This paper considers multivariate extension of smooth estimator of the distribution and density function based on Bernstein polynomials studied in Babu et al. [2002. Application of Bernstein polynomials for smooth estimation of a distribution and density function. J. Statist. Plann. Inference...

The validity of the one-term Edgeworth expansion is proved for the multivariate mean of a random sample drawn without replacement under a limiting non-latticeness condition on the population. The theorem is applied to deduce the one-term expansion for the univariate statistics which can be...