scholarly journals Modified Robust Ridge M-Estimators in Two-Parameter Ridge Regression Model

2021 ◽  
Vol 2021 ◽  
pp. 1-24
Author(s):  
Seyab Yasin ◽  
Sultan Salem ◽  
Hamdi Ayed ◽  
Shahid Kamal ◽  
Muhammad Suhail ◽  
...  
Keyword(s):  
Ridge Regression ◽  
Mean Squared Error ◽  
Least Square ◽  
Ridge Estimator ◽  
Least Square Estimator ◽  
Squared Error ◽  
Joint Problem ◽  
Ridge Regression Estimator ◽  
Simulation Results ◽  
Two Parameter

The methods of two-parameter ridge and ordinary ridge regression are very sensitive to the presence of the joint problem of multicollinearity and outliers in the y-direction. To overcome this problem, modified robust ridge M-estimators are proposed. The new estimators are then compared with the existing ones by means of extensive Monte Carlo simulations. According to mean squared error (MSE) criterion, the new estimators outperform the least square estimator, ridge regression estimator, and two-parameter ridge estimator in many considered scenarios. Two numerical examples are also presented to illustrate the simulation results.

scholarly journals Modelling of Horizontal Flexible Plate Structure Using Artificial Bee Colony Algorithm

2018 ◽  
Vol 7 (4.36) ◽  
pp. 415
Author(s):  
Muhamad Sukri Hadi ◽  
Sukri Hadi Zaurah Mat Darus
Keyword(s):  
System Identification ◽  
Artificial Bee Colony Algorithm ◽  
Artificial Bee Colony ◽  
Mean Squared Error ◽  
Least Square ◽  
Flexible Plate ◽  
Plate Structure ◽  
Bee Colony ◽  
Squared Error ◽  
Plate System

This paper presents the performance of system identification for modeling the horizontal flexible plate system using artificial bee colony and recursive least square algorithms. Initially, the experimental rig of flexible plate was designed and fabricated with all edges clamped boundary condition at the horizontal position. Then, the instrumentation and data acquisition systems were integrated into the rig for acquiring the input-output vibration experimentally. The collected data in the experiment will be used later for modeling the dynamic system of horizontal flexible plate system using system identification. The effectiveness of the developed model will be validated using mean squared error, one step ahead prediction, correlation tests and pole zero diagram stability. The estimated of the developed models were found are acceptable and possible to be used as a platform of controller development for vibration suppression of the undesirable vibration in the flexible plate structure. It was found that the artificial bee colony algorithm has performed better in this study by achieving the lowest mean squared error, good correlation test and high stability in the pole zero diagram.  

scholarly journals On shrinkage and selection: ANOVA model

2018 ◽  
Vol 51 (2) ◽  
pp. 165-191 ◽  
Author(s):  
A. K. Md. Ehsanes Saleh ◽  
M. Arashi ◽  
M. Norouzirad ◽  
B M Goalm Kibria
Keyword(s):  
Lower Bound ◽  
Preliminary Test ◽  
Least Square ◽  
Graphical Display ◽  
Ridge Estimator ◽  
Least Square Estimator ◽  
Projection Scheme ◽  
Anova Model ◽  
Compare And Contrast ◽  
Risk Equivalent

This paper considers the estimation of the parameters of an ANOVA model when sparsity is suspected. Accordingly, we consider the least square estimator (LSE), restricted LSE, preliminary test and Stein-type estimators, together with three penalty estimators, namely, the ridge estimator, subset selection rules (hard threshold estimator) and the LASSO (soft threshold estimator). We compare and contrast the L2-risk of all the estimators with the lower bound of L2-risk of LASSO in a family of diagonal projection scheme which is also the lower bound of the exact L2-risk of LASSO. The result of this comparison is that neither LASSO nor the LSE, preliminary test, and Stein-type estimators outperform each other uniformly. However, when the model is sparse, LASSO outperforms all estimators except “ridge” estimator since both LASSO and ridge are L2-risk equivalent under sparsity. We also find that LASSO and the restricted LSE are L2-risk equivalent and both outperform all estimators (except ridge) depending on the dimension of sparsity. Finally, ridge estimator outperforms all estimators uniformly. Our finding are based on L2-risk of estimators and lower bound of the risk of LASSO together with tables of efficiency and graphical display of efficiency and not based on simulation.

scholarly journals KINERJA JACKKNIFE RIDGE REGRESSION DALAM MENGATASI MULTIKOLINEARITAS

2014 ◽  
Vol 3 (4) ◽  
pp. 146
Author(s):  
HANY DEVITA ◽  
I KOMANG GDE SUKARSA ◽  
I PUTU EKA N. KENCANA
Keyword(s):  
Linear Correlation ◽  
Ridge Regression ◽  
Minimum Variance ◽  
Sum Of Squares ◽  
Least Square ◽  
Bias Parameter ◽  
Ridge Estimator ◽  
Ordinary Least Square ◽  
Parameter Estimations

Ordinary least square is a parameter estimations for minimizing residual sum of squares. If the multicollinearity was found in the data, unbias estimator with minimum variance could not be reached. Multicollinearity is a linear correlation between independent variabels in model. Jackknife Ridge Regression(JRR) as an extension of Generalized Ridge Regression (GRR) for solving multicollinearity.  Generalized Ridge Regression is used to overcome the bias of estimators caused of presents multicollinearity by adding different bias parameter for each independent variabel in least square equation after transforming the data into an orthoghonal form. Beside that, JRR can  reduce the bias of the ridge estimator. The result showed that JRR model out performs GRR model.

