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AbstractModeling with the gamma regression model is common when the dependent variable is positively skewed and follows a gamma distribution. The maximum likelihood (ML) estimator is used to estimate the parameters for this model. However, when there is multicollinearity, the ML estimator is inefficient. As a result, we propose a new improved gamma (NIG) estimator for this model’s parameter estimation in the presence of multicollinearity. Theoretical comparisons of the NIG estimator with some existing gamma estimators are done via mean squared error. Additionally, a real-data example and a simulation study are conducted to provide a clear view of the NIG estimator’s superior performance over other available ones. The results show that the NIG estimator outperforms previous gamma estimators in terms of mean squared error. [ABSTRACT FROM AUTHOR]

AbstractInfluential observations constitute a significant threat that affects the regression model’s performance. So, many influential statistics, such as Cook’s Distance and DFFITS have been provided using ordinary least squares. Another problem is multicollinearity, which affects the efficiency of these measures. However, these problems can coexist in the regression model. Therefore, in this study, new diagnostic measures based on the Dawoud-Kibria estimator (DKE) are proposed as alternatives to the available ones. The Cook’s distance, as well as the DFFITS, are introduced for the DKE. Additionally, the above measures and approximate formulas are proposed for the DKE. Two real-world applications and a simulation study are conducted to evaluate the performance of the methodologies presented in this study. [ABSTRACT FROM AUTHOR]

Recent studies focus on modelling count data, which often shows overdispersion or underdispersion. The Conway–Maxwell–Poisson (COMP) regression model effectively handles such dispersion. However, multicollinearity can negatively impact the maximum likelihood estimator (MLE) by increasing variance. To address this, biased estimators like the ridge estimator have been suggested to mitigate multicollinearity effects. This research proposes a new COMP hybrid estimator to further address multicollinearity issues. Theoretical comparisons between the COMP hybrid estimator, MLE, and other COMP estimators reveal that the hybrid estimator reduces mean squared error. Monte Carlo simulations and practical applications confirm that these proposed estimators outperform both MLE and existing COMP estimators. [ABSTRACT FROM AUTHOR]

In this paper, we propose three stochastic restricted biased estimators for the linear regression model. These new estimators generalize the least squares estimator, mixed estimator, and biased estimator. We derive the necessary and sufficient conditions for the superiority of the proposed estimators over existing ones, as well as their relative superiority among each other, using the mean squared error matrix as a criterion. A simulation study is conducted to validate the theoretical findings, and two real-world examples are provided to demonstrate the practical advantages of the proposed estimators. [ABSTRACT FROM AUTHOR]

The least-squares (LS) is a known estimator for the estimation of the linear regression model parameter. The LS is inefficient in the happening of the significant correlations among the explanatory variables. Alternatively, we propose a new regression estimator for the purpose of the reduction of multicollinearity effects. The comparisons between the new regression estimator with each of the available regression estimators are performed theoretically. Then, a massive simulation with different factors is done. The main finding point of this study is that the new regression estimator is superior to other available regression estimators under some determined conditions using the mean squared error. Finally, a numerical example is also done to ensure the superiority of the new regression estimator. [ABSTRACT FROM AUTHOR]

The ordinary least‐squares estimator is commonly used to estimate the parameters of a linear regression model but gives unreliable and unfavorable results when two problems occur together: multicollinearity and outliers. This article proposes two different robust estimators of the regression parameters to cope with these problems together. The proposed estimators are a robust version of the Özkale–Kaçiranlar and Yang–Chang estimators. Theoretical calculations, numerical simulations, and real‐life data on manufacturing production are presented to demonstrate the superiority of the proposed robust estimators to existing estimators at dealing with multicollinearity and outliers at the same time. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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 MA(q) model. We run a simulation using the three above examining methods under specific conditions. The main finding is that, 5th Exponential Weighted Moving Average (5-th EWMA) Autoregressive Integrated Moving Average (ARIMA) model is the best forecasting model among others, which means the optimal k = 5. For Turkish Telecommunications (TTKOM), stock market real data reveals the similar results of the simulation study. [ABSTRACT FROM AUTHOR]

In this article, we discuss finding the optimalkof (i)kth simple moving average, (ii)kth weighted moving average, and (iii)kth exponential weighted moving average based on simulatedARIMA(p,d,q) model. We run a simulation using the three above examining methods under specific conditions. The main finding is that 5th exponential weighted moving average (5th EWMA) ARIMA model is the best forecasting model among others, which means the optimalk= 5. For Turkish Telecommunications (TTKOM) stock market, real data reveal the similar results of simulation study. [ABSTRACT FROM AUTHOR]

In this note, we make some comments about the paper of Alheety and Kibria (2014) and correct the wrongly proved Theorems in that paper. [ABSTRACT FROM AUTHOR]

This article discusses the predictive performance of the Liu type (LT) estimator compared to ordinary least squares, principal components, ridge regression, and Liu estimators. The theoretical results are illustrated by a numerical example and a region is established where the LT estimator is uniformly superior to the other mentioned estimators. [ABSTRACT FROM AUTHOR]

In this article, we discuss finding the optimal k of (i) kth simple moving average, (ii) kth weighted moving average, and (iii) kth exponentialweightedmoving 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. [ABSTRACT FROM AUTHOR]