dualbounds.bootstrap.multiplier_bootstrap

dualbounds.bootstrap.multiplier_bootstrap(samples: array, alpha: float, B: int = 1000, maxarrsize: int = 10000000000, param: str = 'max', verbose: int = False)[source]

Computes multiplier bootstrap lower confidence bounds.

Precisely, computes a lower confidence bound on \(\max(\mu_1, \dots, \mu_d)\), where \(\mu_i\) is the mean of samples[i].

Parameters:
samples : np.array

(n,d)-shaped array where samples[i] is i.i.d. with mean \(\mu_i\).

alpha : float

Nominal error control level.

B : int

Number of bootstrap replications

maxarrsize : float

Maximum size of an array; used to save memory.

param : str

  • If param=’max’, computes a lower confidence bound on \(\max(\mu_1, \dots, \mu_d)\).

  • Else, computes an upper confidence bound on \(\min(\mu_1, \dots, \mu_d)\),

verbose : bool

If True, shows a progress bar. Only useful if samples is a very large matrix.

Returns:

  • estimate (float) – Estimate of \(\max(\mu_1, \dots, \mu_d)\).

  • ci (float) – Lower confidence bound on \(\max(\mu_1, \dots, \mu_d)\).