Performance of Non-Parametric Regression Estimators in Presence of Skewed Distribution: An Application to Determinants of Poverty in selected Districts of Punjab
Author: Usama Sattar

Classical linear regression model has very nice statistical properties subject to validity of certain assumptions. However, in real life these assumptions often fail to hold, and the OLS does not possess its nice properties. Sometimes, the OLS gives very misleading results when the assumptions do not hold. The Non-Parametric methods are robust to such assumptions. However, there are lots of Non-Parametric methods that can be applied to real data that does not exhibit the classical assumptions, and one has to choose between these estimators. Unfortunately, existing literature does not provide clear guidance on how to choose between these estimators. This study compares five non-parametric regression methods on the basis of their performance in real data. For the real data, the underlying data generating process is not known, Therefore, the size and power cannot be utilized. We use the forecast performance as a measure of performance of estimator. we have taken data of determinants of poverty from PSLM (Pakistan Social and Living Standard Measurement) for ten districts of Punjab. These kinds of data usually violate the standard OLS assumptions and such type of data need to treat using non-parametric Regression methods. Forecast Mean Square Error (FMSE) and Residual Sum of Square (RSS) are computed to check the performance of non-parametric regression estimators. We analyze Non-Parametric methods separately for highly and moderately skewed data. In presence of highly skewed data, we observe Theil-Sen and Least absolute deviation estimators perform better for highly skewed data and Quantile regression, Mestimator and least trimmed square estimator perform poorly for this kind of data. On the other hand, the M-estimator and least trimmed square estimator are very better nonparametric estimators for Moderately skewed data. While the Theil-Sen and LAD estimator shows very poor performance in Moderately skewed distribution. We can also say that the Quantile Regression is not bad for this type of analysis. Supervisor:- Dr. Atiq-ur-Rehman

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Supervisor: Atiq Ur Rahman

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