Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Warped Kernel Estimator for I.I.D. Paths of Diffusion Processes

Nicolas Marie, Amélie Rosier

Abstract

This paper deals with a nonparametric warped kernel estimator $\widehat b$ of the drift function computed from independent continuous observations of a diffusion process. A risk bound on $\widehat b$ is established. The paper also deals with an extension of the PCO bandwidth selection method for $\widehat b$. Finally, some numerical experiments are provided.

Warped Kernel Estimator for I.I.D. Paths of Diffusion Processes

Abstract

This paper deals with a nonparametric warped kernel estimator of the drift function computed from independent continuous observations of a diffusion process. A risk bound on is established. The paper also deals with an extension of the PCO bandwidth selection method for . Finally, some numerical experiments are provided.
Paper Structure (9 sections, 6 theorems, 67 equations, 2 figures, 1 table)

This paper contains 9 sections, 6 theorems, 67 equations, 2 figures, 1 table.

Table of Contents

  1. Introduction
  2. Risk bound on the warped kernel estimator
  3. A PCO type bandwidth selection method
  4. Numerical experiments
  5. Proofs
  6. Proof of Proposition \ref{['risk_bound_warped_estimator']}
  7. Proof of Theorem \ref{['risk_bound_PCO_estimator_b']}
  8. Steps of the proof
  9. Proof of Proposition \ref{['kernel_properties_Phi']}

Key Result

Proposition 2.4

Consider $A,B\in\overline{\mathbb R}$ such that $A < B$. Under Assumptions assumption_b_sigma and assumption_K, with

Figures (2)

  • Figure 1: PCO adaptative estimator for Model 1 (Langevin equation), $\widehat{h} = 0.04$ and $h_{\rm oracle} = 0.02$.
  • Figure 2: PCO adaptative estimator for Model 2, $\widehat{h} = 0.05$ and $h_{\rm oracle} = 0.07$.

Theorems & Definitions (7)

  • Remark 2.2
  • Proposition 2.4
  • Theorem 3.2
  • Proposition 5.1
  • Lemma 5.2
  • Lemma 5.3
  • Lemma 5.4