scholarly journals A New Ridge-Type Estimator for the Linear Regression Model: Simulations and Applications

Scientifica ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-16 ◽  
Author(s):  
B. M. Golam Kibria ◽  
Adewale F. Lukman
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Linear Regression Model ◽  
Ridge Regression ◽  
Real Life ◽  
Economic Data ◽  
Nonlinear Regression Models ◽  
Shrinkage Methods ◽  
Regression Estimators ◽  
Better Than

The ridge regression-type (Hoerl and Kennard, 1970) and Liu-type (Liu, 1993) estimators are consistently attractive shrinkage methods to reduce the effects of multicollinearity for both linear and nonlinear regression models. This paper proposes a new estimator to solve the multicollinearity problem for the linear regression model. Theory and simulation results show that, under some conditions, it performs better than both Liu and ridge regression estimators in the smaller MSE sense. Two real-life (chemical and economic) data are analyzed to illustrate the findings of the paper.

scholarly journals Modified One-Parameter Liu Estimator for the Linear Regression Model

2020 ◽  
Vol 2020 ◽  
pp. 1-17
Author(s):  
Adewale F. Lukman ◽  
B. M. Golam Kibria ◽  
Kayode Ayinde ◽  
Segun L. Jegede
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Linear Regression Model ◽  
Ridge Regression ◽  
Real Life ◽  
Liu Estimator ◽  
Real Life Data ◽  
Squared Prediction Error ◽  
Simulation Results ◽  
Better Than

Motivated by the ridge regression (Hoerl and Kennard, 1970) and Liu (1993) estimators, this paper proposes a modified Liu estimator to solve the multicollinearity problem for the linear regression model. This modification places this estimator in the class of the ridge and Liu estimators with a single biasing parameter. Theoretical comparisons, real-life application, and simulation results show that it consistently dominates the usual Liu estimator. Under some conditions, it performs better than the ridge regression estimators in the smaller MSE sense. Two real-life data are analyzed to illustrate the findings of the paper and the performances of the estimators assessed by MSE and the mean squared prediction error. The application result agrees with the theoretical and simulation results.

scholarly journals Feasible Generalized Stein-Rule Restricted Ridge Regression Estimators

2017 ◽  
Vol 13 (1) ◽  
pp. 77-97
Author(s):  
Nimet Özbay ◽  
Issam Dawoud ◽  
Selahattin Kaçıranlar
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Linear Regression ◽  
Regression Model ◽  
Linear Regression Model ◽  
Ridge Regression ◽  
Simulation Experiment ◽  
Regression Estimators ◽  
Coefficient Vector ◽  
General Linear Regression Model

Abstract Several versions of the Stein-rule estimators of the coefficient vector in a linear regression model are proposed in the literature. In the present paper, we propose new feasible generalized Stein-rule restricted ridge regression estimators to examine multicollinearity and autocorrelation problems simultaneously for the general linear regression model, when certain additional exact restrictions are placed on these coefficients. Moreover, a Monte Carlo simulation experiment is performed to investigate the performance of the proposed estimator over the others.

scholarly journals Performance of Some Stochastic Restricted Ridge Estimator in Linear Regression Model

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Jibo Wu ◽  
Chaolin Liu
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Simulation Study ◽  
Linear Regression Model ◽  
Ridge Regression ◽  
Ridge Estimator ◽  
Numerical Example ◽  
Regression Estimators ◽  
Mixed Estimator

This paper considers several estimators for estimating the stochastic restricted ridge regression estimators. A simulation study has been conducted to compare the performance of the estimators. The result from the simulation study shows that stochastic restricted ridge regression estimators outperform mixed estimator. A numerical example has been also given to illustrate the performance of the estimators.

Applying Artificial Neural Networks. I. Estimating Nicotine in Tobacco from near Infrared Data

1995 ◽  
Vol 3 (3) ◽  
pp. 133-142 ◽  
Author(s):  
M. Hana ◽  
W.F. McClure ◽  
T.B. Whitaker ◽  
M. White ◽  
D.R. Bahler
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Linear Regression Model ◽  
Near Infrared ◽  
Back Propagation ◽  
Linear Network ◽  
Data Set ◽  
Input Layer ◽  
Propagation Network ◽  
Better Than

Two artificial neural network models were used to estimate the nicotine in tobacco: (i) a back-propagation network and (ii) a linear network. The back-propagation network consisted of an input layer, an output layer and one hidden layer. The linear network consisted of an input layer and an output layer. Both networks used the generalised delta rule for learning. Performances of both networks were compared to the multiple linear regression method MLR of calibration. The nicotine content in tobacco samples was estimated for two different data sets. Data set A contained 110 near infrared (NIR) spectra each consisting of reflected energy at eight wavelengths. Data set B consisted of 200 NIR spectra with each spectrum having 840 spectral data points. The Fast Fourier transformation was applied to data set B in order to compress each spectrum into 13 Fourier coefficients. For data set A, the linear regression model gave better results followed by the back-propagation network which was followed by the linear network. The true performance of the linear regression model was better than the back-propagation and the linear networks by 14.0% and 18.1%, respectively. For data set B, the back-propagation network gave the best result followed by MLR and the linear network. Both the linear network and MLR models gave almost the same results. The true performance of the back-propagation network model was better than the MLR and linear network by 35.14%.

scholarly journals Urban Population Distribution Mapping with Multisource Geospatial Data Based on Zonal Strategy

2020 ◽  
Vol 9 (11) ◽  
pp. 654
Author(s):  
Guanwei Zhao ◽  
Muzhuang Yang
Keyword(s):  
Random Forest ◽  
Linear Regression ◽  
Regression Model ◽  
Linear Regression Model ◽  
Population Distribution ◽  
Random Forest Model ◽  
Geospatial Data ◽  
Forest Model ◽  
Distribution Mapping ◽  
Better Than

