Kde1d

class Kde1d(*args, **kwargs)

A class for univariate kernel density estimation.

The Kde1d class provides methods for univariate kernel density estimation using local polynomial fitting. It can handle data with bounded, unbounded, and discrete support.

The estimator uses a Gaussian kernel in all cases. A log-transform is used if there is only one boundary; a probit transform is used if there are two boundaries. Discrete variables are handled via jittering.

Zero-inflated densities are estimated by a hurdle-model with discrete mass at 0 and the remainder estimated as for continuous data.

Examples

>>> import numpy as np
>>> import pyvinecopulib as pv
>>>
>>> # Unbounded data
>>> x = np.random.normal(0, 1, 500)
>>> fit = pv.Kde1d()
>>> fit.fit(x)
>>> pdf_vals = fit.pdf(np.array([0.0]))
>>> fit.plot(x)
>>>
>>> # Bounded data
>>> x = np.random.gamma(1, size=500)
>>> fit = pv.Kde1d(xmin=0.0, degree=1)
>>> fit.fit(x)
>>> fit.plot(x)
>>>
>>> # Discrete data
>>> x = np.random.binomial(5, 0.5, 500)
>>> fit = pv.Kde1d(xmin=0, xmax=5, type="discrete")
>>> fit.fit(x)
>>> fit.plot(x)

References

Geenens, G. (2014). Probit transformation for kernel density estimation on the unit interval. Journal of the American Statistical Association, 109(505), 346–358. [arXiv:1303.4121](https://arxiv.org/abs/1303.4121)

Geenens, G., & Wang, C. (2018). Local-likelihood transformation kernel density estimation for positive random variables. Journal of Computational and Graphical Statistics, 27(4), 822–835. [arXiv:1602.04862](https://arxiv.org/abs/1602.04862)

Loader, C. (2006). Local Regression and Likelihood. Springer Science & Business Media.

Nagler, T. (2018a). A generic approach to nonparametric function estimation with mixed data. Statistics & Probability Letters, 137, 326–330. [arXiv:1704.07457](https://arxiv.org/abs/1704.07457)

Nagler, T. (2018b). Asymptotic analysis of the jittering kernel density estimator. Mathematical Methods of Statistics, 27, 32–46. [arXiv:1705.05431](https://arxiv.org/abs/1705.05431)

Attributes

`bandwidth`	Bandwidth parameter.
`degree`	Degree of the local polynomial.
`edf`	Effective degrees of freedom.
`grid_points`	Grid points used for interpolation.
`grid_size`	Number of grid points for interpolation.
`loglik`	Log-likelihood of the fitted model.
`multiplier`	Bandwidth multiplier.
`prob0`	Point mass at 0 (for zero-inflated models).
`type`	Variable type as VarType enum.
`values`	Density values at grid points.
`xmax`	Upper bound of the density support.
`xmin`	Lower bound of the density support.

Methods

`__init__`	Constructor for the `Kde1d` class.
`cdf`	Evaluate the cumulative distribution function.
`fit`	Fit the kernel density estimate to data.
`from_grid`	Create a Kde1d object from grid points and density values.
`from_params`	Create a Kde1d object from parameters.
`pdf`	Evaluate the probability density function.
`plot`	Generates a plot for the Kde1d object.
`quantile`	Evaluate the quantile function.
`set_xmin_xmax`	Set the boundary parameters.
`simulate`	Simulate data from the fitted density.