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  • 1. A. Alkhamisi, Mahdi
    et al.
    Shukur, Ghazi
    Jönköping University, Jönköping International Business School, JIBS, Economics.
    Developing Ridge Parameters for SUR Model2008In: Communications in Statistics - Theory and Methods, ISSN 0361-0926, E-ISSN 1532-415X, Vol. 37, no 4, p. 544-564Article in journal (Refereed)
  • 2. Alkamisi, M. A.
    et al.
    Khalaf, G.
    Shukur, Ghazi
    Jönköping University, Jönköping International Business School, JIBS, Economics.
    Some Modifications for Choosing Ridge Parameters2006In: Communications in Statistics - Theory and Methods, ISSN 0361-0926, E-ISSN 1532-415X, Vol. 35, no 11, p. 2005-2020Article in journal (Refereed)
  • 3.
    Holgersson, Thomas
    Jönköping University, Jönköping International Business School, JIBS, Economics, Finance and Statistics.
    A Note on a commonly used ridge regression Monte Carlo design2014In: Communications in Statistics - Theory and Methods, ISSN 0361-0926, E-ISSN 1532-415X, Vol. 44, no 10, p. 2176-2179Article in journal (Refereed)
    Abstract [en]

    Ridge estimators are usually examined through Monte Carlo simulations since their properties are difficult to obtain analytically. In this paper we argue that a simulation design commonly used in the literature will give biased results of Monte Carlo simulations in favour of ridge regression over ordinary least square (OLS) estimators. Specifically, it is argued that the properties of ridge estimators that are functions of p distinct regressor eigenvalues should not be evaluated through Monte Carlo designs using only two distinct eigenvalues.

  • 4.
    Holgersson, Thomas
    Jönköping University, Jönköping International Business School, JIBS, Economics.
    Robust Testing for Skewness2006In: Communications in Statistics - Theory and Methods, ISSN 0361-0926, E-ISSN 1532-415X, Vol. 36, no 3, p. 485-498Article in journal (Refereed)
  • 5. Khalaf, G.
    et al.
    Shukur, Ghazi
    Jönköping University, Jönköping International Business School, JIBS, Economics.
    Choosing Ridge Parameter for Regression Problems2005In: Communications in Statistics - Theory and Methods, ISSN 0361-0926, E-ISSN 1532-415X, Vol. 34, no 5, p. 1177-1182Article in journal (Refereed)
  • 6.
    Khalaf, Ghadban
    et al.
    Department of Mathematics, King Khalid University, Abha, Saudi Arabia.
    Månsson, Kristofer
    Jönköping University, Jönköping International Business School, JIBS, Economics, Finance and Statistics.
    Shukur, Ghazi
    Jönköping University, Jönköping International Business School, JIBS, Economics, Finance and Statistics.
    Modified Ridge Regression Estimators2013In: Communications in Statistics - Theory and Methods, ISSN 0361-0926, E-ISSN 1532-415X, Vol. 42, no 8, p. 1476-1487Article in journal (Refereed)
    Abstract [en]

    Ridge regression is a variant of ordinary multiple linear regression whose goal is to circumvent the problem of predictors collinearity. It gives up the Ordinary Least Squares (OLS) estimator as a method for estimating the parameters [] of the multiple linear regression model [] . Different methods of specifying the ridge parameter k were proposed and evaluated in terms of Mean Square Error (MSE) by simulation techniques. Comparison is made with other ridge-type estimators evaluated elsewhere. The new estimators of the ridge parameters are shown to have very good MSE properties compared with the other estimators of the ridge parameter and the OLS estimator. Based on our results from the simulation study, we may recommend the new ridge parameters to practitioners.

  • 7.
    Khalaf, Ghadban
    et al.
    Department of Mathematics, King Khalid University, Saudi Arabia.
    Månsson, Kristofer
    Jönköping University, Jönköping International Business School, JIBS, Economics, Finance and Statistics.
    Sjölander, Pär
    Jönköping University, Jönköping International Business School, JIBS, Economics, Finance and Statistics.
    Shukur, Ghazi
    Jönköping University, Jönköping International Business School, JIBS, Economics, Finance and Statistics.
    A Tobit Ridge Regression Estimator2014In: Communications in Statistics - Theory and Methods, ISSN 0361-0926, E-ISSN 1532-415X, Vol. 43, no 1, p. 131-140Article in journal (Refereed)
    Abstract [en]

    This article analyzes the effects of multicollienarity on the maximum likelihood (ML) estimator for the Tobit regression model. Furthermore, a ridge regression (RR) estimator is proposed since the mean squared error (MSE) of ML becomes inflated when the regressors are collinear. To investigate the performance of the traditional ML and the RR approaches we use Monte Carlo simulations where the MSE is used as performance criteria. The simulated results indicate that the RR approach should always be preferred to the ML estimation method.

