Ridge Estimator Research Articles

Tobit Liu estimation of censored regression model: an application to Mroz data and a Monte Carlo simulation study

Multicollinearity is often ignored in censored regression model. In this respect, Tobit Liu estimation is proposed as an alternative in order to dispel the adverse effects of multicollinearity on the maximum likelihood estimation. Tobit Liu estimator is compared with Tobit ridge estimator and Tobit maximum likelihood estimator, theoretically via mean square error. For empirical analysis, we prefer Mroz dataset which is a phenomenon in the context of censored regression. Since many studies have investigated Mroz dataset by neglecting multicollinearity, we handle this dataset in the context of multicollinearity in this paper. Moreover, it is seen that multicollinearity is not included in pioneer studies' simulation designs. Therefore, we conduct a Monte Carlo simulation study where we take account of different levels of multicollinearity while generating data. Briefly, this study contributes to filling an important gap in the literature and proposes to investigate other econometrically censored data in the context of multicollinearity.

Biased Adjusted Poisson Ridge Estimators-Method and Application

Månsson and Shukur (Econ Model 28:1475–1481, 2011) proposed a Poisson ridge regression estimator (PRRE) to reduce the negative effects of multicollinearity. However, a weakness of the PRRE is its relatively large bias. Therefore, as a remedy, Türkan and Özel (J Appl Stat 43:1892–1905, 2016) examined the performance of almost unbiased ridge estimators for the Poisson regression model. These estimators will not only reduce the consequences of multicollinearity but also decrease the bias of PRRE and thus perform more efficiently. The aim of this paper is twofold. Firstly, to derive the mean square error properties of the Modified Almost Unbiased PRRE (MAUPRRE) and Almost Unbiased PRRE (AUPRRE) and then propose new ridge estimators for MAUPRRE and AUPRRE. Secondly, to compare the performance of the MAUPRRE with the AUPRRE, PRRE and maximum likelihood estimator. Using both simulation study and real-world dataset from the Swedish football league, it is evidenced that one of the proposed, MAUPRRE ( hat{k}_{q4} ) performed better than the rest in the presence of high to strong (0.80–0.99) multicollinearity situation.

Differentially Private Precision Matrix Estimation

In this paper, we study the problem of precision matrix estimation when the dataset contains sensitive information. In the differential privacy framework, we develop a differentially private ridge estimator by perturbing the sample covariance matrix. Then we develop a differentially private graphical lasso estimator by using the alternating direction method of multipliers (ADMM) algorithm. Furthermore, we prove theoretical results showing that the differentially private ridge estimator for the precision matrix is consistent under fixed-dimension asymptotic, and establish a convergence rate of differentially private graphical lasso estimator in the Frobenius norm as both data dimension p and sample size n are allowed to grow. The empirical results that show the utility of the proposed methods are also provided.

On the Asymptotic Distribution of Ridge Regression Estimators Using Training and Test Samples

The asymptotic distribution of the linear instrumental variables (IV) estimator with empirically selected ridge regression penalty is characterized. The regularization tuning parameter is selected by splitting the observed data into training and test samples and becomes an estimated parameter that jointly converges with the parameters of interest. The asymptotic distribution is a nonstandard mixture distribution. Monte Carlo simulations show the asymptotic distribution captures the characteristics of the sampling distributions and when this ridge estimator performs better than two-stage least squares. An empirical application on returns to education data is presented.

Comparative Analysis of Some Structural Equation Model Estimation Methods with Application to Coronary Heart Disease Risk

This study compared a ridge maximum likelihood estimator to Yuan and Chan (2008) ridge maximum likelihood, maximum likelihood, unweighted least squares, generalized least squares, and asymptotic distribution-free estimators in fitting six models that show relationships in some noncommunicable diseases. Uncontrolled hypertension has been shown to be a leading cause of coronary heart disease, kidney dysfunction, and other negative health outcomes. It poses equal danger when asymptomatic and undetected. Research has also shown that it tends to coexist with diabetes mellitus (DM), with the presence of DM doubling the risk of hypertension. The study assessed the effect of obesity, type II diabetes, and hypertension on coronary risk and also the existence of converse relationship with structural equation modelling (SEM). The results showed that the two ridge estimators did better than other estimators. Nonconvergence occurred for most of the models for asymptotic distribution-free estimator and unweighted least squares estimator whilst generalized least squares estimator had one nonconvergence of results. Other estimators provided competing outputs, but unweighted least squares estimator reported unreliable parameter estimates such as large chi-square test statistic and root mean square error of approximation for Model 3. The maximum likelihood family of estimators did better than others like asymptotic distribution-free estimator in terms of overall model fit and parameter estimation. Also, the study found that increase in obesity could result in a significant increase in both hypertension and coronary risk. Diastolic blood pressure and diabetes have significant converse effects on each other. This implies those who are hypertensive can develop diabetes and vice versa.

