A non-parametric reconstruction of the deceleration parameter $q$ is carried out. The observational datasets are so chosen that they are model independent as much as possible. The present acceleration and the epoch at which the cosmic acceleration se
ts in is quite as expected, but beyond a certain redshift ($z sim 2$), a negative value of $q$ appears to be in the allowed region. A survey of existing literature is given and compared with the results obtained in the present work.
The cosmological jerk parameter $j$ is reconstructed in a non-parametric way from observational data independent of a fiducial cosmological model. From this kinematical quantity, the equation of state parameter for composite matter distribution is al
so found out. The result shows that there is a deviation from the $Lambda$CDM model close to $z=1.5$, at the $3sigma$ confidence level.
