Efficient nonparametric inference for discretely observed compound Poisson processes

DOI10.1007/s00440-017-0761-5zbMath1383.62081arXiv1512.08472OpenAlexW2199664410MaRDI QIDQ681527

Alberto J. Coca

Publication date: 12 February 2018

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1512.08472

zbMATH Keywords

compound Poisson processLévy distributionuniform central limit theoremnonlinear inverse problemdiscrete measure kernel estimatorefficient nonparametric inference

Mathematics Subject Classification ID

Processes with independent increments; Lévy processes (60G51) Density estimation (62G07) Asymptotic properties of nonparametric inference (62G20) Nonparametric estimation (62G05) Central limit and other weak theorems (60F05)

Related Items (8)

Nonparametric estimation for compound Poisson process via variational analysis on measures ⋮ Minimax rates for the covariance estimation of multi-dimensional Lévy processes with high-frequency data ⋮ Approximate Bayesian computations to fit and compare insurance loss models ⋮ Spectral-free estimation of Lévy densities in high-frequency regime ⋮ Efficient nonparametric inference for discretely observed compound Poisson processes ⋮ Nonparametric inference on Lévy measures of compound Poisson-driven Ornstein-Uhlenbeck processes under macroscopic discrete observations ⋮ Adaptive procedure for Fourier estimators: application to deconvolution and decompounding ⋮ Bernstein-von Mises theorems for statistical inverse problems. II: Compound Poisson processes

Cites Work

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• Nonparametric Bayesian inference for multidimensional compound Poisson processes
• Nonparametric estimation of a renewal reward process from discrete data
• Confidence sets in nonparametric calibration of exponential Lévy models
• Lévy matters IV. Estimation for discretely observed Lévy processes
• Nonparametric estimation for Lévy processes from low-frequency observations
• Efficient nonparametric inference for discretely observed compound Poisson processes
• Nonparametric estimation for a class of Lévy processes
• Some limit theorems for empirical processes (with discussion)
• Spectral calibration of exponential Lévy models
• Information bounds for inverse problems with application to deconvolution and Lévy models
• Decompounding random sums: a nonparametric approach
• Uniform central limit theorems for kernel density estimators
• Decompounding: an estimation problem for Poisson random sums.
• A non-parametric Bayesian approach to decompounding from high frequency data
• A Donsker theorem for Lévy measures
• Weak convergence and empirical processes. With applications to statistics
• A uniform central limit theorem and efficiency for deconvolution estimators
• Density estimation for compound Poisson processes from discrete data
• Nonparametric inference for discretely sampled Lévy processes
• Adaptive nonparametric estimation for Lévy processes observed at low frequency
• Weighted empirical processes in the nonparametric inference for Lévy processes
• Nonparametric density estimation in compound Poisson processes using convolution power estimators
• When is it no longer possible to estimate a compound Poisson process?
• Testing the characteristics of a Lévy process
• A kernel type nonparametric density estimator for decompounding
• Decompounding Poisson random sums: recursively truncated estimates in the discrete case
• High-frequency Donsker theorems for Lévy measures
• Mathematical Foundations of Infinite-Dimensional Statistical Models
• Estimation of the Jump Size Density in a Mixed Compound Poisson Process
• Nonparametric estimation of the characteristic triplet of a discretely observed Lévy process
• Weak Convergence of the Empirical Characteristic Function
• Uniform Central Limit Theorems
• Asymptotic Statistics

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