6.5.1. statsmodels.sandbox.nonparametric.densityorthopoly

density estimation based on orthogonal polynomials

Author: Josef Perktold Created: 2011-05017 License: BSD

2 versions work: based on Fourier, FPoly, and chebychev T, ChebyTPoly also hermite polynomials, HPoly, works other versions need normalization

TODO:

  • check fourier case again: base is orthonormal, but needs offsetfact = 0 and doesn’t integrate to 1, rescaled looks good

  • hermite: works but DensityOrthoPoly requires currently finite bounds I use it with offsettfactor 0.5 in example

  • not implemented methods: - add bonafide density correction - add transformation to domain of polynomial base - DONE

    possible problem: what is the behavior at the boundary, offsetfact requires more work, check different cases, add as option moved to polynomial class by default, as attribute

  • convert examples to test cases

  • need examples with large density on boundary, beta ?

  • organize poly classes in separate module, check new numpy.polynomials, polyvander

  • MISE measures, order selection, ...

enhancements:
  • other polynomial bases: especially for open and half open support
  • wavelets
  • local or piecewise approximations

6.5.1.1. Functions

density_orthopoly(x, polybase[, order, xeval])
inner_cont(polys, lower, upper[, weight]) inner product of continuous function (with weight=1)
is_orthonormal_cont(polys, lower, upper[, ...]) check whether functions are orthonormal
polyvander(x, polybase[, order])

6.5.1.2. Classes

ChebyTPoly(order) Orthonormal (for weight=1) Chebychev Polynomial on (-1,1)
DensityOrthoPoly([polybase, order]) Univariate density estimation by orthonormal series expansion
F2Poly(order) Orthogonal (for weight=1) Fourier Polynomial on [0,pi]
FPoly(order) Orthonormal (for weight=1) Fourier Polynomial on [0,1]
HPoly(order) Orthonormal (for weight=1) Hermite Polynomial, uses finite bounds