Censored Stein test for uniformity

Description

Performs a censored Stein-type U-statistic test for the hypothesis of uniformity on the interval \([a, b]\). When no censoring is supplied, the implementation falls back to SteinUniformGofStatistic.

Hypothesis of Uniformity The null hypothesis is that the observed sample comes from a uniform distribution on the interval \([a, b]\).

Usage

from pysatl_criterion.statistics.goodness_of_fit import (
    CensoredSteinUniformGofStatistic,
)


test_statistic = CensoredSteinUniformGofStatistic(a=0, b=1)
statistic_result = test_statistic.execute_statistic(
    [0.12, 0.25, 0.41, 0.53, 0.77, 0.91],
    censoring_indices=[0, 0, 0, 0, 0, 0],
)
print(statistic_result)

Arguments

a - left boundary of the uniform distribution. Default value is 0.

b - right boundary of the uniform distribution. Default value is 1.

rvs - array-like sample data passed to execute_statistic.

censoring_indices - binary array where 1 indicates a censored observation and 0 indicates an uncensored observation.

Details

The implementation standardizes observations to \([0, 1]\). For censored data, it estimates survival with a Kaplan-Meier-style estimator and computes a weighted pairwise Stein kernel statistic over uncensored observations.

Author(s)

Aleksandr Podmarev, Alexey Mironov

References

Stein, C. (1972): A bound for the error in the normal approximation to the distribution of a sum of dependent random variables. - Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability, vol. 2, pp. 583-602.

Examples

from pysatl_criterion.statistics.goodness_of_fit import (
    CensoredSteinUniformGofStatistic,
)


test_statistic = CensoredSteinUniformGofStatistic(a=0, b=1)
statistic_result = test_statistic.execute_statistic(
    [0.12, 0.25, 0.41, 0.53, 0.77, 0.91],
    censoring_indices=[0, 0, 0, 0, 0, 0],
)
print(statistic_result)