Saima Altaf

Efficient Estimation and Robust Inference of Linear Regression Models in the Presence of Heteroscedastic Errors and High Leverage Points

It is common for linear regression models that the error variances are not the same for all observations and there are some high leverage data points. In such situations, the available literature advocates the use of heteroscedasticity consistent covariance matrix estimators (HCCME) for the testing of regression coefficients. Primarily, such estimators are based on the residuals derived from the ordinary least squares (OLS) estimator that itself can be seriously inefficient in the presence of heteroscedasticity. To get efficient estimation, many efficient estimators, namely the adaptive estimators are available but their performance has not been evaluated yet when the problem of heteroscedasticity is accompanied with the presence of high leverage data. In this article, the presence of high leverage data is taken into account to evaluate the performance of the adaptive estimator in terms of efficiency. Furthermore, our numerical work also evaluates the performance of the robust standard errors based on this efficient estimator in terms of interval estimation and null rejection rate (NRR).

Bayesian analysis of the amended Davidson model for paired comparison using noninformative and informative priors

In recent years, numerous statisticians have focused their attention on the Bayesian analysis of different paired comparison models. While studying paired comparison techniques, the Davidson model is considered to be one of the famous paired comparison models in the available literature. In this article, we have introduced an amendment in the Davidson model which has been commenced to accommodate the option of not distinguishing the effects of two treatments when they are compared pairwise. Having made this amendment, the Bayesian analysis of the Amended Davidson model is performed using the noninformative (uniform and Jeffreys’) and informative (Dirichlet–gamma–gamma) priors. To study the model and to perform the Bayesian analysis with the help of an example, we have obtained the joint and marginal posterior distributions of the parameters, their posterior estimates, graphical presentations of the marginal densities, preference and predictive probabilities and the posterior probabilities to compare the treatment parameters.

Analysis of the amended Davidson model with order effect for paired comparison in the Bayesian paradigm

We commonly observe many types of paired nature of competitions in which the objects are compared by the respondents pairwise in a subjective manner. The Bayesian statistics, contrary to the classical statistics, presents a generic tool to incorporate new experimental evidence and update the existing information. These and other properties have ushered the statisticians to focus their attention on the Bayesian analysis of different paired comparison models. The present article focuses on the amended Davidson model for paired comparison in which an amendment has been introduced that accommodates the option of not distinguishing the effects of two treatments when they are compared pairwise. However, Bayesian analysis of the amended Davidson model is performed using the noninformative priors after making another small modification of incorporating the parameter of order effect factor. The joint and marginal posterior distributions of the parameters, their posterior estimates, predictive and posterior probabilities to compare the treatment parameters are obtained.

Evaluation of anthropometric parameters of central obesity in Pakistani children aged 5-12 years, using receiver operating characteristic (ROC) analysis.

Abstract 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.

efficient estimation of distributed lag model in presence of heteroscedasticity of unknown form:A monte carlo evidence

Abstract In the presence of heteroscedasticity, the ordinary least-squares (OLS) estimator remains no more efficient while the popular Almon technique is being considered for a finite distributed lag model (DLM). The available literature proposes few adaptive estimators which are more efficient than the OLS estimator when there is heteroscedasticity of unknown form. This study suggests the similar adaptation combined with the Almon technique in order to get more efficient estimator of vector of lag coefficients in the DLM. Performance of the proposed estimator has been evaluated through the Monte Carlo simulations. The simulation results show an attractive performance of the proposed estimator in terms of efficiency.

Improved Testing of Distributed Lag Model in Presence of Heteroscedasticity of Unknown Form

The finite distributed lag models (DLM) are often used in econometrics and statistics. Application of the ordinary least square (OLS) directly on the DLM for estimation may have serious problems. To overcome these problems, some alternative estimation procedures are available in the literature. One popular method to estimate these models is the Almon technique, proposed by Almon (1965). However, testing of the DLM has not attained the attention of researchers. The present study covers this gap and proposes some methods for testing the DLM combined with the Almon technique. Furthermore, the testing of DLM in presence of heteroscedasticity may be invalid due to adverse consequences of heteroscedasticity when applying the OLS procedure combined with the Almon technique. The present article suggests to use heteroscedasticity-consistent covariance matrix (HCCM) estimators to draw valid inference for the parameters of the DLM with heteroscedastic errors. The HCCM estimators based confidence intervals, t- and F-tests are proposed and the performance of these tests and confidence intervals is evaluated through the Monte Carlo simulations by computing empirical null rejection rate (NRR) and coverage. Keywords : Almon technique; coverage; Finite distributed lag model; heteroscedasticity-consistent covariance matrix estimator; Null rejection rate.