Multi-Label Systematic Sampling Design: A Generalized Unbiased Estimator in the Presence of Linear Trend

For practical utility, multi-stage sampling design is used by researchers when the population is large. This conventional sampling design omits portions of the populations in stages, as a result production of unbiased estimates to population parameter become uncertain. To overcome this limitation, a design called multi-label systematic sampling is introduced in this paper. This sampling design deals with both equal and unequal number of arrays of population with the associate factors which exist in multiple dimensions. All the array labels of sampling units are identified in a single attempt in a linear fashion by this sampling design. For population arranged as (N x N xh times) or (N1 x N2 x N3 x. . xNh) cells, this sampling design is useful in selecting the samples. To estimate the population parameter of study variable in the population, if one identifies multiple numbers of associate factors of the study variable, it is possible to arrive at generalized unbiased estimate of population parameter by this sampling design for the population exhibiting linear trend.