What is kernel in the kernel density estimate
If the Epanechnikov kernel is theoretically optimal at kernel density estimation, why isn't it used more often?
The reason the Epanechnikov kernel is not widely used because of its theoretical optimality may well be that the Epanechnikov kernel is theoretically not optimal . Tsybakov explicitly criticizes the argument that the Epanechnikov kernel is "theoretically optimal" on pages 16-19 of the Introduction to nonparametric estimation (Section 1.2.4).
The attempt, under some assumptions about the kernel K and a fixed density p, takes the form of the mean integrated square error
The main criticism of Tsybakov seems to be the minimization versus non-negative kernels, as it is often possible to get more powerful estimators that are even non-negative without limiting yourself to non-negative kernels.
The first step of the argument for the Epanechnikov kernel begins with minimizing (1) over h and all non-negative kernels (and not all kernels of a broader class) to get an "optimal" bandwidth for K
and the "optimal" kernel (Epanechnikov)
whose mean integrated square error is:
However, these are not feasible decisions since they depend on the knowledge (about p ″) of the unknown density p - therefore they are "oracle" qualities.
A suggestion from Tsybakov implies that the asymptotic MISE for the Epanechnikov oracle is:
SK = 0ε> 0
Even if p n is not necessarily not negative, one still has the same result for the positive part of the estimator, p + p ^ np + n: = max (0,
- Is the Tetra Pak milk really fresh?
- Can you describe Arduino IDE
- Is the sun worth worshiping?
- Markets are still open after 4 p.m.
- Why did Madeleine Hightower leave The Mentalist
- Why did Modi set up free bank accounts
- What is the IRS in remote sensing
- What does PG
- Is belief in the divine a priori
- Hypnotherapists hypnotize themselves as therapy
- Is self hypnosis better than hypnosis
- Which is better Android or Oxygen OS
- What is a real business
- Vietnamese consider themselves Indians
- Herbert Hoover was a psychopath
- What does chemistry teach
- Where do white bumblebees live
- Why is DSM so ambiguous
- What does the leaked crypto currency bill say
- What does enjoy 2
- Why do people sleep with plush animals
- What are the best restaurants in Munich
- When will Tesla release the Model X?
- What is a CDP chef