Ridge Fuzzy Regression Modelling for Solving Multicollinearity

This paper proposes an α-level estimation algorithm for ridge fuzzy regression modeling, addressing the multicollinearity phenomenon in the fuzzy linear regression setting. By incorporating α-levels in the estimation procedure, we are able to construct a fuzzy ridge estimator which does not depend on the distance between fuzzy numbers. An optimized α-level estimation algorithm is selected which minimizes the root mean squares for fuzzy data. Simulation experiments and an empirical study comparing the proposed ridge fuzzy regression with fuzzy linear regression is presented. Results show that the proposed model can control the effect of multicollinearity from moderate to extreme levels of correlation between covariates, across a wide spectrum of spreads for the fuzzy response.

Generalized ridge estimators adapted in structural equation models

Multicollinearity is detected via regression models, where independent variables are strongly correlated. Since they entail linear relations between observed or latent variables, the structural equation models (SEM) are subject to the multicollinearity effect, whose numerous consequences include the singularity between the inverse matrices used in estimation methods. Given to this behavior, it is natural to understand that the suitability of these estimators to structural equation models show the same features, either in the simulation results that validate the estimators in different multicollinearity degrees, or in their application to real data. Due to the multicollinearity overview arose from the fact that the matrices inversion is impracticable, the usage of numerical procedures demanded by the maximum likelihood methods leads to numerical singularity problems. An alternative could be the use of the Partial Least Squares (PLS) method, however, it is demanded that the observed variables are built by assuming a positive correlation with the latent variable. Thus, theoretically, it is expected that the load signals are positive, however, there are no restrictions to these signals in the algorithms used in the PLS method. This fact implies in corrective areas, such as the observed variables removal or new formulations of the theoretical model. In view of this problem, this paper aimed to propose adaptations of six generalized ridge estimators as alternative methods to estimate SEM parameters. The conclusion is that the evaluated estimators presented the same performance in terms of accuracy, precision while considering the scenarios represented by model without specification error and model with specification error, different levels of multicollinearity and sample sizes.

New ridge estimators in the inverse Gaussian regression: Monte Carlo simulation and application to chemical data

In numerous application areas, when the response variable is continuous, positively skewed, and well fitted to the inverse Gaussian distribution, the inverse Gaussian regression model (IGRM) is an effective approach in such scenarios. The problem of multicollinearity is very common in several application areas like chemometrics, biology, finance, and so forth. The effects of multicollinearity can be reduced using the ridge estimator. This research proposes new ridge estimators to address the issue of multicollinearity in the IGRM. The performance of the new estimators is compared with the maximum likelihood estimator and some other existing estimators. The mean square error is used as a performance evaluation criterion. A Monte Carlo simulation study is conducted to assess the performance of the new ridge estimators based on the minimum mean square error criterion. The Monte Carlo simulation results show that the performance of the proposed estimators is better than the available methods. The comparison of proposed ridge estimators is also evaluated using two real chemometrics applications. The results of Monte Carlo simulation and real applications confirmed the superiority of the proposed ridge estimators to other competitor methods.

Intuitionistic Fuzzy Partial Logistic Regression Model Using Ridge Methodology

This paper applies a ridge estimation approach in an existing partial logistic regression model with exact predictors, intuitionistic fuzzy responses, intuitionistic fuzzy coefficients and intuitionistic fuzzy smooth function to improve an existing intuitionistic fuzzy partial logistic regression model in the presence of multicollinearity. For this purpose, ridge methodology is also involved to estimate the parametric intuitionistic fuzzy coefficients and nonparametric intuitionistic fuzzy smooth function. Some common goodness-of-fit criteria are also used to examine the performance of the proposed regression model. The potential application of the proposed method are illustrated and compared with the intuitionistic partial logistic regression model through two numerical examples. The results clearly indicate the proposed ridge method is quite efficient in model’s performances when there is multicollinearity among the predictors.

A New Spectrum Driven Index for the Assessment of ECG Signal Quality.

