Skip to contents

Theorem 4.4: asymptotic normality of the boundary-free MRL estimators

Source: R/fauzi_native.R
morie_fauzi_theorem_4_4.Rd

The standardised estimators are asymptotically N(0, 1), and the statement holds AT the boundary as well as inside. The Lyapunov condition needs no extra assumption because V is bounded in [0, 1], so every moment exists automatically.

Usage

morie_fauzi_theorem_4_4(mrl_hat, mrl_true, variance)

Arguments

mrl_hat

estimated mean residual life.

mrl_true

the value under the null.

variance

the Theorem 4.3 variance.

Value

list: z, p_two_sided, holds_for, why_lyapunov_works, valid_at_boundary, method.

References

Fauzi and Maesono (2023), Theorem 4.4.

Examples

morie_fauzi_theorem_4_4(1.2, 1, 0.01)$z
#> [1] 2