itp_root

This finds the value \(x \in [a, b]\) such that \(f(x) = 0\) using the one-dimensional root finding ITP method (Interpolate Truncate Project). Also see itp.

We consider the problem where we observe k vectors (possibly of different lengths), each representing an independent multinomial random vector. For a given function that takes in the concatenated vector of multinomial probabilities and outputs a real number, this is a Monte Carlo estimation procedure of an exact p-value and confidence interval. The resulting inference is valid even in small samples, when the parameter is on the boundary, and when the function is not differentiable at the parameter value, all situations where asymptotic methods and the bootstrap would fail. For more details see Sachs, Fay, and Gabriel (2025) <doi:10.48550/arXiv.2406.19141>.

Michael Sachs

xactonomial

Inference for Functions of Multinomial Parameters

Michael C Sachs

Michael P Fay

Erin E Gabriel

David B Dahl

itp_root function

<dl><dt>f</dt>
<dd>The function to find the root of in terms of its first (one-dimensional) argument</dd>
<dt>a</dt>
<dd>The lower limit</dd>
<dt>b</dt>
<dd>The upper limit</dd>
<dt>k1</dt>
<dd>A tuning parameter</dd>
<dt>k2</dt>
<dd>Another tuning parameter</dd>
<dt>n0</dt>
<dd>Another tuning parameter</dd>
<dt>eps</dt>
<dd>Convergence tolerance</dd>
<dt>maxiter</dt>
<dd>Maximum number of iterations</dd>
<dt>fa</dt>
<dd>The value of f(a), if NULL then will be calculated</dd>
<dt>fb</dt>
<dd>The value of f(b), if NULL then will be calculated</dd>
<dt>verbose</dt>
<dd>Prints out information during iteration</dd>
<dt>...</dt>
<dd>Other arguments passed on to f</dd></dl>

Arguments

Find a univariate root of the function f — itp_root

<dl>

<dt>f</dt>
<dd>The function to find the root of in terms of its first (one-dimensional) argument</dd>


<dt>a</dt>
<dd>The lower limit</dd>


<dt>b</dt>
<dd>The upper limit</dd>


<dt>k1</dt>
<dd>A tuning parameter</dd>


<dt>k2</dt>
<dd>Another tuning parameter</dd>


<dt>n0</dt>
<dd>Another tuning parameter</dd>


<dt>eps</dt>
<dd>Convergence tolerance</dd>


<dt>maxiter</dt>
<dd>Maximum number of iterations</dd>


<dt>fa</dt>
<dd>The value of f(a), if NULL then will be calculated</dd>


<dt>fb</dt>
<dd>The value of f(b), if NULL then will be calculated</dd>


<dt>verbose</dt>
<dd>Prints out information during iteration</dd>


<dt>...</dt>
<dd>Other arguments passed on to f</dd>

</dl>

itp_root: Find a univariate root of the function f

Description

Usage

Value

Arguments

References

Examples