In econometrics, three types of data are studied like cross-sectional, timeseries and panel data. Panel data is based on various observations, collected from same individuals over several time periods. It is combination of crosssectional and time-series data. The regression model formulated for such data is called panel data model (PDM). Heteroscedasticity is a usual problem in the PDM and it is desirable to concentrate on it for making robust inference. The ordinary techniques used for estimation of PDM do not lead e cient estimation and correct inference in the presence of heteroscedasticity. Moreover, presence of the high leverage points in given dataset may also lead to incorrect inference. Therefore, focus of this study is to bring improvement in inference of linear PDM su ering from heteroscedasticity of both known and unknown form. For linear regression model, White (1980) consistent estimator can be applied in the presence of heteroscedasticity in order to get correct inference. In context of the PDM, the amended version of White''s estimator has been presented by Arellano (1987). The variant of White''s estimator like HC5, the HCCME for true generalised least square (TGLS) and feasible GLS (FGLS) and some adaptive version of the HCCMEs have been proposed in this thesis for the PDM which are not available in the existing literature. Besides, Efron (1979), Freedman (1981) and Wu (1986) bootstrap estimators, another estimator is also available in the literature. This estimator is known as kernel estimator. The kernel bootstrap estimator of Racine and MacKinnon (2007) has been proposed for the PDM which is previously given only for linear regression model. In this work, improved inferences via kernel smoothing is also presented and compared with conventional approaches. For novelty of the approach, kernel version of Wu''s bootstrap estimator has been improved. In this work, heteroscedasticity related to unit speci c is studied as considered by Roy (2002), Aslam (2006) and Aslam and Pasha (2007). Roy''s adaptive estimator is studied for e cient estimation of the PDM. Adaptive based consistent estimators are given by Aslam and Pasha (2007). For this study, new versions of adaptive based consistent estimators are presented for the PDM. Empirical results are based on the Monte Carlo study as used by Roy (2002) and Aslam (2006). The results indicate that kernel based bootstrap show better performance than other considered estimators. The new versions of adaptive based consistent estimators perform better than the previous ones. Performance of estimators are justi ed in terms of interval estimation, size and power of test. Illustrative examples are also given in the thesis.