Multicollinearity Problem

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Hu Yang - One of the best experts on this subject based on the ideXlab platform.

  • On the Principal Component Liu-type Estimator in Linear Regression
    Communications in Statistics - Simulation and Computation, 2014
    Co-Authors: Hu Yang
    Abstract:

    In this article, we present a principal component Liu-type estimator (LTE) by combining the principal component regression (PCR) and LTE to deal with the Multicollinearity Problem. The superiority of the new estimator over the PCR estimator, the ordinary least squares estimator (OLSE) and the LTE are studied under the mean squared error matrix. The selection of the tuning parameter in the proposed estimator is also discussed. Finally, a numerical example is given to explain our theoretical results.

  • Two Classes of Almost Unbiased Type Principal Component Estimators in Linear Regression Model
    Journal of Applied Mathematics, 2014
    Co-Authors: Hu Yang
    Abstract:

    This paper is concerned with the parameter estimator in linear regression model. To overcome the Multicollinearity Problem, two new classes of estimators called the almost unbiased ridge-type principal component estimator (AURPCE) and the almost unbiased Liu-type principal component estimator (AULPCE) are proposed, respectively. The mean squared error matrix of the proposed estimators is derived and compared, and some properties of the proposed estimators are also discussed. Finally, a Monte Carlo simulation study is given to illustrate the performance of the proposed estimators.

  • On the Stochastic Restricted Almost Unbiased Estimators in Linear Regression Model
    Communications in Statistics - Simulation and Computation, 2013
    Co-Authors: Hu Yang
    Abstract:

    In this article, the stochastic restricted almost unbiased ridge regression estimator and stochastic restricted almost unbiased Liu estimator are proposed to overcome the well-known Multicollinearity Problem in linear regression model. The quadratic bias and mean square error matrix of the proposed estimators are derived and compared. Furthermore, a numerical example and a Monte Carlo simulation are given to illustrate some of the theoretical results.

  • More on the Bias and Variance Comparisons of the Restricted Almost Unbiased Estimators
    Communications in Statistics-theory and Methods, 2011
    Co-Authors: Hu Yang
    Abstract:

    Sarkar (1992) and Kac\i ranlar et al. (1999), respectively, proposed the restricted ridge regression estimator (RRE) and restricted Liu estimator (RLE) to combat the well-known Multicollinearity Problem in linear regression. In this article, the restricted almost unbiased ridge estimator (RAURE) based on the RRE by Sarkar (1992) and the restricted almost unbiased Liu estimator (RAULE) by Kac\i ranlar et al. (1999) are introduced. The biases and variance matrices of the proposed estimators are derived and compared with the corresponding competitors in literatures. Furthermore, a Monte Carlo evaluation of the estimators is given to illustrate some of the theoretical results.

  • A new stochastic mixed ridge estimator in linear regression model
    Statistical Papers, 2008
    Co-Authors: Hu Yang
    Abstract:

    This paper is concerned with the parameter estimation in linear regression model with additional stochastic linear restrictions. To overcome the Multicollinearity Problem, a new stochastic mixed ridge estimator is proposed and its efficiency is discussed. Necessary and sufficient conditions for the superiority of the stochastic mixed ridge estimator over the ridge estimator and the mixed estimator in the mean squared error matrix sense are derived for the two cases in which the parametric restrictions are correct and are not correct. Finally, a numerical example is also given to show the theoretical results.

Takashi Yamagata - One of the best experts on this subject based on the ideXlab platform.

  • The small sample performance of the Wald test in the sample selection model under the Multicollinearity Problem
    Economics Letters, 2006
    Co-Authors: Takashi Yamagata
    Abstract:

    This paper investigates the finite sample behaviour of the Wald test of a slope coefficient (t-ratio) in sample selection models following the maximum likelihood estimation, specifically under Multicollinearity identified by Nawata [Nawata, K., 1993. A note on the estimation of models with sample-selection biases. Economics Letters 42, 15–24]. The evidence shows that the conventional Wald test can perform very poorly under the Multicollinearity Problem, but the proposed bootstrap method can control the size successfully.

  • On Testing Sample Selection Bias Under the Multicollinearity Problem
    Econometric Reviews, 2005
    Co-Authors: Takashi Yamagata, Chris D. Orme
    Abstract:

    This paper reviews and extends the literature on the finite sample behavior of tests for sample selection bias. Monte Carlo results show that, when the “Multicollinearity Problem” identified by Nawata (1993) is severe, (i) the t-test based on the Heckman-Greene variance estimator can be unreliable, (ii) the Likelihood Ratio test remains powerful, and (iii) nonnormality can be interpreted as severe sample selection bias by Maximum Likelihood methods, leading to negative Wald statistics. We also confirm previous findings (Leung and Yu, 1996) that the standard regression-based t-test (Heckman, 1979) and the asymptotically efficient Lagrange Multiplier test (Melino, 1982), are robust to nonnormality but have very little power.