In this paper, a new simple index has been introduced for the assessment of electrocardiography (ECG) signal quality. In the proposed method, first, the initial spectrum of the ECG is derived by applying synchrosqueezed wavelet transform (SSWT). Then, the main frequency rhythm of heart rate with maximum-energy embedded in the spectrum of the ECG signal is reconstructed using time-frequency ridge estimation algorithm. The ridge is subjected to the inverse SSW and SSW subsequently to reconstruct a clear spectrum corresponding to the main heart rhythm. Subtracting it from the initial spectrum, the resulting differential spectrum is converted to a single time-series by simply summing all the energy levels at each time-point. It has been shown that the derived time-series is proportional to the quality of ECG signal in terms of preserving its physiological features. The results of this research provide a profound basis for signal quality assessment of both ECG and photoplethysmography (PPG) signals under various noisy conditions and abnormal heart rate.

An improved ridge estimation (IRE) method for troposphere water vapor tomography

Water vapor tomography technique is a research point in global navigation satellite system (GNSS) meteorology. However, GNSS tomography technique has an inherent issue of design matrix sparsity, which leads to the ill-posed problem in the inversion of normal equation. Singular value decomposition (SVD) method is commonly used to resolve this problem but performs poorly due to the large fluctuation in tomographic results caused by the small singular values. To overcome the above issue, this study proposes an improved ridge estimation (IRE) method, which only revises the relatively small singular values and retains the large singular values unchanged on the basis of the minimum deviation principle in the processing of regularization matrix. An adjustment coefficient is introduced to determine the node of small singular value with large influence on the tomographic result. Twelve GNSS stations from Hong Kong Satellite Positioning Reference Station Network (SatRef) were used to validate the performance of the proposed method over the period of day of year (Doy) 84–101, 2014. The established tomography model in SatRef was resolved using SVD and IRE methods, respectively. Statistical results show that the accuracy of average root mean square error (RMSE) of IRE method is improved by 16.7% compared with that of SVD method when the corresponding radiosonde is considered as the reference. Additionally, the comparisons of water vapor profile, relative error (RE) and the reconstructed SWV derived from IRE and SVD methods were also carried out and the numerical result indicates a good performance of the proposed IRE method. Such results verify that the applicability of proposed IRE method in this paper for GNSS water vapor tomography.

Optimal Sensor Placement Algorithm for Structural Damage Identification

Background: Structural damage identification is a very important subject in the field of civil, mechanical and aerospace engineering according to recent patents. Optimal sensor placement is one of the key problems to be solved in structural damage identification. Methods: This paper presents a simple and convenient algorithm for optimizing sensor locations for structural damage identification. Unlike other algorithms found in the published papers, the optimization procedure of sensor placement is divided into two stages. The first stage is to determine the key parts in the whole structure by their contribution to the global flexibility perturbation. The second stage is to place sensors on the nodes associated with those key parts for monitoring possible damage more efficiently. With the sensor locations determined by the proposed optimization process, structural damage can be readily identified by using the incomplete modes yielded from these optimized sensor measurements. In addition, an Improved Ridge Estimate (IRE) technique is proposed in this study to effectively resist the data errors due to modal truncation and measurement noise. Two truss structures and a frame structure are used as examples to demonstrate the feasibility and efficiency of the presented algorithm. Results: From the numerical results, structural damages can be successfully detected by the proposed method using the partial modes yielded by the optimal measurement with 5% noise level. Conclusion: It has been shown that the proposed method is simple to implement and effective for structural damage identification.

A jackknifed ridge estimator in probit regression model

In this study, the effects of multicollinearity on the maximum likelihood estimator are analyzed in the probit regression model. It is known that the near-linear dependencies in the design matrix affect the maximum likelihood estimation negatively, namely, the standard errors become so large so that the estimations are said to be inconsistent. Therefore, a new jackknifed ridge estimator is introduced as an alternative to the maximum likelihood technique and the well-known ridge estimator. The mean squared error properties of the listed estimators are investigated theoretically. In order to evaluate the performance of the estimators, a Monte Carlo simulation study is designed, and simulated mean squared error and squared bias are used as performance criteria. Finally, the benefits of the new estimator are illustrated via a real data application.

