Class Jackknife
This class applies the jackknife method (see, e.g., “A leisurely look at the bootstrap, the jackknife, and cross-validation”, by Bradley Efron and Gail Gong,
The American Statistician, 37(1):36−48, 1983) to reduce the bias in the estimation of a nonlinear
statistic of interest (linear statistics, such as the mean, pass through the jackknife without change).
The statistic must take a sample (an array of big decimals) and return
corresponding values (again as an array of big decimals). In case high-precision
arithmetic is not required, an instance of Jackknife.AbstractStatistic
just takes an array of doubles and returns an
array of doubles, handling all necessary type conversions.
The static method compute(List, Statistic, MathContext)
takes a list
of samples (arrays of doubles of the same length) and returns an instance of this class containing
estimates and standard errors for every
value computed by the statistic (estimates of the statistic are available both as
an array of big decimals and as an array of doubles,
whereas estimates of standard errors are provided in double format, only).
All computations are performed internally using BigDecimal
and a provided MathContext
.
The method compute(List, Statistic)
uses 100 decimal digits.
The identical statistic can be used to compute the (pointwise) empirical mean and standard error of a sample.
- Author:
- Sebastiano Vigna
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Nested Class Summary
Modifier and TypeClassDescriptionstatic class
An abstract statistic with a template method that accepts an array of doubles, returns an array of doubles and handles the data conversions that are necessary to callJackknife.Statistic.compute(BigDecimal[], MathContext)
.static interface
A statistic to be estimated using the jackknife on a set of samples. -
Field Summary
Modifier and TypeFieldDescriptionfinal BigDecimal[]
A vector of high-precision estimates for a statistic of interest.static final MathContext
final double[]
A vector of estimates for a statistic of interest (obtained by invokingBigDecimal.doubleValue()
onbigEstimate
).static Jackknife.Statistic
A statistic that returns the sample.final double[]
A vector of (estimates of the) standard error parallel tobigEstimate
/estimate
. -
Method Summary
Modifier and TypeMethodDescriptionstatic double[]
bigDecimalArray2DoubleArray
(BigDecimal[] input) static Jackknife
compute
(List<double[]> samples, Jackknife.Statistic f) Applies the jackknife to a statistic of interest using a list of samples usingDEFAULT_MATH_CONTEXT
as context.static Jackknife
compute
(List<double[]> samples, Jackknife.Statistic f, MathContext mc) Applies the jackknife to a statistic of interest using a list of samples.static BigDecimal[]
doubleArray2BigDecimalArray
(double[] input) toString()
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Field Details
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DEFAULT_MATH_CONTEXT
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bigEstimate
A vector of high-precision estimates for a statistic of interest. -
estimate
public final double[] estimateA vector of estimates for a statistic of interest (obtained by invokingBigDecimal.doubleValue()
onbigEstimate
). -
standardError
public final double[] standardErrorA vector of (estimates of the) standard error parallel tobigEstimate
/estimate
. -
IDENTITY
A statistic that returns the sample. Useful to compute the average and the empirical standard error.
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Method Details
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bigDecimalArray2DoubleArray
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doubleArray2BigDecimalArray
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toString
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compute
Applies the jackknife to a statistic of interest using a list of samples usingDEFAULT_MATH_CONTEXT
as context.- Parameters:
samples
- a list of samples (arrays of doubles of the same length).f
- a statistic of interest.- Returns:
- an instance of this class containing estimates of
f
and corresponding standard errors obtained by the jackknife on the given set of samples.
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compute
Applies the jackknife to a statistic of interest using a list of samples.- Parameters:
samples
- a list of samples (arrays of doubles of the same length).f
- a statistic of interest.mc
- the mathematical context to be used when dividing big decimals.- Returns:
- an instance of this class containing estimates of
f
and corresponding standard errors obtained by the jackknife on the given set of samples.
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