Mapping population distribution at fine resolutions with high accuracy is crucial to urban planning and management. This paper takes Guangzhou city as the study area, illustrates the gridded population distribution map by using machine learning methods based on zoning strategy with multisource geospatial data such as night light remote sensing data, point of interest data, land use data, and so on. The street-level accuracy evaluation results show that the proposed approach achieved good overall accuracy, with determinant coefficient (R2) being 0.713 and root mean square error (RMSE) being 5512.9. Meanwhile, the goodness of fit for single linear regression (LR) model and random forest (RF) regression model are 0.0039 and 0.605, respectively. For dense area, the accuracy of the random forest model is better than the linear regression model, while for sparse area, the accuracy of the linear regression model is better than the random forest model. The results indicated that the proposed method has great potential in fine-scale population mapping. Therefore, it is advised that the zonal modeling strategy should be the primary choice for solving regional differences in the population distribution mapping research.

CASE-BASED SOFTWARE QUALITY PREDICTION

2000 ◽  
Vol 10 (02) ◽  
pp. 139-152 ◽  
Author(s):  
K. GANESAN ◽  
TAGHI M. KHOSHGOFTAAR ◽  
EDWARD B. ALLEN
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Software Quality ◽  
Linear Regression Model ◽  
Multiple Linear Regression Model ◽  
Case Based Reasoning ◽  
Quality Prediction ◽  
Software Quality Prediction ◽  
Case Based ◽  
Better Than

Highly reliable software is becoming an essential ingredient in many systems. However, assuring reliability often entails time-consuming costly development processes. One cost-effective strategy is to target reliability-enhancement activities to those modules that are likely to have the most problems. Software quality prediction models can predict the number of faults expected in each module early enough for reliability enhancement to be effective. This paper introduces a case-based reasoning technique for the prediction of software quality factors. Case-based reasoning is a technique that seeks to answer new problems by identifying similar "cases" from the past. A case-based reasoning system can function as a software quality prediction model. To our knowledge, this study is the first to use case-based reasoning systems for predicting quantitative measures of software quality. A case study applied case-based reasoning to software quality modeling of a family of full-scale industrial software systems. The case-based reasoning system's accuracy was much better than a corresponding multiple linear regression model in predicting the number of design faults. When predicting faults in code, its accuracy was significantly better than a corresponding multiple linear regression model for two of three test data sets and statistically equivalent for the third.

scholarly journals The selective regularization of a linear regression model

2021 ◽  
Vol 2099 (1) ◽  
pp. 012024
Author(s):  
V N Lutay ◽  
N S Khusainov
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Linear Regression Model ◽  
Ridge Regression ◽  
Triangular Decomposition ◽  
System Matrix ◽  
Original Dataset ◽  
The Matrix ◽  
Matrix Conditioning ◽  
Selection Of

Abstract This paper discusses constructing a linear regression model with regularization of the system matrix of normal equations. In contrast to the conventional ridge regression, where positive parameters are added to all diagonal terms of a matrix, in the method proposed only those matrix diagonal entries that correspond to the data with a high correlation are increased. This leads to a decrease in the matrix conditioning and, therefore, to a decrease in the corresponding coefficients of the regression equation. The selection of the entries to be increased is based on the triangular decomposition of the correlation matrix of the original dataset. The effectiveness of the method is tested on a known dataset, and it is performed not only with a ridge regression, but also with the results of applying the widespread algorithms LARS and Lasso.

Predicting the performance of multi-media filters using artificial neural networks

2016 ◽  
Vol 74 (9) ◽  
pp. 2225-2233 ◽  
Author(s):  
Alaa H. Hawari ◽  
Wael Alnahhal
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Linear Regression Model ◽  
Real Life ◽  
Absolute Error ◽  
Ann Model ◽  
Model Complex ◽  
Multi Media ◽  
Artificial Neural ◽  
The Impact

The impact of flow rate and turbidity on the performance of multi-media filtration has been studied using an artificial neural network (ANN) based model. The ANN model was developed and tested based on experimental data collected from a pilot scale multi-media filter system. Several ANN models were tested, and the best results with the lowest errors were achieved with two hidden layers and five neurons per layer. To examine the significance and efficiency of the developed ANN model it was compared with a linear regression model. The R2 values for the actual versus predicted results were 0.9736 and 0.9617 for the ANN model and the linear regression model, respectively. The ANN model showed an R-squared value increase of 1.22% when compared to the linear regression model. In addition, the ANN model gave a significant reduction of 91.5% and 97.9% in the mean absolute error and the root mean square error, respectively when compared to the linear regression model. The proposed model has proven to give plausible results to model complex relationships that can be used in real life water treatment plants.

scholarly journals The Performance of Some Restricted Estimators In Restricted Linear Regression Model

2021 ◽  
Vol 26 (2) ◽  
Author(s):  
Bader Aboud ◽  
Mustafa Ismaeel Naif
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Simulation Study ◽  
Linear Regression Model ◽  
Regression Estimator ◽  
Mean Square ◽  
Ridge Regression Estimator ◽  
The Mean ◽  
Biased Estimators ◽  
Better Than

In the linear regression model, the restricted biased estimation as one of important  methods to addressing the high variance and the  multicollinearity problems. In this paper, we make the simulation study of the some restricted biased estimators. The mean square error (MME) criteria are used to make a comparison  among them. According to the simulation study we observe that, the performance of the restricted modified unbiased  ridge regression estimator (RMUR) was proposed by  Bader and Alheety (2020)  is better than  of these estimators. Numerical example have been considered to illustrate the performance of the estimators.

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