  • 8.
    Li, Yushu
    et al.
    Department of Economic and Statistics, Center for Labor Market Policy Research (CAFO), Linnaeus University, Sweden .
    Shukur, Ghazi
    Jönköping University, Jönköping International Business School, JIBS, Economics.
    Wavelet Improvement of the Over-rejection of Unit root test under GARCH errors: An Application to Swedish Immigration Data2011In: Communications in Statistics - Theory and Methods, ISSN 0361-0926, E-ISSN 1532-415X, Vol. 40, no 13, p. 2385-2396Article in journal (Refereed)
    Abstract [en]

    In this article, we use the wavelet technique to improve the over-rejection problem of the traditional Dickey-Fuller tests for unit root when the data is associated with volatility like the GARCH(1, 1) effect. The logic of this technique is based on the idea that the wavelet spectrum decomposition can separate out information of different frequencies in the data series. We prove that the asymptotic distribution of the test in the wavelet environment is still the same as the traditional Dickey-Fuller type of tests. The finite sample property is improved when the data suffers from GARCH error. The investigation of the size property and the finite sample distribution of the test is carried out by Monte Carlo experiment. An empirical example with data on the net immigration to Sweden during the period 1950-2000 is used to illustrate the performance of the wavelet improved test under GARCH errors. The results reveal that using the traditional Dickey-Fuller type of tests, the unit root hypothesis is rejected while our wavelet improved test do not reject as it is more robust to GARCH errors in finite samples.

  • 9.
    Månsson, Kristofer
    Jönköping University, Jönköping International Business School, JIBS, Economics, Finance and Statistics.
    A Wavelet-Based Approach of Testing for Granger Causality in the Presence of GARCH Effects2012In: Communications in Statistics - Theory and Methods, ISSN 0361-0926, E-ISSN 1532-415X, Vol. 41, no 4, p. 717-728Article in journal (Refereed)
    Abstract [en]

    The size and power of the most commonly used tests and a new wavelet-based approach of testing for Granger causality is evaluated in this paper by means of a Monte Carlo study in which the error term follows a generalized autoregressive conditional heteroscedasticity consistent (GARCH) process. In the simulation study it is shown that the commonly used causality tests tends to over-reject the true null hypothesis in the presence of GARCH errors and that the new wavelet-based approach improves the size properties of the Granger causality test for all of the different situations evaluated.

  • 10.
    Månsson, Kristofer
    et al.
    Jönköping University, Jönköping International Business School, JIBS, Statistics.
    Kibria, B. M. Golam
    Department of Mathematics and Statistics, Florida International University, Miami, FL, USA.
    Shukur, Ghazi
    Jönköping University, Jönköping International Business School, JIBS, Statistics.
    Performance of some weighted Liu estimators for logit regression model: An application to Swedish accident data2015In: Communications in Statistics - Theory and Methods, ISSN 0361-0926, E-ISSN 1532-415X, Vol. 44, no 2, p. 363-375Article in journal (Refereed)
    Abstract [en]

    In this article, we propose some new estimators for the shrinkage parameter d of the weighted Liu estimator along with the traditional maximum likelihood (ML) estimator for the logit regression model. A simulation study has been conducted to compare the performance of the proposed estimators. The mean squared error is considered as a performance criteria. The average value and standard deviation of the shrinkage parameter d are investigated. In an application, we analyze the effect of usage of cars, motorcycles, and trucks on the probability that pedestrians are getting killed in different counties in Sweden. In the example, the benefits of using the weighted Liu estimator are shown. Both results from the simulation study and the empirical application show that all proposed shrinkage estimators outperform the ML estimator. The proposed D9 estimator performed best and it is recommended for practitioners.

  • 11.
    Månsson, Kristofer
    et al.
    Jönköping University, Jönköping International Business School, JIBS, Economics. Jönköping University, Jönköping International Business School, JIBS, Economics, Finance and Statistics.
    Shukur, Ghazi
    Jönköping University, Jönköping International Business School, JIBS, Economics. Jönköping University, Jönköping International Business School, JIBS, Economics, Finance and Statistics.
    On Ridge Parameters in Logistic Regression2011In: Communications in Statistics - Theory and Methods, ISSN 0361-0926, E-ISSN 1532-415X, Vol. 40, no 18, p. 3366-3381Article in journal (Refereed)
    Abstract [en]

    This article applies and investigates a number of logistic ridge regression (RR) parameters that are estimable by using the maximum likelihood (ML) method. By conducting an extensive Monte Carlo study, the performances of ML and logistic RR are investigated in the presence of multicollinearity and under different conditions. The simulation study evaluates a number of methods of estimating the RR parameter k that has recently been developed for use in linear regression analysis. The results from the simulation study show that there is at least one RR estimator that has a lower mean squared error (MSE) than the ML method for all the different evaluated situations.

