Class Jackknife


  • public class Jackknife
    extends java.lang.Object
    Applies the jackknife to generic statistics.

    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
    • Field Detail

      • DEFAULT_MATH_CONTEXT

        public static final java.math.MathContext DEFAULT_MATH_CONTEXT
        The default MathContext used by compute(List, Statistic): 100 digits and RoundingMode.HALF_EVEN.
      • bigEstimate

        public final java.math.BigDecimal[] bigEstimate
        A vector of high-precision estimates for a statistic of interest.
      • estimate

        public final double[] estimate
        A vector of estimates for a statistic of interest (obtained by invoking BigDecimal.doubleValue() on bigEstimate).
      • standardError

        public final double[] standardError
        A vector of (estimates of the) standard error parallel to bigEstimate/estimate.
      • IDENTITY

        public static Jackknife.Statistic IDENTITY
        A statistic that returns the sample. Useful to compute the average and the empirical standard error.
    • Method Detail

      • bigDecimalArray2DoubleArray

        public static double[] bigDecimalArray2DoubleArray​(java.math.BigDecimal[] input)
      • doubleArray2BigDecimalArray

        public static java.math.BigDecimal[] doubleArray2BigDecimalArray​(double[] input)
      • toString

        public java.lang.String toString()
        Overrides:
        toString in class java.lang.Object
      • compute

        public static Jackknife compute​(java.util.List<double[]> samples,
                                        Jackknife.Statistic f)
        Applies the jackknife to a statistic of interest using a list of samples using DEFAULT_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.
      • compute

        public static Jackknife compute​(java.util.List<double[]> samples,
                                        Jackknife.Statistic f,
                                        java.math.MathContext mc)
        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.