• Corpus ID: 235421665

Statistical Analysis from the Fourier Integral Theorem

@article{Ho2021StatisticalAF,
  title={Statistical Analysis from the Fourier Integral Theorem},
  author={Nhat Ho and Stephen G. Walker},
  journal={ArXiv},
  year={2021},
  volume={abs/2106.06608}
}
Taking the Fourier integral theorem as our starting point, in this paper we focus on natural Monte Carlo and fully nonparametric estimators of multivariate distributions and conditional distribution functions. We do this without the need for any estimated covariance matrix or dependence structure between variables. These aspects arise immediately from the integral theorem. Being able to model multivariate data sets using conditional distribution functions we can study a number of problems, such… 

References

SHOWING 1-10 OF 24 REFERENCES

Multivariate Smoothing via the Fourier Integral Theorem and Fourier Kernel

Starting with the Fourier integral theorem, we present natural Monte Carlo estimators of multivariate functions including densities, mixing densities, transition densities, regression functions, and

On kernel estimation of a multivariate distribution function

Methods for estimating a conditional distribution function

Motivated by the problem of setting prediction intervals in time series analysis, we suggest two new methods for conditional distribution estimation. The first method is based on locally fitting a

Nonparametric estimation of copula functions for dependence modelling

TLDR
A kernel estimator of the copula that is mean square consistent everywhere on the support is proposed and a smoothing bandwidth selection rule is proposed based on the derived bias and variance of this estimator.

Error analysis for general multtvariate kernel estimators

Kernel estimators for d dimensional data are usually parametrized by either a single smoothing parameter, or d smoothing parameters corresponding to each of the coordinate directions. A

Transformation-Kernel Estimation of the Copula Density

TLDR
This work proposes an improved transformationkernel estimator that employs a smooth directional tapering device to counter the undesirable influence of the multiplier, and establishes the theoretical properties of the new estimator, its asymptotic dominance over the naive transformation-kernel estimators, and automatic higher order improvement under Gaussian copulas.

Comparison of Smoothing Parameterizations in Bivariate Kernel Density Estimation

Abstract The basic kernel density estimator in one dimension has a single smoothing parameter, usually referred to as the bandwidth. For higher dimensions, however, there are several options for

Probit Transformation for Nonparametric Kernel Estimation of the Copula Density

TLDR
It is shown that the kernel-type copula density estimator is very good and easy to implement estimators, fixing boundary issues in a natural way and able to cope with unbounded copula densities, if combined with local likelihooddensity estimation methods.

Nonparametric Quantile Regression

In regression, the desired estimate of y|x is not always given by a conditional mean, although this is most common. Sometimes one wants to obtain a good estimate that satisfies the property that a

Local Linear Quantile Regression

Abstract In this article we study nonparametric regression quantile estimation by kernel weighted local linear fitting. Two such estimators are considered. One is based on localizing the