  • 12.
    Månsson, Kristofer
    et al.
    Jönköping University, Jönköping International Business School, JIBS, Statistics.
    Shukur, Ghazi
    Jönköping University, Jönköping International Business School, JIBS, Statistics.
    Kibria, B. M. Golam
    Department of Mathematics and Statistics, Florida International University, Miami, Florida, USA.
    Performance of Some Ridge Regression Estimators for the Multinomial Logit Model2018In: Communications in Statistics - Theory and Methods, ISSN 0361-0926, E-ISSN 1532-415X, Vol. 47, no 12, p. 2795-2804Article in journal (Refereed)
    Abstract [en]

    This article considers several estimators for estimating the ridge parameter k for multinomial logit model based on the work of Khalaf and Shukur (2005), Alkhamisi et al. (2006), and Muniz et al. (2012). The mean square error (MSE) is considered as the performance criterion. A simulation study has been conducted to compare the performance of the estimators. Based on the simulation study we found that increasing the correlation between the independent variables and the number of regressors has negative effect on the MSE. However, when the sample size increases the MSE decreases even when the correlation between the independent variables is large. Based on the minimum MSE criterion some useful estimators for estimating the ridge parameter k are recommended for the practitioners

  • 13.
    Månsson, Kristofer
    et al.
    Jönköping University, Jönköping International Business School, JIBS, Economics, Finance and Statistics.
    Shukur, Ghazi
    Jönköping University, Jönköping International Business School, JIBS, Economics, Finance and Statistics.
    Sjölander, Pär
    Jönköping University, Jönköping International Business School, JIBS, Economics, Finance and Statistics.
    A New Asymmetric Interaction Ridge (AIR) Regression Method2014In: Communications in Statistics - Theory and Methods, ISSN 0361-0926, E-ISSN 1532-415X, Vol. 43, no 3, p. 616-643Article in journal (Refereed)
    Abstract [en]

    Despite that interaction terms are standard tools of regression analysis, the side effects of the inclusion of these terms in models estimated by ordinary least squares (OLS) are yet not fully penetrated. The inclusion of interaction effects induces multicollinearity problems since all non zero values are equal between the interaction term and the regressor. In this article, we propose a procedure to remedy this problem by the use of new ridge regression (RR) shrinkage parameters—which we call the asymmetric interaction ridge (AIR) regression method. By means of Monte Carlo simulations we evaluate both OLS and AIR using the mean square error (MSE) performance criterion. The result from the simulation study confirms our hypothesis that AIR always should be preferred to OLS since it has a lower estimated MSE. Moreover, the advantages of our new method are demonstrated in an empirical application where positive asymmetric price transmission effects are exposed for the mortgage interest rates of Handelsbanken Stadshypotek. It is observed that the mortgage interest rates increase more fully and rapidly to an increase in the bank's borrowing costs than to a decrease. This asymmetry is defined as positive asymmetric price transmission (APT).

  • 14.
    Månsson, Kristofer
    et al.
    Jönköping University, Jönköping International Business School, JIBS, Economics, Finance and Statistics.
    Shukur, Ghazi
    Jönköping University, Jönköping International Business School, JIBS, Economics, Finance and Statistics.
    Sjölander, Pär
    Jönköping University, Jönköping International Business School, JIBS, Economics, Finance and Statistics.
    A New Ridge Regression Causality Test in the Presence of Multicollinearity2014In: Communications in Statistics - Theory and Methods, ISSN 0361-0926, E-ISSN 1532-415X, Vol. 43, no 2, p. 235-248Article in journal (Refereed)
    Abstract [en]

    The VAR lag structure applied for the traditional Granger causality (GC) test is always severely affected by multicollinearity due to autocorrelation among the lags. Therefore, as a remedy to this problem we introduce a new Ridge Regression Granger Causality (RRGC) test, which is compared to the GC test by means of Monte Carlo simulations. Based on the simulation study we conclude that the traditional OLS version of the GC test over-rejects the true null hypothesis when there are relatively high (but empirically normal) levels of multicollinearity, while the new RRGC test will remedy or substantially decrease this problem.

