Sampling a two dimensional matrix

Abstract

A new sampling design for populations whose units can be arranged as an N ×M matrix is proposed. The sample must satisfy some constraints: row and column sample sizes are set in advance. The proposed sampling method gives the same selection probability to all the sample matrices that satisfy the constraints.Three algorithms to select a sample uniformly in the feasible set are presented: an exact algorithm based on the multivariate hypergeometric distribution, an MCMC algorithm, and the cube method. Their performances are evaluated using Monte Carlo simulations. The designs for sampling elements in a given row or a given column are investigated and the single inclusion and joint selection probabilities under the proposed design are evaluated. Several variance estimators are proposed for the Horvitz-Thompson estimator of the population mean of the survey variable y and their performances are compared in a Monte Carlo study. A numerical example dealing with a creel survey of fishermen found at 9 sites over 36 days is presented.

A Generic Multilevel Structure for Educational Escape Rooms

“…Hence, the escape room proposed is composed of a series of sequential levels, which are the linear-paths, such that each level is formed by a string of sequential stages. This type of structure could be compared to a bidimensional array or matrix [15], where its rows are considered as levels and its columns are seen as the stages forming each level, where all stages within a given level must be traversed before getting into the next level.…”

Using Survey Sampling Algorithms For Exact Inference in Logistic Regression

“…The cube method is implemented in two R packages: sampling, see Tillé & Matei (2015), and BalancedSampling, see Grafström & Lisic (2018), that features a fast C++ program for the flight phase. Investigations reported in Rivest & Ebouele (2020) show that the linear program for the landing phase implemented in Tillé & Matei (2015) is more likely to produce a sample that is balanced, exactly. The cube algorithm proposed here and implemented in Section 4 uses the fast flight phase in the function fligthphase of BalancedSampling and the linear program for the landing phase in sampling.…”

Limiting properties of an equiprobable sampling scheme for 0–1 matrices

“…They are found in ecology: the rows are species and the columns are sites and they enter in Monte Carlo tests of association between species [5]. In survey sampling, these matrices are used to sample populations with a matrix structure, for instance when N sites can be sampled over M days [8].…”

“…In the numerical section we used this so-called " trial swap" algorithm implemented in the R-package vegan [6]. Algorithms based on importance sampling [4] and rejective methods [8] have also been considered.…”

“…converges to 0 where P M is defined by (8). To simplify the presentation, this proof evaluates (8) as a ratio of sums involving terms such as M !/( x ω !…”