## Optimal Sample Allocation in the Presence of Non-response

Assume stratified simple random sampling design. Population is split in strata. We have fixed sample size . The aim is to find optimal sample allocation , where and is minimised.

There is some population information available. The population size by strata: , population standard deviation of variable: , and expected response rate in each stratum: .

Optimal sample allocation in the presence of non-response can be computed as .

I do not have a proof but I have done some numerical calculations to test the optimality of the allocation. The R code of the calculations is available here.

The presented allocation is equal to the well known Neyman allocation [1] in case we have the same response expectation in each stratum.

[1] Neyman, Jerzy (1937). *Outline of a Theory of Statistical Estimation Based on the Classical Theory of Probability*. Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences 236 (767): 333–380

Pārāk gudra doma priekš manis .