hell.ci: Confidence interval for Hellinger distance estimators

In nilanjanalaha/SDNNtests: SHAPE CONSTRAINED TESTS OF STOCHASTIC DOMINANCE

Description

Calculates the confidence interval of the squared Hellinger distance, as discussed in Laha et al. (2021). This function employs shape constrained methods to estimate the underlying densities. See below for more details. which include the log-concave density estimator of Dumbgen and Rufibatch (2009), and the smoothed log-concave density estimator given by ,

Usage

hell.ci(x, y, alpha = 0.05)

Arguments

x	Vector of m independent and identically distributed random variables; corresponds to the first sample.
y	Vector of n independent and identically distributed random variables; corresponds to the second sample.
alpha	Level of significance; returns a 1-α\% confidence interval.

Details

The confidence intervals follow the construnction of Laha et al. (2021). One confidence interval is based on the unimodal density estimator of Birges (1997), and provably requires the underlying densities to be unimodal to work. The other confidence intervals are based on the log-concave density estimators, i.e. the log-concave MLE of Dumbgen and Rufibatch (2009), and the smoothed log-concave MLE of Chen and Samworth (2013) . Both are computed using the function logConDens of logcondens package.

Value

• lc.ci - Confidence intervals based on the log-concave MLE.

• sm.lc.ci - Confidence intervals based on the smoothed log-concave MLE.

• um.ci - Confidence intervals based on unimodal density estimator.

Author(s)

Nilanjana Laha (maintainer), [e-mail],

Alex Luedtke, [e-mail].

References

Laha, N., Moodie, Z., Huang, Y., and Luedtke (2020), A. Improved inference for vaccine-induced immune responses via shape-constrained methods. Submitted.

Dumbgen, L. and Rufibatch, K. (2009). Maximum likelihood estimation of a logconcave density and its distribution function: Basic properties and uniform consistency, Bernoulli, 15, 40–68.

Chen, Y. and Samworth, R. J. (2013). Smoothed log-concave maximum likelihood estimation with applications, Statistica Sinica, 23, 1303-1398.

Birge, L. (1997). Estimation of unimodal densities without smoothness assumptions, Ann. Statist., 25, 970–981.

See Also

hd.uni, hd.lc.sm, hd.uni

Examples

x <- sort(rnorm(100)); y <- sort(rgamma(50, shape=1));
hell.ci(x,y)$lc.ci

nilanjanalaha/SDNNtests documentation built on June 15, 2021, 8:20 p.m.