cmp::statistics::Bootstrap Class Reference

Bootstrap resampling index generator. More...

#include <statistics.h>

Public Member Functions
	Bootstrap (size_t n_obs, size_t n_obs_resample, bool with_replacement=true, unsigned int random_state=42)
	Constructor for the Bootstrap resampler.
Eigen::VectorXs	operator() ()
	Executes the bootstrap sampling process.

Private Attributes
size_t	nObs_
	Original number of observations \( N \).
size_t	nObsResample_
	Target number of observations to resample \( M \).
unsigned int	rngState_
	Seed for the random number generator.
std::default_random_engine	rng_
	Random number engine.
std::uniform_int_distribution< size_t >	dist_
	Uniform integer distribution for sampling with replacement.
Eigen::VectorXs	indices_
	Internal array storing the base indices for sampling.
bool	withReplacement_
	Flag indicating whether to sample with replacement.

Detailed Description

Bootstrap resampling index generator.

Mathematical Formulation

Draws a random sample \(\mathcal{D}^*\) of size \(M\) from a dataset \(\mathcal{D}\) of size \(N\).

• If with replacement:

  \[ P(x_i^* = x_j) = \frac{1}{N} \quad \forall i \in \{1,\dots,M\}, \ j \in \{1,\dots,N\} \]

• If without replacement:

  \[ P(x_i^* = x_j) = \frac{1}{N - i + 1} \]

  subject to all selections being distinct.
• ### Implementation Algorithm

1. If withReplacement_ is true, generates \(M\) random integers uniformly distributed in the range \([0, N-1]\).
2. If false, shuffles the index array using std::shuffle and extracts the first \(M\) elements.

Constructor & Destructor Documentation

Bootstrap()

cmp::statistics::Bootstrap::Bootstrap ( size_t  n_obs, size_t  n_obs_resample, bool  with_replacement = true, unsigned int  random_state = 42  )

inline

Constructor for the Bootstrap resampler.

Parameters

n_obs	Total number of original observations \( N \).
n_obs_resample	Number of samples to draw \( M \).
with_replacement	Boolean flag indicating whether duplicates are allowed.
random_state	Seed for the random number generator.

Exceptions

std::invalid_argument

if invalid sizes are provided.

Member Function Documentation

operator()()

Eigen::VectorXs cmp::statistics::Bootstrap::operator() ( )

inline

Executes the bootstrap sampling process.

Returns

A vector containing the \( M \) randomly sampled indices.

Member Data Documentation

dist_

std::uniform_int_distribution<size_t> cmp::statistics::Bootstrap::dist_

private

Uniform integer distribution for sampling with replacement.

indices_

Eigen::VectorXs cmp::statistics::Bootstrap::indices_

private

Internal array storing the base indices for sampling.

nObs_

size_t cmp::statistics::Bootstrap::nObs_

private

Original number of observations \( N \).

nObsResample_

size_t cmp::statistics::Bootstrap::nObsResample_

private

Target number of observations to resample \( M \).

rng_

std::default_random_engine cmp::statistics::Bootstrap::rng_

private

Random number engine.

rngState_

unsigned int cmp::statistics::Bootstrap::rngState_

private

Seed for the random number generator.

withReplacement_

bool cmp::statistics::Bootstrap::withReplacement_

private

Flag indicating whether to sample with replacement.

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The documentation for this class was generated from the following file:

• include/statistics.h