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Variance-minimising overlap weight for a dual-frame estimator

Source: R/median_frames_dose_native.R
morie_optimal_overlap_weight.Rd

Hartley's estimator is unbiased for every \(\theta\) in [0, 1], so the choice is purely about efficiency. With independent samples the variance \(\theta^2 V_A + (1-\theta)^2 V_B\) is minimised at \(\theta^* = V_B/(V_A + V_B)\) – weight goes to the frame that measures the overlap MORE precisely.

Usage

morie_optimal_overlap_weight(var_a, var_b)

Arguments

var_a, var_b

Domain variances from each frame.

Value

The optimal weight.

References

Hartley HO (1962). Lohr SL, Rao JNK (2000) JASA 95(449):271-280, doi:10.1080/01621459.2000.10473920 .

Examples

morie_optimal_overlap_weight(var_a = 5L, var_b = 5L)
#> [1] 0.5