SGLR_CI_additive: GLR-like, Stitching and Discrete Mixture CS for additive...

In shinjaehyeok/SGLRT_paper: Sequential Generalized Likelihood Ratio Test for sub-psi Family Distributions

Description

SGLR_CI_additive is used to compute R functions which compute bounds of GLR-like, stitching and discrete mixture confidence sequences for additive sub-psi class designed to a finite target time interval.

Usage

SGLR_CI_additive(
  alpha,
  nmax = NULL,
  nmin = 1L,
  d = NULL,
  m_upper = 1000L,
  psi_star_inv = function(x) {     sqrt(2 * x) },
  psi_star_derv = function(x) {     x },
  n_0 = 1L
)

Arguments

alpha	An upper bound on the boundary crossing probability (positive numeric in [1e-16,0.5]).
nmax	Upper bound of the target time interval. If both nmax and d are provided, nmax will be ignored. (default = NULL)
nmin	Lower bound of the target time interval. (default = 1L)
d	Bregman divergence between the null and alternative spaces. Either d or nmax must be specified (default = NULL).
m_upper	Upper bound on the grid-search for m (default = 1e+3L).
psi_star_inv	R function of ψ_{+}^{*-1} (Default: √{2x}) .
psi_star_derv	R function of \nablaψ^* (Default: x).
n_0	Lower bound of the sample size on which test statistics and CI will be computed (default = 1L).

Value

A list of R functions for GLR-like, stitching and discrete mixture bound which takes the sample size n as the input and return the distance from the sample mean to the upper bound of confidence interval at n. The list also contains related quantities to compute these bounds. See ADD_CITE for detailed explanations of these quantities.

GLR_like_fn

R function for the GLR-like bound.

stitch_fn

R function for the stitching bound.

dis_mix_fn

R function for the discrete mixture bound.

log_mtg_fn

R function for the log of the underlying log super-martingale.

g

The constant bouandry value.

eta

The eta value used to construct underlying martingales

K

The number of LR-like martingales used to construct bounds for n ≥q n_{\min} part.

Examples

SGLR_CI_additive(0.025, 1e+5)
SGLR_CI_additive(0.025, 1e+6, 1e+2)

shinjaehyeok/SGLRT_paper documentation built on Oct. 25, 2020, 8:11 a.m.