make_sd_matrix: Create a quadratic form's matrix to represent a...

In svrep: Tools for Creating, Updating, and Analyzing Survey Replicate Weights

Create a quadratic form's matrix to represent a successive-difference variance estimator

Description

A successive-difference variance estimator can be represented as a quadratic form. This function determines the matrix of the quadratic form.

Usage

make_sd_matrix(n, f = 0, type = "SD1")

Arguments

n	Number of rows or columns for the matrix
f	A single number between 0 and 1, representing the sampling fraction. Default value is 0.
type	Either "SD1" or "SD2". See the "Details" section for definitions.

Details

Ash (2014) describes each estimator as follows:

\hat{v}_{SD1}(\hat{Y}) = (1-f) \frac{n}{2(n-1)} \sum_{k=2}^n\left(\breve{y}_k-\breve{y}_{k-1}\right)^2

\hat{v}_{SD2}(\hat{Y}) = \frac{1}{2}(1-f)\left[\sum_{k=2}^n\left(\breve{y}_k-\breve{y}_{k-1}\right)^2+\left(\breve{y}_n-\breve{y}_1\right)^2\right]

where \breve{y}_k is the weighted value y_k/\pi_k of unit k with selection probability \pi_k, and f is the sampling fraction \frac{n}{N}.

Value

A matrix of dimension n

References

Ash, S. (2014). "Using successive difference replication for estimating variances." Survey Methodology, Statistics Canada, 40(1), 47–59.

svrep documentation built on May 29, 2024, 2:21 a.m.