hermite_int_lower

The method calculates \(\int_{-\infty}^{x} h_k(t) dt\) 
for \(k=0,\dots,N\) and the vector of values x.

Facilitates estimation of full univariate and bivariate
probability density functions and cumulative distribution functions along with
full quantile functions (univariate) and nonparametric correlation
(bivariate) using Hermite series based estimators. These estimators are
particularly useful in the sequential setting (both stationary and
non-stationary) and one-pass batch estimation setting for large data sets.
Based on: Stephanou, Michael, Varughese, Melvin and Macdonald, Iain. "Sequential quantiles via Hermite series density estimation." Electronic Journal of Statistics 11.1 (2017): 570-607 <doi:10.1214/17-EJS1245>,
Stephanou, Michael and Varughese, Melvin. "On the properties of Hermite series based distribution function estimators." Metrika (2020) <doi:10.1007/s00184-020-00785-z> and Stephanou, Michael and Varughese, Melvin. "Sequential estimation of Spearman rank correlation using Hermite series estimators." Journal of Multivariate Analysis (2021) <doi:10.1016/j.jmva.2021.104783>.

Michael Stephanou

hermiter

Efficient Sequential and Batch Estimation of Univariate and
Bivariate Probability Density Functions and Cumulative
Distribution Functions along with Quantiles (Univariate) and
Nonparametric Correlation (Bivariate)

Melvin Varughese

hermite_int_lower function

<dl><dt>N</dt>
<dd>An integer number.</dd>
<dt>x</dt>
<dd>A numeric vector.</dd>
<dt>hermite_function_matrix</dt>
<dd>A numeric matrix. A matrix of Hermite 
function values.</dd></dl>

Arguments

Convenience function to output a definite integral of the orthonormal 
Hermite functions — hermite_int_lower

<dl>

<dt>N</dt>
<dd>An integer number.</dd>


<dt>x</dt>
<dd>A numeric vector.</dd>


<dt>hermite_function_matrix</dt>
<dd>A numeric matrix. A matrix of Hermite 
function values.</dd>

</dl>

hermite_int_lower: Convenience function to output a definite integral of the orthonormal Hermite functions

Description

Usage

Value

Arguments