SpatialJackknife.jl

This package can be used to perform jackknife resampling on spatial data in an arbitrary number of dimensions with arbitrary geometry. It exports two function get_subvols, for assigning jackknife subvolumes to the data points, and jackknife for performing jackknife estimation of the mean and variance of a given estimator function. An example of how to use this code with SDSS data can be found in the notebooks directory. To run this, however, you will have to download the data separately.

get_subvols has two methods which can be used for data that is either distributed in a regular cubic volume or distributed in a more complex geometry for which you must provide a set of randomly distributed points that define the geometry:

1. Regular cubic geometry

get_subvols(data::Array{Float64, 2};
            side_divs::Int = 3,
            edges::Array{Array{Float64, 1}, 1} = Array{Array{Float64, 1}, 1}(undef, 0))

• data is a 2-dimensional array of shape (N, ndims)
• 'side_divs' is the number of volumes per dimension to divide the data into
• 'edges' can be given either as the extrema in each dimension or just once and taken as the extrema for all dimensions

2. Arbitrary geometry defined by random points

get_subvols(data::Array{Float64, 2},
            randmask::Array{Float64, 2},
            side_divs::Int,
            metric::Metric = Euclidean())::Array{Int, 1}

• data is a 2-D array as above
• randmask is a 2-D array with the same number of dimensions defining the geometry of your dataset
• side_divs is the number of volumes per dimension to subdivide the sample into
• metric is an optional parameter to define the distance between points, assumed to be Euclidean

Once the subvolumes have been determined, the 'jackknife' function can be used to find the mean and covariance of your desired estimator:

jackknife(obsfunc::Function,
          data::Array{Float64, 2},
          subvolinds::Array{Int, 1},
          args::Tuple = ();
          covar::Bool = true)

• 'obsfunc' is a function that computes your estimator and takes the form

  obsfunc(data, args...)

• 'subvolinds' is an integer array of subvolume indices that has the same length as the number of data points and is returned by 'get_subvols'
• 'args' is an optional tuple of other arguments to pass to your estimator function
• 'covar' is a boolean that determines whether a full covariance matrix is computed (for 'true') for multidimensional estimators, or just the diagonals ('false')