The Liu estimator has consistently been demonstrated to be an attractive shrinkage method for reducing the effects of multicollinearity. The Poisson regression model is a well-known model in applications when the response variable consists of count data. However, it is known that multicollinearity negatively affects the variance of the maximum likelihood estimator (MLE) of the Poisson regression coefficients. To address this problem, a Poisson Liu estimator has been proposed by numerous researchers. In this paper, a Jackknifed Liu-type Poisson estimator (JPLTE) is proposed and derived. The idea behind the JPLTE is to decrease the shrinkage parameter and, therefore, improve the resultant estimator by reducing the amount of bias. Our Monte Carlo simulation results suggest that the JPLTE estimator can bring significant improvements relative to other existing estimators. In addition, the results of a real application demonstrate that the JPLTE estimator outperforms both the Poisson Liu estimator and the maximum likelihood estimator in terms of predictive performance.

Brain and other CNS cancers have evidenced increase in Iraq over the study period (2000-2015). Spatial variation of brain and CNS cancers in Iraq at the district level has not been explored. This study aimed to explore the spatial patterns of the Age-Standardized Incidence Rates (ASIRs) of brain and CNS cancers throughout Iraq (except Kurdish region) during 2000-2015 using spatial autocorrelation analyses. Data were obtained from the Iraqi Cancer Registry. The ASIRs were calculated according to geographical region (provinces and districts) for each period (2000-2004, 2005- 2009, and 2010-2015). spatial statistical tools were employed to evaluate hotspots, cold spots, spatial clustering and outliers for each period. Results showed a spatial correlation with hotspots, cold spots, and detecting spatial outliers. This study identified 7 districts as high-risk areas for brain and CNS cancers during 2010-2015,  including  Al-Sadir, Al-Kadhimiyah, Adhamia, Al-Karkh, Al-Rissafa, and Al-Madain districts in Baghdad province) and southern region (Abu-Al-Khaseeb district in Al-Basrah provinces, and we have evidenced an increase of brain and CNS cancers incidence rates during 2010-2015. The government efforts should focus on those regions, and the factors related to the spatial pattern of the brain and CNS cancers incidence in Iraq should be investigated.

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