fastmath.stats.bootstrap — generateme/fastmath 2.2.1

Bootstrap methods and confidence intervals

bootstrap clj

(bootstrap input)

(bootstrap input statistic)

(bootstrap input
           statistic
           {:keys [rng samples size method antithetic? smoothing dimensions
                   include?]
            :or {samples 500}
            :as params})

Create set of samples from given data (nonparametric) or model (parametric).

Input:

• sequence of values (any type) or sequence of sequences for multidimensional data
• a map containing:
  • :data - sequence
  • :model - model for parametric bootstrap (optional)
• statistic function which returns statistic value (optional)

Parameters:

• :samples - number of bootstrapped samples (default: 500)
• :size - forced size of individual sample (default: same as source)
• :method
  • nil (default) - random
  • :jackknife for leave-one-out jackknife
  • :jackknife+ for positive jackknife
  • any method accepted by fastmath.random/->seq
• :rng - random number generator (see: fastmath.random/rng)
• :smoothing - smoothing bootstrap:
  • :kde - kernel density estimation, additional options are: :kernel (default) and :bandwidth (auto)
  • :gaussian - add random value from N(0,standard error)
• :distribution - distribution used to auto generate model (distribution) from data:
  • :real-discrete-distribution - default
  • :integer-discrete-distribution - for integer values
  • :categorical-distribution - for any other type
• :dimensions - if set to :multi - multidimensional data and models are created
• :antithetic? - antithetic sampling (default: false)
• :include? - if set to true (default: false) original dataset is included in samples

Model can be:

• any distribution object
• any 0-arity function which returns random sample

When model is ommited, function creates discrete distribution. When multidimensional data are provided, models should be created for every dimension (as a sequence).

bootstrap-stats clj

(bootstrap-stats {:keys [data samples] :as input} statistic)

Calculate bootstrap analysis.

Arguments:

• a map containing :data and :samples
• statistic - bootstrap statistic

Returns a map containing:

• :data, :samples, model and :statistic - from input
• :t0 - statistic from data (single value)
• :ts - statistic from bootstrap samples (sequence)
• :bias - difference between mean of ts and t0
• :mean, :median, :variance, :stddev, :sem - statistics from ts

ci-basic clj

(ci-basic boot-data)

(ci-basic boot-data alpha)

(ci-basic {:keys [t0 ts]} alpha estimation-strategy)

Basic percentile confidence interval

:t0 and :ts are obligatory

ci-bc clj

(ci-bc boot-data)

(ci-bc boot-data alpha)

(ci-bc {:keys [t0 ts]} alpha estimation-strategy)

Bias-corrected confidence interval

ci-bca clj

(ci-bca boot-data)

(ci-bca boot-data alpha)

(ci-bca {:keys [t0 ts data statistic]} alpha estimation-strategy)

Bias-corrected and accelerated confidence interval.

There are two ways to calculate acceleration:

• jackknife method (when boot-data contains :data and :statistic)
• empirical from bootstrap estimations ts otherwise

ci-normal clj

(ci-normal boot-data)

(ci-normal {:keys [t0 ts stddev bias]} alpha)

Normal (gaussian) bias-corrected confidence interval

:t0 and :ts are obligatory

ci-percentile clj

(ci-percentile boot-data)

(ci-percentile boot-data alpha)

(ci-percentile {:keys [t0 ts]} alpha estimation-strategy)

Percentile confidence interval

:t0 and :ts are obligatory

ci-studentized clj

(ci-studentized boot-data)

(ci-studentized boot-data alpha)

(ci-studentized {:keys [t0 ts data samples]} alpha estimation-strategy)

Confidence interval from studentized data.

:t0, :ts, :data and :samples are obligatory in boot-data

ci-t clj

(ci-t boot-data)

(ci-t {:keys [t0 ts stddev]} alpha)

Student's T confidence interval.

:t0 and :ts are obligatory

jackknife clj

(jackknife vs)

Generates set of samples using jackknife leave-one-out method

jackknife+ clj

(jackknife+ vs)

Generates set of samples using jackknife positive method