Analyzing big data sets by using different panelized regression methods with application: Surveys of multidimensional poverty in Iraq

Poverty phenomenon is very substantial topic that determines the future of societies and governments and the way that they deals with education, health and economy. Sometimes poverty takes multidimensional trends through education and health. The research aims at studying multidimensional poverty in Iraq by using panelized regression methods, to analyze Big Data sets from demographical surveys collected by the Central Statistical Organization in Iraq. We choose classical penalized regression method represented by The Ridge Regression, Moreover; we choose another penalized method which is the Smooth Integration of Counting and Absolute Deviation (SICA) to analyze Big Data sets related to the different poverty forms in Iraq. Euclidian Distance (ED) was used to compare the two methods and the research conclude that the SICA method is better than Ridge estimator with Big Data conditions.

Multicollinearity in Logistic Regression Model -Subject Review-

The logistic regression model is one of the modern statistical methods developed to predict the set of quantitative variables (nominal or monotonous), and it is considered as an alternative test for the simple and multiple linear regression equation as well as it is subject to the model concepts in terms of the possibility of testing the effect of the overall pattern of the group of independent variables on the dependent variable and in terms of its use For concepts of standard matching criteria, and in some cases there is a correlation between the explanatory variables which leads to contrast variation and this problem is called the problem of Multicollinearity. This research included an article review to estimate the parameters of the logistic regression model in several biased ways to reduce the problem of multicollinearity between the variables. These methods were compared through the use of the mean square error (MSE) standard. The methods presented in the research have been applied to Monte Carlo simulation data to evaluate the performance of the methods and compare them, as well as the application to real data and the simulation results and the real application that the logistic ridge estimator is the best of other method.

Measuring Variability and Factors Affecting the Agricultural Production: A Ridge Regression Approach

The present investigation deals with the use of ridge regression in the presence of high degree multicollinearity, to determine the major factors influencing the agricultural production in Haryana state, India. Time series data for the period (1980–1981 to 2017–2018) on area, production, yield and different factors influencing the production of wheat, gram, paddy and cotton have been used in this study. Time series data was divided into four sub-periods of 10 year interval to measure the variability in area, production and yield of selected crops into different periods. Coefficient of variation around trend was also observed as the stability (or instability) index. Estimates for the factors affecting the agricultural production were observed by using the ordinary least squares technique and ridge regression both. A comparison is made and ridge estimates were found appropriate to measure the effect of different factors on agricultural production in the presence of multicollinearity. Total study period has been separated into training and testing parts and validity of the developed ridge regression model has been done on the basis of adjusted R2, percent deviation of forecast values and RMSE (%).

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

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.  Â

Efficiency of the generalized restricted difference-based almost unbiased ridge estimator in partially linear model

In this paper, the generalized restricted difference-based almost unbiased ridge estimator in partially linear model is presented, when it is supposed that the regression parameters may be restricted to a subspace and compare the proposed estimators in the sense of the quadratic bias and scalar mean squared error criteria. Finally, a simulation study is given to explain the performances of the estimators.

Uncertain stochastic ridge estimation in partially linear regression models with elliptically distributed errors

ABSTRACTIn fitting a regression model to survey data, using additional information or prior knowledge, stochastic uncertainty occurs in specifying linear programming due to economic and financial studies. These stochastic constraints, definitely cause some changes in the classic estimators and their efficiencies. In this paper, stochastic shrinkage estimators and their positive parts are defined in the partially linear regression models when the explanatory variables are multicollinear. Also, it is assumed that the errors are dependent and follow the elliptically contoured distribution. The exact risk expressions are derived to determine the relative dominance properties of the proposed estimators. We used generalized cross validation (GCV) criterion for selecting the bandwidth of the kernel smoother and optimal shrinkage parameter. Finally, the Monté-Carlo simulation studies and an application to real world data set are illustrated to support our theoretical findings.

A test of harmful multicollinearity: A generalized ridge regression approach

This paper introduces a new test of harmful multicollinearity based on the ratio of the levels of significance of ordinary least squares and generalized ridge regression estimates of the coefficients. Harmful multicollinearity is the degree of multicollinearity that leads to an incorrect statistical inference. The proposed test is based on a rule that an insignificant regressor will not change to a significant regressor by adding ridge factors to the design matrix; however, insignificant coefficients that have become insignificant because of multicollinearity will change to significant coefficients by using ridge estimation. The simulation results show that the power of the proposed test is high—even for small sample sizes—and converges to one as the sample size increases. In addition, the empirical size of the test is less than the nominal value in most cases, with a tendency to zero in larger samples. Therefore, the proposed test is consistent. The comparison of the proposed test with the main diagnostic measures confirms the success of the test because the diagnostic measures have the wrong nominal sizes in all cases. The application of the test to real-world data shows that it can be helpful for detecting harmful multicollinearity.