Developing Interaction Shrinkage Parameters for the Liu Estimator — with an Application to the Electricity Retail Market

Abstract

In this article we examine multicollinearity in the standard OLS interactionterm model-a problem often disregarded by practitioners and in previous research. As a remedy we propose a number of new shrinkage parameters based on the Liu (Commun Stat 22:393-402, 1993) estimator. Using Monte Carlo simulations, we evaluate the robustness of all models for different data-generating processes under varying conditions such as altered sample sizes and error distributions. In the simulation study it is demonstrated that the Liu estimator, which is robust to multicollinearity, systematically outperforms the traditionally applied OLS approach. The simple reason is that interaction models by definition always induce substantial multicollinearity, which in turn distorts the inference of OLS. Conversely, the Liu estimator is robust against multicollinearity in interaction-term models. The advantages of our Liu-based method are also demonstrated in practice when examining the efficiency of the Swedish power retailing market. By the use of this unique data set we find strong evidence of positive asymmetric price transmission effects. Increases in Nord Pool electricity wholesale spot prices lead to immediate and full increases in the electricity retail prices, but

Improved estimators for the zero-inflated Poisson regression model in the presence of multicollinearity: simulation and application of maternal death data

“…We introduce an approach to solve the problem of inflated variances for the ML estimation technique-which is a standard approach to estimate these types of count data models. In our paper we generalize some methods of estimating the shrinkage parameter d that were developed for the linear regression model by Liu (1993), Kibria (2003), Muniz and Kibria (2009), and Shukur, Månsson, and Sjölander (2015). A Monte Carlo simulation study is conducted to evaluate and compare the performances of the ML and the proposed Liu estimators (where MSE, MAE and the average lengths of confidence intervals are chosen as performance criteria).…”

“…The following five shrinkage estimators (D 1 , D 2 , D 3 , D 4 and D 5 ) are based on Shukur, Månsson, and Sjölander (2015), which follows the works of Kibria (2003), Khalaf and Shukur (2005) and Muniz and Kibria (2009). The first estimator is define as follows,…”

“…Thus, the estimated coefficient variances can be considerably reduced with the very small cost of a minor bias (see, for instance, Saleh andKibria 1993, Wichern andChurchill 1978;Amin et al 2017;Kibria 2003;Qasim, Amin, and Omer 2019). Since, the ridge regression estimator is a complicated function of the ridge parameter k, Liu (1993) introduced an alternative biased estimator, which is a linear function of the shrinkage parameter d (see, e.g., Akdeniz and Kaçiranlar 1995;Alheety and Kibria 2009;Kibria 2012;Månsson 2013;Shukur, Månsson, and Sjölander 2015;Al-Taweel and Algamal 2020;Ullah 2018 and2019 among others). Kibria et al (2013) considered some ridge regression estimators for the zero-inflated Poisson regression model and showed the usefulness of the model in presence of the multicollinearity.…”

Quantile-Based Estimation of Liu Parameter in the Linear Regression Model: Applications to Portland Cement and US Crime Data

“…Following [9], the eigenvector corresponding to maximum eigenvalue of the X ′ X matrix is taken as the vector of regression coefficients. Following [4][5][6], the different factors we choose to vary in our study are given below:…”

“…e optimal value of biasing parameter d in Liu regression plays an important role in minimizing the variance. Many researchers have suggested several estimators for estimating d. Few of them are [4][5][6]. In this paper, the performance of some existing LEs is investigated, and a new method called as quantile based estimation of Liu or biasing parameter d is proposed.…”