engineerMetric: Engineer Metric

In DataSimilarity: Quantifying Similarity of Datasets and Multivariate Two- And k-Sample Testing

Engineer Metric

Description

The function implements the L_q-engineer metric for comparing two multivariate distributions.

Usage

engineerMetric(X1, X2, type = "F", seed = 42)

Arguments

X1	First dataset as matrix or data.frame
X2	Second dataset as matrix or data.frame
type	Character specifying the type of L_q-norm to use. Reasonable options are "O", "o", "1", for the L_1-norm, "I", and "i", for the L_\infty-norm, and "F", "f", "E", "e" (the default) for the L_2-norm (Euclidean norm).
seed	Random seed (default: 42). Method is deterministic, seed is only set for consistency with other methods.

Details

The engineer is a primary propability metric that is defined as

\text{EN}(X_1, X_2; q) = \left[ \sum_{i = 1}^{p} \left| \text{E}\left(X_{1i}\right) - \text{E}\left(X_{2i}\right)\right|^q\right]^{\min(q, 1/q)} \text{ with } q> 0,

where X_{1i}, X_{2i} denote the ith component of the p-dimensional random vectors X_1\sim F_1 and X_2\sim F_2.

In the implementation, expectations are estimated by column means of the respective datasets.

Value

An object of class htest with the following components:

method	Description of the test
statistic	Observed value of the test statistic
data.name	The dataset names
method	Description of the test
alternative	The alternative hypothesis

Applicability

Target variable?	Numeric?	Categorical?	K-sample?
No	Yes	No	No

Note

The seed argument is only included for consistency with other methods. The result of the metric calculation is deteministic.

References

Rachev, S. T. (1991). Probability metrics and the stability of stochastic models. John Wiley & Sons, Chichester.

Stolte, M., Kappenberg, F., Rahnenführer, J., Bommert, A. (2024). Methods for quantifying dataset similarity: a review, taxonomy and comparison. Statist. Surv. 18, 163 - 298. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1214/24-SS149")}

See Also

Jeffreys

Examples

# Draw some data
X1 <- matrix(rnorm(1000), ncol = 10)
X2 <- matrix(rnorm(1000, mean = 0.5), ncol = 10)
# Calculate engineer metric
engineerMetric(X1, X2)

DataSimilarity documentation built on April 3, 2025, 9:39 p.m.