Buys-Ballot Estimates for Overall Sample Variances and Their Statistical Properties: A Mixed Model Case

Abstract

This article proposes an estimation procedure of overall sample variances for the mixed model while comparing them with those of the additive and multiplicative models. The estimation procedure is based on the row, column and overall means and variances of time series data arranged in a Buys-Ballot table. The procedure assumes that (1) the underlying distribution of the variable, X i j , i = 1, 2, ..., m , j = 1, 2, ..., s , under study is normal. (2) the trending curve is either linear or quadratic and (3) the decomposition method is either multiplicative or mixed. Statistical properties of the overall sample variances of the Buys-Ballot table are also considered in this study. Result indicates that, under the stated assumptions, the expected value of the overall sample variances involve sum of square and cross-product of trend parameters and seasonal indices.