Bootstrap methods and confidence intervals
Bootstrap methods and confidence intervals
(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:
: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 jackknifefastmath.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 samplesModel can be:
When model is ommited, function creates discrete distribution. When multidimensional data are provided, models should be created for every dimension (as a sequence).
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 {:keys [data samples] :as input} statistic)
Calculate bootstrap analysis.
Arguments:
:data
and :samples
statistic
- bootstrap statisticReturns 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 tsCalculate 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 boot-data)
(ci-basic boot-data alpha)
(ci-basic {:keys [t0 ts]} alpha estimation-strategy)
Basic percentile confidence interval
:t0
and :ts
are obligatory
Basic percentile confidence interval `:t0` and `:ts` are obligatory
(ci-bc boot-data)
(ci-bc boot-data alpha)
(ci-bc {:keys [t0 ts]} alpha estimation-strategy)
Bias-corrected confidence interval
Bias-corrected confidence interval
(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:
:data
and :statistic
)ts
otherwiseBias-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 boot-data)
(ci-normal {:keys [t0 ts stddev bias]} alpha)
Normal (gaussian) bias-corrected confidence interval
:t0
and :ts
are obligatory
Normal (gaussian) bias-corrected confidence interval `:t0` and `:ts` are obligatory
(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
Percentile confidence interval `:t0` and `:ts` are obligatory
(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
Confidence interval from studentized data. `:t0`, `:ts`, `:data` and `:samples` are obligatory in `boot-data`
(ci-t boot-data)
(ci-t {:keys [t0 ts stddev]} alpha)
Student's T confidence interval.
:t0
and :ts
are obligatory
Student's T confidence interval. `:t0` and `:ts` are obligatory
(jackknife vs)
Generates set of samples using jackknife leave-one-out method
Generates set of samples using jackknife leave-one-out method
(jackknife+ vs)
Generates set of samples using jackknife positive method
Generates set of samples using jackknife positive method
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