BlockwiseRankTest (version 0.1.0)

BRISE: Block-wise Rank In Similarity graph Edge-count (BRISE) Test

Description

BRISE implements the Two-Sample Test that handles block-wise missingness. It identifies missing-data patterns, constructs a (blockwise) dissimilarity matrix, induces ranks via a k-nearest neighbor style graph, and computes a quadratic statistic under two versions: the congregated form (‘con’) and vectorized form (‘vec’). Permutation p-values are optionally available.

Usage

BRISE(
  X = NULL,
  Y = NULL,
  D = NULL,
  ptn_list = NULL,
  k = 10,
  perm = 0,
  skip = 1,
  ver = "con"
)

Value

A list with elements:

test.statistic

Numeric. The computed test statistic.

pval.approx

Numeric. Asymptotic p-value (chi-square based).

Cov

Covariance matrix used in computing the test statistic.

pval.perm

(Optional) Permutation p-value if perm > 0.

Arguments

X

Numeric matrix (m × p) of observations for X (Sample 1). Optional if D and ptn_list are provided.

Y

Numeric matrix (n × p) of observations for Y (Sample 2). Optional if D and ptn_list are provided.

D

Numeric square dissimilarity matrix (N × N), where N = m + n. Required when X and Y are not given.

ptn_list

List of integer vectors. Each element contains indices (1…N) of observations that share the same missing-data pattern.

k

Positive integer. Neighborhood size offset for rank truncation in nearest-neighbor ranking. Default is 10.

perm

Integer. Number of permutations for computing permutation p-value. Default is 0 (no permutation).

skip

Integer (0 or 1). When set to 1 (default), skip rank-based dissimilarity for modality pairs with no shared observed variables; setting to 0 computes them (slower).

ver

Character. Version of the test statistic: "con" (congregated form, default) or "vec" (vectorized form).

Details

If both X and Y are supplied, Identify_mods is used to detect missing patterns and reorganize variables by modality. The dissimilarity matrix D is then constructed via Blockdist. Patterns with too few observations in either sample (e.g. fewer than 2) or patterns that are very small relative to the largest pattern are filtered out for robustness. A symmetric rank matrix is built based on truncated nearest-neighbor ranks. Under ver="con" the contrast statistic (two degrees of freedom) is used; under ver="vec" a higher-dimensional vector statistic is used. Asymptotic p-values use chi-square approximations; if perm > 0, empirical permutation p-values are also computed.

References

Zhang, K., Liang, M., Maile, R. & Zhou, D. (2025). Two-Sample Testing with Block-wise Missingness in Multi-source Data. arXiv preprint arXiv:2508.17411.

See Also

BRISE_Rank, Cov_mu.c, Cov_mu.v

Examples

set.seed(1)
X <- matrix(rnorm(50*200, mean = 0), nrow=50)
Y <- matrix(rnorm(50*200, mean = 0.3), nrow=50)
X[1:20, 1:100] <- 0
X[30:50, 101:200] <- 0
Y[1:10, 1:100] <- 0
Y[30:40, 101:200] <- 0
out <- BRISE(X = X, Y = Y, k = 5, perm = 1000, ver = "con")
print(out$test.statistic)
print(out$pval.approx)