a specific multi-antenna structure. However, its imaging performance is severely affected by the array errors, including the inter-channel errors and the position errors of all the transmitting and receiving elements (TEs/REs). Conventional calibration methods are suitable for the narrow-band signal model, and cannot separate the element position errors from the array errors. This paper proposes a method for estimating and compensating the array errors of wideband MIMO imaging radar based on multiple prominent targets. Firstly, a high-precision target position estimation method is proposed to acquire the prominent targets’ positions without other equipment. Secondly, the inter-channel amplitude and delay errors are estimated by solving an equation-constrained least square problem. After this, the element position errors are estimated with the genetic algorithm to eliminate the spatial-variant error phase. Finally, the feasibility and correctness of this method are validated with both simulated and experimental datasets.

Application of Fitting Estimation Method in GPS Height Fitting

2013 ◽  
Vol 694-697 ◽  
pp. 2545-2549 ◽  
Author(s):  
Qian Wen Cheng ◽  
Lu Ben Zhang ◽  
Hong Hua Chen
Keyword(s):  
Least Squares ◽  
Estimation Method ◽  
Least Square ◽  
Least Squares Collocation ◽  
Normal Height ◽  
Geodetic Height ◽  
The Given ◽  
Surveying And Mapping

The key point researched by many scholars in the field of surveying and mapping is how to use the given geodetic height H measured by GPS to obtain the normal height. Although many commonly-used fitting methods have solved many problems, they all value the pending parameters as the nonrandom variables. Figuring out the best valuations, according to the traditional least square principle, only considers its trend or randomness, which is theoretically incomprehensive and have limitations in practice. Therefore, a method is needed not only considers its trend but also takes randomness into account. This method is called the least squares collocation.

The effects of plant density and fertilizer application on yield components in three marrow-stem kale (Brassica oleracea L.) varieties

1971 ◽  
Vol 77 (1) ◽  
pp. 83-89 ◽  
Author(s):  
T. D. Johnston
Keyword(s):  
Brassica Oleracea ◽  
Plant Height ◽  
Yield Components ◽  
Plant Density ◽  
Fertilizer Application ◽  
Varietal Differences ◽  
Crop Density ◽  
Leaf Yield ◽  
Brassica Oleracea L ◽  
Effects Of Density

SummaryThe effects of crop density and fertilizer application on three varieties of marrowstem kale were investigated. The yield of stem, yield of leaf, components of leaf yield and plant height were studied separately. Varietal differences and effects of density and fertilizer application were significant for all characters, except for the effect of crop density on leaf and stem yield per ha.Significant variety x treatment interactions occurred for a number of the characters measured. The possible importance of these is discussed.

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