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 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 Employing particle swarm optimization algorithm for shrinkage parameter estimation in generalized Liu estimator

2020 ◽  
Vol 8 (1) ◽  
pp. 10
Author(s):  
Qamar Abdulkareem Abdulazeez ◽  
Zakariya Yahya Algamal
Keyword(s):  
Particle Swarm Optimization ◽  
Particle Swarm ◽  
Optimization Method ◽  
Least Square ◽  
Superior Performance ◽  
Ridge Estimator ◽  
Swarm Optimization ◽  
Liu Estimator ◽  
Ordinary Least Square ◽  
Parameter Matrix

It is well-known that in the presence of multicollinearity, the Liu estimator is an alternative to the ordinary least square (OLS) estimator and the ridge estimator. Generalized Liu estimator (GLE) is a generalization of the Liu estimator. However, the efficiency of GLE depends on appropriately choosing the shrinkage parameter matrix which is involved in the GLE. In this paper, a particle swarm optimization method, which is a metaheuristic continuous algorithm, is proposed to estimate the shrinkage parameter matrix. The simulation study and real application results show the superior performance of the proposed method in terms of prediction error.   

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.

scholarly journals Exploring relationships among recall effectiveness indicators in the US meat and poultry industry

2019 ◽  
Vol 22 (1) ◽  
pp. 97-106 ◽  
Author(s):  
Jianbin Yu ◽  
Neal H. Hooker
Keyword(s):  
Simultaneous Equation ◽  
Equation Model ◽  
Vital Role ◽  
Economic Consequences ◽  
Least Square ◽  
Least Square Estimator ◽  
Recovery Rates ◽  
The Us ◽  
Food Recalls ◽  
Completion Times

Food recalls need to balance speed and completeness, consumer and firm interests and thus meet managerial and social goals. Effective recalls play a vital role in protecting public health and reducing economic consequences. This paper develops a simultaneous equation model to explore the relationships among three effectiveness indicators; discovery time, completion time and recovery rate. A three-stage least square estimator is applied to control for endogeneity among these indicators. The results suggest that higher recovery rates are associated with shorter discovery times. Longer discovery times led to longer completion times. Longer completion times elicited higher recovery rates. Recalls with high risk to human health had shorter discovery times but longer completion times and lower recovery rates. Recalls issued by large plants had shorter discovery times. Large recalls and national distribution channels negatively impacted discovery times. Compared to other stakeholders, government agencies took longer to discover the problem leading to a recall.

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.

An Analysis of the Structure, Validity, and Reliability of the Collegian Attitudes Toward Inclusive Campus Recreation (CAICR) Scale

2019 ◽  
Vol 43 (2) ◽  
pp. 73-83
Author(s):  
Cathy McKay ◽  
Jung Yeon Park ◽  
Justin Haegele
Keyword(s):  
Internal Consistency ◽  
Factor Model ◽  
Least Square ◽  
Suitable Model ◽  
Campus Recreation ◽  
Validity And Reliability ◽  
Least Square Estimator ◽  
Collegiate Level ◽  
Fitness Sport ◽  
Sport And Recreation

The purpose of this study was to test the construct validity and internal consistency of the Collegian Attitudes toward Inclusive Campus Recreation (CAICR) Scale, a collegiate adaptation of the Children’s Attitudes toward Integrated Physical Education–Revised Scale. The CAICR seeks to measure attitudes toward inclusive lifetime fitness, sport, and recreation at the collegiate level. Participants were 192 college students. The factor structure of the scale was investigated using a confirmatory factor analysis with the weighted least square estimator. The CAICR Scale demonstrated acceptable internal consistency levels for the complete scale (11 items), inclusion subscale (6 items), and sport modification subscale (5 items). Results suggest that the 2-factor model (indicating inclusion and sport modification) showed suitable model fit, and the model outperformed a single-factor solution. Current findings suggest that the CAICR has the ability to contribute to sociocultural attitude research at the collegiate level in a valid and reliable manner.

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