The current pandemic of the Novel Corona virus (COVID-19) has resulted in multifold challenges related to health, economy, and society, etc. for the entire world. Many mathematical epidemiological models have been tried for the available data of the COVID-19 pandemic with the core objective to observe the trend and trajectories of infected cases, recoveries, and deaths, etc. However, these models have their own assumptions and parameters and vary with regional demography. This article suggests the use of a more pragmatic approach of the Kalman filter with the Autoregressive Integrated Moving Average (ARIMA) models in order to obtain more precise forecasts for the figures of prevalence, active cases, recoveries, and deaths related to the COVID-19 outbreak in Pakistan.

The ordinary least squares and ridge regression estimators in a multiple linear regression model with multicollinearity and y-direction outliers lead to unfavorable results. In order to mitigate such situation, the available literature provides few ridge M-estimators to get precise estimates. The ridge parameter, k, plays a vital role in a bias-variance tradeoff for these estimators. However, for high signal-to-noise ratio and multicollinearity with y-direction outliers, the available methods may not perform well in terms of their mean squared error. In this article, we propose a new quantile based ridge M-estimator. The new estimator gives an automated choice of quantile probability of ridge parameter according to the level of noise and multicollinearity. Based on a simulation study, the new estimator outperforms the ordinary least square estimator, ridge estimator, and other considered ridge M-estimators especially for high multicollinearity, significant error variance, and y-direction outliers. Besides normal distribution, new estimator also performs well for heavy-tailed error distribution. Finally, two real-life examples are used to illustrate the application of the proposed estimator.

In this article, we present a new general class of biased estimators which includes some popular estimators as special cases and discuss its properties for multiple linear regression models when regressors are correlated. This proposal is based on some modification in the existing new two-parameter estimator. Performance of the proposed estimator is compared with many of the leading estimators, using the mean squared error matrix criterion, mitigating the adverse effects of multicollinearity. An extensive simulation study has been provided with a numerical example to illustrate the superiority of the proposed estimator.

Background: Different anthropometric parameters have been proposed for assessing central obesity in children, but the ability of these anthropometric parameters to correctly measure central obesity in Pakistani children is questionable and needs to be assessed. The aims of this investigation were to examine the diagnostic performance of anthropometric parameters as indicators of central obesity in Pakistani children as measured by waist circumference (WC) and to determine the sex-specific best cut-off values for these parameters that would identify obese children. Methods: Anthropometric measurements – height, weight, WC, waist-to-hip ratio (WHR), waist-to-height ratio (WHtR), conicity index (CI) and neck circumference (NC) – from a cross-sectional sample of 5964 Pakistani children aged 5–12 years were analyzed. Receiver operating characteristics (ROC) analysis was used to examine the diagnostic performance and to determine the optimal cut-off point of each anthropometric parameter for identifying centrally obese children. Results: It was found that WC had a significantly positive correlation with all studied anthropometric parameters. The ROC curve analysis indicated that all the parameters analyzed had good performance but WHtR had the highest value of the area under the curve (AUC). Optimal cut-off points associated with central obesity for boys and girls were, respectively, 0.47 and 0.48 for WHtR, 1.20 and 1.23 for CI, 0.96 and 0.96 for WHR and 26.36 and 26.54 cm for NC. Conclusions: The sex-specific cut-off points for WHtR, CI, WHR and NC can be used to detect central obesity in Pakistani children.

This article proposes another general class of biased estimators which includes some popular estimators as special cases and discusses its properties for multiple linear regression models with the issue of multicollinearity. We proposed the estimator by modifying the Liu estimator (LE) with the use of the existing modified ridge-type estimator and provide its properties. Performance of the proposed estimator is compared with many of the leading estimators, using the mean squared error (MSE) matrix criterion. We conducted an extensive simulation study to illustrate the superiority of the proposed estimator.