A note on the standard errors of the members of the Alkire Foster family and its components

Consider a matrix X, whose N rows have information on the attainments of N inviduals. Each column, therefore, hosts the distribution of each attainment across the population. The number of columns/variables is D. A typical attainment element of the matrix is: xnd (2 R), that is, the attainment of individual n in dimension/variable d. In the identi…cation stage, the variable-speci…c poverty lines are denoted by zd; and for the second identi…cation stage, i.e. to determine who is multidimensionally poor, variables are weighted by weights wd such that: wd 2 R+ ^ XD