Robust two parameter ridge M-estimator for linear regression

Ertaş, Hasan; Toker, Selma; Kaçıranlar, Selahattin

doi:10.1080/02664763.2014.1000577

Cited by 11 publications

(8 citation statements)

References 9 publications

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“…. , λ p > 0 are the ordered eigenvalues of X ′ X. e estimators in canonical form are (8) where q * � y ′ Z(Λ + kI) − 1 Z ′ y/y ′ Z ′ (Λ + kI) −1 Λ (Λ + kI) −1 Z ′ y, T k � (Λ + kI) − 1 Λ and k > 0. [4].…”

Section: Methodsmentioning

confidence: 99%

“…Later on, many researchers worked on TPR, see e.g., [6][7][8][9][10][11][12][13]. e selection of ridge M-estimator plays an important role to reduce the MSE of TPR in the presence of multicollinearity and outliers.…”

Section: Introduction E Matrix Form Of the Multiple Linear Regression Model Ismentioning

confidence: 99%

“…Motivated by the work of Ref. [8] and following the idea of Ref. [1], we proposed the modified ridge M-estimators in TPR.…”

Section: Introduction E Matrix Form Of the Multiple Linear Regression Model Ismentioning

confidence: 99%

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Modified Robust Ridge M-Estimators in Two-Parameter Ridge Regression Model

Yasin

Salem

Ayed

et al. 2021

Mathematical Problems in Engineering

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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.

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Section: Methodsmentioning

confidence: 99%

Section: Introduction E Matrix Form Of the Multiple Linear Regression Model Ismentioning

confidence: 99%

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Modified Robust Ridge M-Estimators in Two-Parameter Ridge Regression Model

Yasin

Salem

Ayed

et al. 2021

Mathematical Problems in Engineering

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“…In this paper, we use following methods to choose k and q parameters. This procedures modified from the work of [9]. We called as IGT P RE 1 if following procedure is used to choose k and q parameters.…”

Section: Selection Of the Parameters K And Qmentioning

confidence: 99%

Two parameter Ridge estimator in the inverse Gaussian regression model

Bulut

Işilar

2021

Hacettepe Journal of Mathematics and Statistics

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It is well known that multicollinearity, which occurs among the explanatory variables, has adverse effects on the maximum likelihood estimator in the inverse Gaussian regression model. Biased estimators are proposed to cope with the multicollinearity problem in the inverse Gaussian regression model. The main interest of this article is to introduce a new biased estimator. Also, we compare newly proposed estimator with the other estimators given in the literature. We conduct a Monte Carlo simulation and provide a real data example to illustrate the performance of the proposed estimator over the maximum likelihood and Ridge estimators. As a result of the simulation study and real data example, the newly proposed estimator is superior to the other estimators used in this study.

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“…1 , where the activation function of the output layer is the identity, represented by and there are no hidden layers The independent observations of the interest variable (response) are denoted by , , where is a vector of explanatory/input variables. Similarly, is a vector of unknown regression coefficients or weights [ 13 ]. Figure 1 presents the architecture of a multiple linear regression model.…”

Section: Artificial Neural Network Architecturesmentioning

confidence: 99%

Comparing Artificial Neural Network Architectures for Brazilian Stock Market Prediction

2020

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Prediction of financial time series is a great challenge for statistical models. In general, the stock market times series present high volatility due to its sensitivity to economic and political factors. Furthermore, recently, the covid-19 pandemic has caused a drastic change in the stock exchange times series. In this challenging context, several computational techniques have been proposed to improve the performance of predicting such times series. The main goal of this article is to compare the prediction performance of five neural network architectures in predicting the six most traded stocks of the official Brazilian stock exchange B3 from March 2019 to April 2020. We trained the models to predict the closing price of the next day using as inputs its own previous values. We compared the predictive performance of multiple linear regression, Elman, Jordan, radial basis function, and multilayer perceptron architectures based on the root of the mean square error. We trained all models using the training set while hyper-parameters such as the number of input variables and hidden layers were selected using the testing set. Moreover, we used the trimmed average of 100 bootstrap samples as our prediction. Thus, our approach allows us to measure the uncertainty associate with the predicted values. The results showed that for all times series, considered all architectures, except the radial basis function, the networks tunning provide suitable fit, reasonable predictions, and confidence intervals.

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Robust two parameter ridge M-estimator for linear regression

Cited by 11 publications

References 9 publications

Modified Robust Ridge M-Estimators in Two-Parameter Ridge Regression Model

Modified Robust Ridge M-Estimators in Two-Parameter Ridge Regression Model

Two parameter Ridge estimator in the inverse Gaussian regression model

Comparing Artificial Neural Network Architectures for Brazilian Stock Market Prediction

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