Composite estimator based on the recursive ratio for an arbitrary rotation scheme

Kowalczyk, Barbara; Juszczak, Dorota

doi:10.1080/08898480.2018.1477385

Cited by 1 publication

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“…This approach was further developed in Rao and Graham (1964), Gurney and Daly (1965), Cantwell (1990), Cantwell and Caldwell (1998), Ciepiela, Gniado, Wesołowski and Wojtyś (2012). Another approach, based on the so-called regression composite extimator has been proposed and studied in Bell (2001), Fuller and Rao (2001), Singh, Kennedy and Wu (2001), Kowalczyk and Juszczak (2018). Different rotation patterns and comparisons of efficiencies of different methods are presented in McLaren and Steel (2000), and McLaren (2002,2008).…”

Section: Introductionmentioning

confidence: 99%

Rotation schemes and Chebyshev polynomials

Wesołowski¹

2023

SiTns

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There is a continuing interplay between mathematics and survey methodology involving different branches of mathematics, not only probability. This interplay is quite obvious as regards the first of the two options: probability vs. non-probability sampling, as proposed and discussed in Kalton (2023). There, mathematics is represented by probability and mathematical statistics. However, sometimes connections between mathematics and survey methodology are less obvious, yet still crucial and intriguing. In this paper we refer to such an unexpected relation, namely between rotation sampling and Chebyshev polynomials. This connection, introduced in Kowalski and Wesołowski (2015), proved fundamental for the derivation of an explicit form of the recursion for the BLUE µˆt of the mean on each occasion t in repeated surveys based on a cascade rotation scheme. This general result was obtained under two basic assumptions: ASSUMPTION I and ASSUMPTION II, expressed in terms of the Chebyshev polynomials. Moreover, in that paper, it was conjectured that these two assumptions are always satisfied, so the derived form of recursion is universally valid. In this paper, we partially confirm this conjecture by showing that ASSUMPTION I is satisfied for rotation patterns with a single gap of an arbitrary size.

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Section: Introductionmentioning

confidence: 99%

Rotation schemes and Chebyshev polynomials

Wesołowski¹

2023

SiTns

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Composite estimator based on the recursive ratio for an arbitrary rotation scheme

Cited by 1 publication

References 9 publications

Rotation schemes and Chebyshev polynomials

Rotation schemes and Chebyshev polynomials

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