Two-step robust estimator in heteroscedastic regression model in the presence of outliers

Although the ordinary least squares (OLS) estimates are unbiased in the presence of heteroscedasticity, these are no longer efficient. This problem becomes more complicated when the violation of constant error variances comes together with the existence of outliers. The weighted least squares (WLS) procedure is often used to estimate the regression parameters when heteroscedasticity occurs in the data. But there is evidence that the WLS estimators suffer a huge set back in the presence of outliers. Moreover, the use of the WLS requires a known form of the heteroscedastic errors structures. To rectify this problem, we proposed a new method that we call two step robust weighted least squares (TSRWLS) method where prior information on the structure of the heteroscedastic errors is not required. In the proposed procedure, the robust technique is used twice. Firstly, the robust weights are used for solving the heteroscedasic error and secondly, the robust weighting function is used for eliminating the effect of outliers. The performance of the newly proposed estimator is investigated extensively by real data sets and Monte Carlo simulations

SERUM VITAMIN E, C AND A LEVEL IN LUNG CANCER: A CASE CONTROL STUDY

Lung cancer is a leading cause of cancer death worldwide, causing approximately 1.2 million deaths per year. Lung cancer is prevalent in smokers. It is documented that smoking induces oxidative stress, which is thought to be associated with the aetiology of carcinogenesis. A case control cross sectional study was conducted on sixty lung cancer patients and sixty smokers as cohort control. Serum levels of antioxidant vitamin E, C and A among the case and control subjects were estimated. It was observed that vitamin E value among the study population did not alter (15.67±3.67μmol/L vs. 14.66±3.88μmol/L). It was within normal range. Conversely, there was significantly high serum concentrations of vitamin C and A in the lung cancer patients as compared to those in the smoker controls (48.26±6.81versus 16.65±4.46μmol/L; 2.76±0.32 versus 1.60±0.35μmol/L respectively)