Two application problems in survey statistics are analyzed from a discrete optimization perspective.
In stratified random sampling, minimizing the variance of a total estimate leads to the optimal sample allocation by Neyman and Tschuprow. We discuss discrete optimization algorithms which solve the allocation problem by minimizing a separable convex function with upper and lower boundary conditions. Exploiting the (poly-)matroid structure of the feasible region, it is shown how the problem can be solved to global optimality by Greedy-type strategies. Subsequently, a polynomial-time algorithm is developed. By minimizing variances on several levels, the problem is further extended to a multi-objective optimization problem. We discuss the scalarization of this problem and present a simulation study based on the open household dataset AMELIA.
The second application addresses the problem of incomplete samples. A common method to deal with missing data is the nearest neighbor hot deck imputation. The method fills missing fields of receiver units with values from "close" donor units. We present a reformulation of the imputation problem as a combinatorial optimization problem and compute an optimal imputation with the help of efficient algorithms.
Venue: TUM Garching Campus, Room 02.04.011
Date: Monday, Nov. 26th, 2018, 14:00