Improved two-parameter estimators for the negative binomial and Poisson regression models

Negative binomial regression (NBR) and Poisson regression (PR) applications have become very popular in the analysis of count data in recent years. However, if there is a high degree of relationship between the independent variables, the problem of multicollinearity arises in these models. We introduce new two-parameter estimators (TPEs) for the NBR and the PR models by unifying the two-parameter estimator (TPE) of Özkale and Kaç?ranlar [The restricted and unrestricted two-parameter estimators. Commun Stat Theory Methods. 2007;36:2707–2725]. These new estimators are general estimators which include maximum likelihood (ML) estimator, ridge estimator (RE), Liu estimator (LE) and contraction estimator (CE) as special cases. Furthermore, biasing parameters of these estimators are given and a Monte Carlo simulation is done to evaluate the performance of these estimators using mean square error (MSE) criterion. The benefits of the new TPEs are also illustrated in an empirical application. The results show that the new proposed TPEs for the NBR and the PR models are better than the ML estimator, the RE and the LE.     

Detecting influential observations in Liu and modified Liu estimators

In regression, detecting anomalous observations is a significant step for model-building process. Various influence measures based on different motivational arguments are designed to measure the influence of observations through different aspects of various regression models. The presence of influential observations in the data is complicated by the existence of multicollinearity. The purpose of this paper is to assess the influence of observations in the Liu [9] and modified Liu [15] estimators by using the method of approximate case deletion formulas suggested by Walker and Birch [14]. A numerical example using a real data set used by Longley [10] and a Monte Carlo simulation are given to illustrate the theoretical results.     

On the almost unbiased generalized liu estimator and unbiased estimation of the bias and mse

In this paper, we derive the almost unbiased generalized Liu estimator and examine an exact unbiased estimator of the bias and mean squared error of the feasible generalized Liu estimator . We compare the almost unbiased generalized Liu estimator (AUGLE) with the generalized Liu estimator (GLE) and with the ordinary least squares estimator (OLSE).     

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 Kaç?ranlar [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 Kaç?ranlar [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.     

INTERNATIONAL CURRENCY SUBSTITUTION AND SEIGNIORAGE IN A SIMPLE MODEL OF MONEY

This paper investigates the economic signcance of currency substitution using a small, open economy model of money. The main result is that in a low-inflation economy the seigniorage-maximizing inflation rate can be quite large despite a very high elasticity of currency substitution when the share of foreign real balances in producing domestic liquidity services is small (as some recent econometric estimates indicate in the case of Canada). This suggests that currency substitution is likely to be of second-order importance to policymakers in a low-inflation economy where foreign real balances provide economically small domestic liquidity services.     

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

Liew (1976a Liew, C.K. (1976a). A two-stage least-squares estimation with inequality restrictions on parameters. Rev. Econ. Stat. LVIII(2):234–238.[Crossref], [Web of Science ®] , [Google Scholar]) 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 Dantzig, G.B., Cottle, R.W. (1967). Positive (semi-) definite matrices and mathematical programming. In: Abadie, J., ed. Nonlinear Programming (pp. 55–73). Amsterdam: North Holland Publishing Co. [Google Scholar]), Cottle and Dantzig (1974 Cottle, R.W., Dantzig, G.B. (1974). Complementary pivot of mathematical programming. In: Dantzig, G.B., Eaves, B.C., eds. Studies in OptimizationVol. 10. Washington: Mathematical Association of America. [Google Scholar]) and solving with Lemke (1962 Lemke, C.E. (1962). A method of solution for quadratic programs. Manage. Sci. 8(4):442–453.[Crossref], [Web of Science ®] , [Google Scholar]) 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.     

An optimal k of kth MA-ARIMA models under a class of ARIMA model

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 ARIMA(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 optimal k = 5. For Turkish Telecommunications (TTKOM) stock market, real data reveal the similar results of simulation study.     

Two-stage Liu estimator in a simultaneous equations model

Two-stage least squares estimation in a simultaneous equations model has several desirable properties under the problem of multicollinearity. So, various kinds of improved estimation techniques can be developed to deal with the problem of multicollinearity. One of them is ridge regression estimation that can be applied at both stages and defined in Vinod and Ullah [Recent advances in regression methods. New York: Marcel Dekker; 1981]. We propose three different kinds of Liu estimators that are named by their implementation stages. Mean square errors are derived to compare the performances of the mentioned estimators and two different choices of the biasing parameter are offered. Moreover, a numerical example is given with a data analysis based on the Klein Model I and a Monte Carlo experiment is conducted.     

Comparisons of the alternative biased estimators for the distributed lag models

The finite distributed lag models include highly correlated variables as well as lagged and unlagged values of the same variables. Some problems are faced for this model when applying the ordinary least squares (OLS) method or econometric models such as Almon and Koyck models. The primary aim of this study is to compare performances of alternative estimators to the OLS estimator defined by combining the Almon estimator with some estimators using Almon (1965) data. A simulation study with different model parameters is performed and the estimators are compared according to the root mean square error (RMSE) and prediction mean square error (PMSE).     

The Restricted and Unrestricted Two-Parameter Estimators

In this article, we introduce a new two-parameter estimator by grafting the contraction estimator into the modified ridge estimator proposed by Swindel (1976 Swindel , B. F. ( 1976 ). Good ridge estimators based on prior information . Commun. Statist. Theor. Meth. A5 : 1065 – 1075 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]). This new two-parameter estimator is a general estimator which includes the ordinary least squares, the ridge, the Liu, and the contraction estimators as special cases. Furthermore, by setting restrictions Rβ = r on the parameter values we introduce a new restricted two-parameter estimator which includes the well-known restricted least squares, the restricted ridge proposed by Groß (2003 Groß , J. ( 2003 ). Restricted ridge estimation . Statist. Probab. Lett. 65 : 57 – 64 .[Crossref], [Web of Science ®] , [Google Scholar]), the restricted contraction estimators, and a new restricted Liu estimator which we call the modified restricted Liu estimator different from the restricted Liu estimator proposed by Kaç?ranlar et al. (1999 Kaç?ranlar , S. , Sakall?o?lu , S. , Akdeniz , F. , Styan , G. P. H. , Werner , H. J. ( 1999 ). A new biased estimator in linear regression and a detailed analysis of the widely-analysed dataset on Portland cement . Sankhya Ser. B., Ind. J. Statist. 61 : 443 – 459 . [Google Scholar]). We also obtain necessary and sufficient condition for the superiority of the new two-parameter estimator over the ordinary least squares estimator and the comparison of the new restricted two-parameter estimator to the new two-parameter estimator is done by the criterion of matrix mean square error. The estimators of the biasing parameters are given and a simulation study is done for the comparison as well as the determination of the biasing parameters.