define_phi: Define the phi vector

In bootstrapFP: Bootstrap Algorithms for Finite Population Inference

Define the phi vector

Description

Define the phi vector used to select the first sample in Antal & Tillé (2011) bootstrap (algorithm 4, first step). If the sum of the elements of \phi is not an integer, phi is decomposed in a convex combination of two vectors \phi_1 and \phi_2, such that the sum of \phi_1i is the integer part of \sum phi_i and the sum of \phi_2i is the integer part of \sum phi_i plus 1 [see Antal and Tille' (2011) bootstrap procedure for unequal probability sampling, p. 539 - Algorithm 4, Case 1] The procedure used to decompose the vector \phi is described in the answer to this question: https://math.stackexchange.com/questions/2700483/vector-decomposition-into-a-convex-combination-of-two-vectors-with-constraints-o

Usage

define_phi(phi)

Arguments

phi	vector of inclusion probabilities for Antal and Tillé (2011) bootstrap, given by 1 - D_kk

Value

a list with the two vectors in which phi is decomposed

bootstrapFP documentation built on July 4, 2024, 1:10 a.m.