Cov_mu.v

Computes the asymptotic covariance matrix and expectation (mu) vector for the vectorized BRISE statistic under the pattern-wise permutation null distribution, based on rank matrix R and the list of pattern indicator. Used to form the quadratic statistic and its chi-square approximation.

internal

Implements the Block-wise Rank in Similarity Graph Edge-count
test (BRISE), a rank-based two-sample test designed for block-wise
missing data. The method constructs (pattern) pair-wise similarity graphs
and derives quadratic test statistics with asymptotic chi-square
distribution or permutation-based p-values. It provides both
vectorized and congregated versions for flexible inference.
The methodology is described in Zhang, Liang, Maile, and
Zhou (2025) <doi:10.48550/arXiv.2508.17411>.

Kejian Zhang

BlockwiseRankTest

Block-Wise Rank in Similarity Graph Edge-Count Two-Sample Test
(BRISE)

Doudou Zhou

Cov_mu.v function

<dl><dt>R</dt>
<dd>Numeric symmetric rank matrix (N × N).</dd>
<dt>m_</dt>
<dd>Integer vector. X's sample sizes in each pattern.</dd>
<dt>n_</dt>
<dd>Integer vector. Y's sample sizes in each pattern.</dd>
<dt>ptn_list</dt>
<dd>List of integer vectors that indexes observations sharing the same missing pattern.</dd></dl>

Arguments

Covariance and Expectation (Vectorized Form) — Cov_mu.v

<dl>

<dt>R</dt>
<dd>Numeric symmetric rank matrix (N × N).</dd>


<dt>m_</dt>
<dd>Integer vector. X's sample sizes in each pattern.</dd>


<dt>n_</dt>
<dd>Integer vector. Y's sample sizes in each pattern.</dd>


<dt>ptn_list</dt>
<dd>List of integer vectors that indexes observations sharing the same missing pattern.</dd>

</dl>

Cov_mu.v: Covariance and Expectation (Vectorized Form)

Description

Usage

Value

Arguments