Vadim V. Strijov - One of the best experts on this subject based on the ideXlab platform.

  • Comprehensive study of feature selection methods to solve Multicollinearity Problem according to evaluation criteria
    Expert Systems With Applications, 2017
    Co-Authors: Alexandr Katrutsa, Vadim V. Strijov
    Abstract:

    Abstract This paper provides a new approach to feature selection based on the concept of feature filters, so that feature selection is independent of the prediction model. Data fitting is stated as a single-objective optimization Problem, where the objective function indicates the error of approximating the target vector as some function of given features. Linear dependence between features induces the Multicollinearity Problem and leads to instability of the model and redundancy of the feature set. This paper introduces a feature selection method based on quadratic programming. This approach takes into account the mutual dependence of the features and the target vector, and selects features according to relevance and similarity measures defined according to the specific Problem. The main idea is to minimize mutual dependence and maximize approximation quality by varying a binary vector that indicates the presence of features. The selected model is less redundant and more stable. To evaluate the quality of the proposed feature selection method and compare it with others, we use several criteria to measure instability and redundancy. In our experiments, we compare the proposed approach with several other feature selection methods, and show that the quadratic programming approach gives superior results according to the criteria considered for the test and real data sets.

  • Stress test procedure for feature selection algorithms
    Chemometrics and Intelligent Laboratory Systems, 2015
    Co-Authors: Alexandr Katrutsa, Vadim V. Strijov
    Abstract:

    Abstract This study investigates the Multicollinearity Problem and the performance of feature selection methods in the case of data sets that have multicollinear features. We propose a stress test procedure for a set of feature selection methods. This procedure generates test data sets with various configurations of the target vector and features. This procedure provides more complex investigations of feature selection methods than procedures described in papers previously. A number of some multicollinear features are inserted in every configuration. A feature selection method results in a set of selected features for a given test data set. To compare given feature selection methods the procedure uses several quality measures. A criterion of the selected feature redundancy is proposed. This criterion estimates the number of multicollinear features among the selected ones. To detect Multicollinearity it uses the eigensystem of the parameter covariance matrix. In computational experiments we consider the following illustrative methods: Lasso, ElasticNet, LARS, Ridge, Stepwise and Genetic algorithms and determine the best one, which solves the Multicollinearity Problem for every considered data set configuration.

Mahmud Ibrahim - One of the best experts on this subject based on the ideXlab platform.

Evren, Atif Ahmet - One of the best experts on this subject based on the ideXlab platform.

  • Intuitionistic fuzzy ridge regression functions
    'Informa UK Limited', 2020
    Co-Authors: Kizilaslan Busenur, Egrioglu Erol, Evren, Atif Ahmet
    Abstract:

    Developing technology shows how useful fuzzy inference systems in lots of applications. Fuzzy functions approach which is one of the important fuzzy inference system for time series forecasting. In fuzzy functions approach, the membership values and their non-linear transformations are used together with original input variables to increase the prediction power. However, Multicollinearity Problem can be occured because of using these correlated variables. Purpose of the paper is to propose a new fuzzy forecasting method with intuitionistic fuzzy sets which has addition information known as hesitation degree. In this case, both intuitionistic fuzzy sets and their non-linear transformations is used to increase the prediction power. Ridge regression method is preferred to obtain intuitionistic fuzzy functions without exposed to multicolinearity Problem. To demonstrate the performances of proposed method, some real world time series data are used and the results have shown that the effectiveness of the proposed method in conrast to other methods

  • Intuitionistic fuzzy ridge regression functions
    'Informa UK Limited', 2020
    Co-Authors: Kizilaslan Busenur, Egrioglu Erol, Evren, Atif Ahmet
    Abstract:

    Kizilaslan, Busenur/0000-0002-5511-8941WOS: 000473463800001Developing technology shows how useful fuzzy inference systems in lots of applications. Fuzzy functions approach which is one of the important fuzzy inference system for time series forecasting. In fuzzy functions approach, the membership values and their non-linear transformations are used together with original input variables to increase the prediction power. However, Multicollinearity Problem can be occured because of using these correlated variables. Purpose of the paper is to propose a new fuzzy forecasting method with intuitionistic fuzzy sets which has addition information known as hesitation degree. In this case, both intuitionistic fuzzy sets and their non-linear transformations is used to increase the prediction power. Ridge regression method is preferred to obtain intuitionistic fuzzy functions without exposed to multicolinearity Problem. To demonstrate the performances of proposed method, some real world time series data are used and the results have shown that the effectiveness of the proposed method in conrast to other methods

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