  • 15.
    Shukur, Ghazi
    et al.
    Jönköping University, Jönköping International Business School, JIBS, Economics, Finance and Statistics.
    Zeebari, Zangin
    Jönköping University, Jönköping International Business School, JIBS, Economics, Finance and Statistics.
    Kibria, B. M. G.
    Department of Mathematics and Statistics, Florida International University, Miami, USA.
    Modified Ridge Parameters for Seemingly Unrelated Regression Model2012In: Communications in Statistics - Theory and Methods, ISSN 0361-0926, E-ISSN 1532-415X, Vol. 41, no 9, p. 1675-1691Article in journal (Refereed)
    Abstract [en]

    In this article, we modify a number of new biased estimators of seemingly unrelated regression (SUR) parameters which are developed by Alkhamisi and Shukur (2008), AS, when the explanatory variables are affected by multicollinearity. Nine estimators of the ridge parameters have been modified and compared in terms of the trace mean squared error (TMSE) and (PR) criterion. The results from this extended study are the also compared with those founded by AS. A simulation study has been conducted to compare the performance of the modified estimators of the ridge parameters. The results showed that under certain conditions the performance of the multivariate ridge regression estimators based on SUR ridge R MSmax is superior to other estimators in terms of TMSE and PR criterion. In large samples and when the collinearity between the explanatory variables is not high, the unbiased SUR, estimator produces a smaller TMSEs.

  • 16.
    Zeebari, Zangin
    Jönköping University, Jönköping International Business School, JIBS, Economics, Finance and Statistics.
    A Simulation Study on the Least Absolute Deviations Method for Ridge Regression2012In: Communications in Statistics - Theory and Methods, ISSN 0361-0926, E-ISSN 1532-415XArticle in journal (Refereed)
    Abstract [en]

    Though the Least Absolute Deviations (LAD) method of estimation is robust, there is still the possibility of having strong multicollinearity of the predictors in a linear regression analysis. The paper consists of the application of the LAD estimation instead of the Ordinary Least Squares (OLS) estimation for the ridge regression and a simulation study to assess the performance of some biasing parameters used in the literature with their new LAD versions. The aim is to deal with the cases when the predictors are highly collinear  and the error terms are asymmetric or heavy-tailed, by giving more room to the bias in order to reduce the Mean Squared Error (MSE) of the LAD estimators.

  • 17.
    Zeebari, Zangin
    et al.
    Department of Public Health Sciences, Karolinska Institute, Stockholm, Sweden.
    Kibria, B. M. G.
    Department of Mathematics and Statistics, Florida International University, Miami, USA.
    Shukur, Ghazi
    Jönköping University, Jönköping International Business School, JIBS, Statistics. Department of Economics and Statistics, Linnaeus University, Växjö, Sweden.
    Seemingly unrelated regressions with covariance matrix of cross-equation ridge regression residuals2018In: Communications in Statistics - Theory and Methods, ISSN 0361-0926, E-ISSN 1532-415X, Vol. 47, no 20, p. 5029-5053Article in journal (Refereed)
    Abstract [en]

    Generalized least squares estimation of a system of seemingly unrelated regressions is usually a two-stage method: (1) estimation of cross-equation covariance matrix from ordinary least squares residuals for transforming data, and (2) application of least squares on transformed data. In presence of multicollinearity problem, conventionally ridge regression is applied at stage 2. We investigate the usage of ridge residuals at stage 1, and show analytically that the covariance matrix based on the least squares residuals does not always result in more efficient estimator. A simulation study and an application to a system of firms' gross investment support our finding.

  • 18.
    Zeebari, Zangin
    et al.
    Jönköping University, Jönköping International Business School, JIBS, Economics, Finance and Statistics.
    Shukur, Ghazi
    Jönköping University, Jönköping International Business School, JIBS, Economics, Finance and Statistics.
    On the least absolute deviations method for ridge estimation of SURE models2014In: Communications in Statistics - Theory and Methods, ISSN 0361-0926, E-ISSN 1532-415XArticle in journal (Other academic)
    Abstract [en]

    In this paper we examine the application of the Least Absolute Deviations (LAD) method for ridge-type parameter estimation of Seemingly Unrelated Regression Equations (SURE) models. The methodology is aimed to deal with the SURE models with non-Gaussian error terms and highly collinear predictors in each equation. Some biasing parameters used in the literature are taken and the efficiency of both Least Squares (LS) ridge estimation and the LAD ridge estimation of the SURE models, through the Mean Squared Error (MSE) of parameter estimators, is evaluated.

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