pmm2_algorithm

Universal PMM2 algorithm for all model types

internal

Implements the Polynomial Maximization Method ('PMM') for parameter estimation
in linear and time series models when error distributions deviate from normality.
The 'PMM2' variant achieves lower variance parameter estimates compared to ordinary
least squares ('OLS') when errors exhibit significant skewness. Includes methods
for linear regression, 'AR'/'MA'/'ARMA'/'ARIMA' models, and bootstrap inference.
Methodology described in Zabolotnii, Warsza, and Tkachenko (2018) <doi:10.1007/978-3-319-77179-3_75>,
Zabolotnii, Tkachenko, and Warsza (2022) <doi:10.1007/978-3-031-03502-9_37>, and
Zabolotnii, Tkachenko, and Warsza (2023) <doi:10.1007/978-3-031-25844-2_21>.

Serhii Zabolotnii

EstemPMM

Polynomial Maximization Method for Non-Gaussian Regression

pmm2_algorithm function

<dl><dt>b_init</dt>
<dd>Initial parameter estimates</dd>
<dt>X</dt>
<dd>Design matrix</dd>
<dt>y</dt>
<dd>Response vector</dd>
<dt>m2, m3, m4</dt>
<dd>Central moments</dd>
<dt>max_iter</dt>
<dd>Maximum number of iterations</dd>
<dt>tol</dt>
<dd>Tolerance for convergence</dd>
<dt>regularize</dt>
<dd>Whether to add regularization</dd>
<dt>reg_lambda</dt>
<dd>Regularization parameter</dd>
<dt>verbose</dt>
<dd>Whether to print progress information</dd>
<dt>poly_terms</dt>
<dd>Pre-computed polynomial coefficients (list with elements <code>A</code>, <code>B</code>, <code>C</code>);
allows passing custom values for special scenarios, otherwise they are computed from moments</dd></dl>

Arguments

Universal PMM2 algorithm for all model types — pmm2_algorithm

<dl>

<dt>b_init</dt>
<dd>Initial parameter estimates</dd>


<dt>X</dt>
<dd>Design matrix</dd>


<dt>y</dt>
<dd>Response vector</dd>


<dt>m2, m3, m4</dt>
<dd>Central moments</dd>


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


<dt>tol</dt>
<dd>Tolerance for convergence</dd>


<dt>regularize</dt>
<dd>Whether to add regularization</dd>


<dt>reg_lambda</dt>
<dd>Regularization parameter</dd>


<dt>verbose</dt>
<dd>Whether to print progress information</dd>


<dt>poly_terms</dt>
<dd>Pre-computed polynomial coefficients (list with elements <code>A</code>, <code>B</code>, <code>C</code>);
allows passing custom values for special scenarios, otherwise they are computed from moments</dd>

</dl>

pmm2_algorithm: Universal PMM2 algorithm for all model types

Description

Usage

Value

Arguments