Adaptive Mismatch Compensation for Rate Integrating Vibratory Gyroscopes With Improved Convergence Rate

2014 ◽  
Author(s):  
Fu Zhang ◽  
Ehsan Keikha ◽  
Behrooz Shahsavari ◽  
Roberto Horowitz
Keyword(s):  
Convergence Rate ◽  
Degrees Of Freedom ◽  
Rotation Angle ◽  
Least Square ◽  
Parameter Estimates ◽  
Unknown Parameters ◽  
Least Square Estimator ◽  
Vibratory Gyroscopes ◽  
Adaptive Compensator ◽  
Simulation Results

This paper presents an online adaptive algorithm to compensate damping and stiffness frequency mismatches in rate integrating Coriolis Vibratory Gyroscopes (CVGs). The proposed adaptive compensator consists of a least square estimator that estimates the damping and frequency mismatches, and an online compensator that corrects the mismatches. In order to improve the adaptive compensator’s convergence rate, we introduce a calibration phase where we identify relations between the unknown parameters (i.e. mismatches, rotation rate and rotation angle). Calibration results show that the unknown parameters lie on a hyperplane. When the gyro is in operation, we project parameters estimated from the least square estimator onto the hyperplane. The projection will reduce the degrees of freedom in parameter estimates, thus guaranteeing persistence of excitation and improving convergence rate. Simulation results show that utilization of the projection method will drastically improve convergence rate of the least square estimator and improve gyro performance.

scholarly journals THE EFFECT OF OPENING TYPE ON THERMAL CONVENIENCE OF THE OLD AND NEW BUILDING CLASSROOM

2019 ◽  
Vol 24 (2) ◽  
pp. 75-87
Author(s):  
Ali Anton Senoaji ◽  
Arif Kusumawanto ◽  
Sentagi Sesotya Utami
Keyword(s):  
Wind Speed ◽  
Air Temperature ◽  
Mean Squared Error ◽  
Comparative Method ◽  
Field Measurements ◽  
Root Mean Squared Error ◽  
Wind Speeds ◽  
Squared Error ◽  
Simulation Results ◽  
New Buildings

This study was aimed at analyzing the effect of opening type on the thermal convenience of classrooms in old and new buildings at SMK Negeri 3 Yogyakarta. This study used a qualitative comparative method and the simulation of IES VE 2018. The field air measurement is carried out at 10 measurement points and 5 measurement points in each class, with a height of 1.5 m. Field measurements were carried out in March 2019, at 06.30-16.30 WIB. The parameters used in the study were air temperature, humidity and wind speed. Air temperature and humidity were measured using a Thermo hygrometer. Wind speed was measured using an anemometer. The data collection method is carried out by observation and measurement. Root Mean Squared Error (RMSE) was used to validate the data. The results show the best thermal convenience of the classroom was obtained during the simulation using the type of Windows Awning, with a full aperture area. Simulation results show a comfortable distribution of airflow in the classroom at wind speeds above 0.15-0.28 m/sec, Temperature 25.07-27.10oC.PENGARUH TIPE BUKAAN TERHADAP KENYAMANAN TERMAL RUANG KELAS BANGUNAN LAMA DAN BARU Tujuan dari penelitian yaitu menganalisis pengaruh bukaan terhadap kenyamanan termal ruang kelas pada bangunan lama dan baru, di SMK Negeri 3 Yogyakarta. Penelitian ini menggunakan metode komparatif kualitatif yaitu dan hasil simulasi IES VE 2018. Pengukuran udara luar dilakukan pada 10 titik pengukuran dan sebanyak 5 titik pengukuran disetiap kelasnya, dengan ketinggian 1,5 m. Pengukuran lapangan dilakukan pada bulan Maret tahun 2019, waktu 06.30-16.30 WIB. Parameter yang digunakan dalam penelitian yaitu temperatur udara, kelembaban dan kecepatan angin. Temperatur udara dan kelembaban diukur dengan menggunakan alat thermo hygrometer. Kecepatan angin diukur dengan menggunakan alat anemometer. Metode pengumpulan data dilakukan dengan metode pengamatan dan pengukuran. Validasi data menggunakan Root Mean Squared Error (RMSE). Hasil penelitian menunjukkan kenyamanan termal ruang kelas terbaik diperoleh pada saat simulasi menggunakan tipe bukaan ke atas atau Awning Windows, dengan area bukaan penuh. Hasil simulasi menunjukkan distribusi aliran udara yang nyaman di dalam ruang kelas pada kecepatan angin di atas 0,15-0,28 m/det, Temperatur 25,07 -27,10o C. 

scholarly journals Two Different Classes of Shrinkage Estimators for the Scale Parameter of the Rayleigh Distribution

2021 ◽  
Vol 19 (1) ◽  
pp. 2-21
Author(s):  
Talha Omer ◽  
Zawar Hussain ◽  
Muhammad Qasim ◽  
Said Farooq Shah ◽  
Akbar Ali Khan
Keyword(s):  
Simulation Study ◽  
Mean Squared Error ◽  
Scale Parameter ◽  
Rayleigh Distribution ◽  
Shrinkage Estimators ◽  
Unbiased Estimators ◽  
Squared Error ◽  
The Mean ◽  
Simulation Results

Shrinkage estimators are introduced for the scale parameter of the Rayleigh distribution by using two different shrinkage techniques. The mean squared error properties of the proposed estimator have been derived. The comparison of proposed classes of the estimators is made with the respective conventional unbiased estimators by means of mean squared error in the simulation study. Simulation results show that the proposed shrinkage estimators yield smaller mean squared error than the existence of unbiased estimators.

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