The bulk motion of star clusters can be determined after careful membership analysis using parametric or non-parametric approaches. This study aims to implement non-parametric membership analysis based on Binned Kernel Density Estimators which takes into account measurements errors (simply called BKDEe) to determine the average proper motion of each cluster. This method is applied to 178 selected star clusters with angular diameters less than 20 arcminutes. Proper motion data from UCAC4 are used for membership determination. Non-parametric analysis using BKDE-e successfully determined the average proper motion of 129 clusters, with good accuracy. Compared to COCD and NCOVOCC, there are 79 clusters with less than 3σ difference. Moreover, we are able to analyse the distribution of the member stars in vector point diagrams which is not always a normal distribution.

Using the Malmquist productivity index, this paper compares the productivity of Korean manufacturing industries from 1999 to 2006. The malmquist productivity index has more advantages than previous methods such as solow model, endogenous growth theory. The malmquist productivity index can be decomposed productivity into two parts. The first part is an index of the technical efficiency change. This index has high value when the elements of production is used more efficiently. The second part is an index of technical change. This index has high value if the advent of new technology and process innovation occur.