Ridge estimator with correlated errors and two-stage ridge estimator under inequality restrictions

Liew (1976a) introduced generalized inequality constrained least squares (GICLS) estimator and inequality constrained two-stage and three-stage least squares estimators by reducing primal–dual relation to problem of Dantzig and Cottle (1967), Cottle and Dantzig (1974) and solving with Lemke (1962) algorithm. The purpose of this article is to present inequality constrained ridge regression (ICRR) estimator with correlated errors and inequality constrained two-stage and three-stage ridge regression estimators in the presence of multicollinearity. Untruncated variance–covariance matrix and mean square error are derived for the ICRR estimator with correlated errors, and its superiority over the GICLS estimator is examined via Monte Carlo simulation. © 2017 Taylor & Francis Group, LLC

Estimation in a linear regression model with stochastic linear restrictions: a new two-parameter-weighted mixed estimator

The present paper considers the weighted mixed regression estimation of the coefficient vector in a linear regression model with stochastic linear restrictions binding the regression coefficients. We introduce a new two-parameter-weighted mixed estimator (TPWME) by unifying the weighted mixed estimator of Schaffrin and Toutenburg [1] and the two-parameter estimator (TPE) of Özkale and Kaçıranlar [2]. This new estimator is a general estimator which includes the weighted mixed estimator, the TPE and the restricted two-parameter estimator (RTPE) proposed by Özkale and Kaçıranlar [2] as special cases. Furthermore, we compare the TPWME with the weighted mixed estimator and the TPE with respect to the matrix mean square error criterion. A numerical example and a Monte Carlo simulation experiment are presented by using different estimators of the biasing parameters to illustrate some of the theoretical results. © 2018 Informa UK Limited, trading as Taylor & Francis Group

The optimal extended balanced loss function estimators

We derive the optimal heterogeneous, homogeneous and homogeneous unbiased estimators of the coefficient vector in a linear regression model under the extended balanced loss function of Shalabh et al. (2009). Risk functions and optimal predictors of the new estimators are evaluated and comparisons among the estimators are made with respect to the extended balanced loss function. Some of the theoretical results are illustrated by a numerical example. Moreover, the behavior of the proposed estimators is studied via a Monte-Carlo experiment in the sense of mean square error. © 2018 Elsevier B.V

Evaluation of the predictive performance of the r-k and r-d class estimators

Multiple linear regression models are frequently used in predicting unknown values of the response variable y. In this case, a regression model's ability to produce an adequate prediction equation is of prime importance. This paper discusses the predictive performance of the r-k and r-d class estimators compared to ordinary least squares (OLS), principal components, ridge regression and Liu estimators and between each other. The theoretical results are illustrated using Portland cement data and a region is established where the r-k and the r-d class estimators are uniformly superior to the other mentioned estimators. © 2017 Taylor & Francis Group, LLC

Erratum to: Comparisons of the r - k class estimator to the ordinary least squares estimator under the Pitman's closeness criterion (Statistical Papers, (2008), 49, (503-512), 10.1007/s00362-006-0029-0)

[No abstract available

Improvement of the Liu-type Shiller estimator for distributed lag models

The problem of multicollinearity produces undesirable effects on ordinary least squares (OLS), Almon and Shiller estimators for distributed lag models. Therefore, we introduce a Liu-type Shiller estimator to deal with multicollinearity for distributed lag models. Moreover, we theoretically compare the predictive performance of the Liu-type Shiller estimator with OLS and the Shiller estimators by the prediction mean square error criterion under the target function. Furthermore, an extensive Monte Carlo simulation study is carried out to evaluate the predictive performance of the Liu-type Shiller estimator. Copyright © 2017 John Wiley & Sons, Ltd

Risk performance of some shrinkage estimators

Shrinkage estimators incorporating homogeneous and heterogeneous minimum mean square error estimators have a great deal of usage in the literature by means of adaptive choices of these estimators. In the present paper, we propose two new shrinkage estimators by utilizing the Lindley’s mean correction. The risk performance of the new estimators in comparison to the existing methods of estimation is conducted with the help of different loss functions through a Monte Carlo experiment. Numerical results prove that our method of estimation works quite well. © 2019, © 2019 Taylor & Francis Group, LLC

The Almon two parameter estimator for the distributed lag models

The two parameter estimator proposed by Özkale and Kaçıranlar [The restricted and unrestricted two parameter estimators. Comm Statist Theory Methods. 2007;36(15):2707–2725] is a general estimator which includes the ordinary least squares, the ridge and the Liu estimators as special cases. In the present paper we introduce Almon two parameter estimator based on the two parameter estimation procedure to deal with the problem of multicollinearity for the distiributed lag models. This estimator outperforms the Almon estimator according to the matrix mean square error criterion. Moreover, a numerical example and a Monte Carlo simulation experiment are presented by using different estimators of the biasing parameters. © 2016 Informa UK Limited, trading as Taylor & Francis Group

An optimal k of kth MA-ARIMA models under AR(p) models

In this article, we discuss finding the optimal k of (i) kth simple moving average, (ii) kth weighted moving average, and (iii) kth exponential weighted moving average based on simulated autoregressive AR(p) model. We run a simulation using the three above examining method under specific conditions. The main finding is that the optimal k = 4 and then k = 3. Especially, the fourth WMA ARIMA model, fourth EWMA ARIMA model, and third EWMA ARIMA model are the best forecasting models among others, respectively. For all the six real data reveal the similar results of simulation study. © 2017 Taylor & Francis Group, LLC

On the performance of the poisson and the negative binomial ridge predictors

Mansson and Shukur (2011) investigated the performance of the Poisson ridge regression (PRR) estimator in terms of the mean square error (MSE) criterion. Similarly, Mansson (2012) investigated the performance of the Negative binomial ridge regression (NBRR) according to the MSE criterion. But there is no any analysis of the predictive performance of the PRR and NBRR estimators. Therefore, we define the PRR and the NBRR predictors to evaluate their predictive performances according to the prediction mean squared error under the target function. The Monte Carlo simulations and the real life numerical example are conducted to investigate the defined predictors' performance. © 2017, © 2017 Taylor & Francis Group, LLC