The performance of robust estimator on linear regression model having both continuous and categorical variables with heteroscedastic errors

The ordinary least squares (OLS) technique is often used in practice to estimate the parameters of a multiple linear regression model with both continuous and categorical variables. It has been the most popular technique due to its optimal properties and ease of computation. Nevertheless, in the presence of outliers, the OLS can result in very poor estimates. Outliers which arise from bad data points may have unduly effect on the OLS estimates. The problem is further complicated when both outliers and heteroscedasticity or non-constant error variances are present in the data. The influence of outliers and heteroscedasticity cannot be removed or reduced by simply transforming the data using known transformation such as logarithmic transformation. In this paper, we proposed a robust technique to deal with these two problems simultaneously. A robust estimate of scales for each level of categorical variables are first estimated by using robust distance S and M (RDSM) estimates. Then we determine the weighting scheme for each level of the categorical variables and transform the model. The reweighted least squares based on RDSM (RLSRDSM) is then applied to the transformed model. The empirical evidence shows that the proposed method has reduced the heteroscedastic effect to a greater extent

Robust estimator to deal with regression models having both continuous and categorical regressors: a simulation study

The Ordinary Least Squares (OLS) method has been the most popular technique for estimating the parameters of the multiple linear regression. However, in the presence of outliers and when the model includes both continuous and categorical (factor) variables, the OLS can result in poor estimates. In this paper we try to introduce an alternative robust method for such a model that is much less influenced by the presence of outliers. A numerical example is presented to compare the performance of the OLS, the Re-weighted Least Squares based on the Robust Distance Least Absolute Value (RLSRDL1), and the Re-weighted Least Squares based on the Robust Distance S/M estimator (RLSRDSM). The latter is the modification of the RDL1. The empirical evidence shows that the performance of the RLSRDSM is fairly close to the RLSRDL1 up to 20% outliers. As the percentage of outliers increases to more than 20%, the RLSRDSM is slightly better than the RLSRDL1. However, the Robust Distance Least Absolute Value (RDL1) estimator posed certain computational problems such as degenerate non-unique solutions while the RLSRDSM do not have such problem

Using Some Wavelet Shrinkage Techniques and Robust Methods to Estimate the Generalized Additive Model Parameters in Non-Linear Models

In this paper, the method of estimating the Generalized Additive Models (GAM) was highlighted, and a proposed robust weighted composition was found by combining the robust M method with the smoothing splines to estimate the Robust Generalized Additive Model and its notation is (RGAM). This estimator is used to deal with the effect of the presence of outliers in the data that do not fit into the overall data pattern by relying on some of the weight functions of the robust M method. Wavelet Shrinkage technique is used as well, which has been proposed as a smoothing of data using several types of wavelet filters in calculating the discrete wavelet transformation and relying on it in estimating the wavelet generalized additive model symbolized by (WGAM). In the case of using the simulation method, when data is contaminated with distributions ((t) Dis., Exp. Dis.) And with contamination rates (5%, 15%, 35%) and with sample sizes (50,150,300) it is noted that the smoothing method is with the Bisequare weight (BRGAM). It had a better performance compared to the rest of the methods for the simulated scenarios covered. The GCV criterion showed a marked advantage over other criteria, especially when estimating the model in the proposed robust M (RGAM) model. Some statistical criteria have been adopted. These criteria of the Generalized Additive Model (GAM) is used to compare estimation methods, the proposed methods were tested on simulation experiments as well as on real data collected from Ibn Sina Learning Hospital on cases of short stature, and the RGAM method gave the best results compared to the ordinary GAM and WGAM methods, and that by obtaining the smallest GCV value, this is because it is responsible for selecting the most suitable smoothing parameter for the smoothing spline estimator

Twelve-month observational study of children with cancer in 41 countries during the COVID-19 pandemic

Childhood cancer is a leading cause of death. It is unclear whether the COVID-19 pandemic has impacted childhood cancer mortality. In this study, we aimed to establish all-cause mortality rates for childhood cancers during the COVID-19 pandemic and determine the factors associated with mortality

Pancreatic surgery outcomes: multicentre prospective snapshot study in 67 countries

Background: Pancreatic surgery remains associated with high morbidity rates. Although postoperative mortality appears to have improved with specialization, the outcomes reported in the literature reflect the activity of highly specialized centres. The aim of this study was to evaluate the outcomes following pancreatic surgery worldwide.Methods: This was an international, prospective, multicentre, cross-sectional snapshot study of consecutive patients undergoing pancreatic operations worldwide in a 3-month interval in 2021. The primary outcome was postoperative mortality within 90 days of surgery. Multivariable logistic regression was used to explore relationships with Human Development Index (HDI) and other parameters.Results: A total of 4223 patients from 67 countries were analysed. A complication of any severity was detected in 68.7 percent of patients (2901 of 4223). Major complication rates (Clavien-Dindo grade at least IIIa) were 24, 18, and 27 percent, and mortality rates were 10, 5, and 5 per cent in low-to-middle-, high-, and very high-HDI countries respectively. The 90-day postoperative mortality rate was 5.4 per cent (229 of 4223) overall, but was significantly higher in the low-to-middle-HDI group (adjusted OR 2.88, 95 per cent c.i. 1.80 to 4.48). The overall failure-to-rescue rate was 21 percent; however, it was 41 per cent in low-to-middle-compared with 19 per cent in very high-HDI countries.Conclusion: Excess mortality in low-to-middle-HDI countries could be attributable to failure to rescue of patients from severe complications. The authors call for a collaborative response from international and regional associations of pancreatic surgeons to address management related to death from postoperative complications to tackle the global disparities in the outcomes of pancreatic surgery (NCT04652271; ISRCTN95140761)