binaryQuantileSearch

Computes the pth quantile of a cumulative distribution function using a
simple binary serach algorithm. This can be extremely slow but has the
benefit of being trivial to implement.

Computes the t* statistic corresponding to the tau* population
coefficient introduced by Bergsma and Dassios (2014) <DOI:10.3150/13-BEJ514>
and does so in O(n^2) time following the algorithm of Heller and
Heller (2016) <DOI:10.48550/arXiv.1605.08732> building off of the work of Weihs,
Drton, and Leung (2016) <DOI:10.1007/s00180-015-0639-x>. Also allows for
independence testing using the asymptotic distribution of t* as described by
Nandy, Weihs, and Drton (2016) <DOI:10.1214/16-EJS1166>.

Julian Karch

TauStar

Efficient Computation and Testing of the Bergsma-Dassios Sign
Covariance

Luca Weihs

Emin Martinian

binaryQuantileSearch function

<dl><dt>pDistFunc</dt>
<dd>a cumulative distribution function on the real numbers, it
should take a single argument x and return the cumualtive distribution
function evaluated at x.</dd>
<dt>p</dt>
<dd>the quantile \(p\in[0,1]\)</dd>
<dt>lastLeft</dt>
<dd>binary search works by continuously decreasing the search
space from the left and right. lastLeft should be a lower bound for
the quantile p.</dd>
<dt>lastRight</dt>
<dd>similar to lastRight but should be an upper bound.</dd>
<dt>error</dt>
<dd>the error tolerated from the binary search</dd></dl>

Arguments

Quantiles of a distribution. — binaryQuantileSearch

<dl>

<dt>pDistFunc</dt>
<dd>a cumulative distribution function on the real numbers, it
should take a single argument x and return the cumualtive distribution
function evaluated at x.</dd>


<dt>p</dt>
<dd>the quantile \(p\in[0,1]\)</dd>


<dt>lastLeft</dt>
<dd>binary search works by continuously decreasing the search
space from the left and right. lastLeft should be a lower bound for
the quantile p.</dd>


<dt>lastRight</dt>
<dd>similar to lastRight but should be an upper bound.</dd>


<dt>error</dt>
<dd>the error tolerated from the binary search</dd>

</dl>

binaryQuantileSearch: Quantiles of a distribution.

Description

Usage

Value

Arguments