On certain alternative mean square error estimators in complex survey sampling

Estimation in Multi-Stage Sampling with Partially Missing First Stage Units

“…writing Ep (later Vp) as operators for expectation (variance) with respect to p. Supposing one may choose certafn non-zero numbers wj's, Chaudhuri and Pal (2002) Next suppose y; is not ascertainable but as in the usual context of multi-stage sampling, vide the works of Raj (1968) and Chaudhuri, Adhikary and Dihidar (2000), let through sampling at subsequent stages ' independently' distributed random variables r;'s be available such that writing EL, VL as the operators for expectation, variance with respect to 'sampling at the later stages' (i) EL(ri) = y;, (2)VL(ri) = V;, (3)v; be available such that EL(v;)…”

Indirect Questioning Technique Related to Sensitive Quantitative Variables with Options for Direct, Randomized and Item Count Responses

“…Hence, 𝑒 ′ is an unbiased estimator of 𝑌 ̅ . Then, following Chaudhuri and Pal (2002), variance of 𝑒 ′ is,…”

“…If every sample 𝑠 1 and 𝑠 2 contains common number of distinct units in it, then, 𝛽 𝑖 = 0 ∀ i and 𝛽 𝑘 = 0 ∀ k throughout in 𝑉(𝑒) above. Then, taking clue fromChaudhuri and Pal (2002), an unbiased estimator for 𝑉(𝑒) is, with 𝛽 𝑖 = 0 ∀ i and 𝛽 𝑘 = 0 ∀ k in 𝑣(𝑒) when applicable. Hence, 𝑣(𝑒) is an unbiased estimator of 𝑉(𝑒) , such that 𝐸{𝑣(𝑒)} = 𝐸 𝑃 𝐸 𝑅 {𝑣(𝑒)} = 𝐸 𝑅 𝐸 𝑃 {𝑣(𝑒)} = 𝑉(𝑒) .…”