Central limit theorem for the robust log-regression wavelet estimation of the memory parameter in the Gaussian semi-parametric context

DOI10.3150/11-BEJ398zbMath1288.62061arXiv1011.4370MaRDI QIDQ1940755

O. Kouamo, Eric Moulines, Céline Lévy-Leduc

Publication date: 7 March 2013

Published in: Bernoulli (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1011.4370

zbMATH Keywords

robustnesswavelet analysissemiparametric estimationlong-range dependencescale estimatormemory parameter estimator

Mathematics Subject Classification ID

Nonparametric regression and quantile regression (62G08) Central limit and other weak theorems (60F05) Robustness and adaptive procedures (parametric inference) (62F35) Inference from stochastic processes and spectral analysis (62M15) Numerical methods for wavelets (65T60)

Related Items

Expectiles for subordinated Gaussian processes with applications, Estimation of long-range dependence in gappy Gaussian time series

Uses Software

• LASS
• longmemo

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Highly Robust Estimation of the Autocovariance Function
• Robust estimation in long-memory processes under additive outliers
• Hurst exponent estimation of locally self-similar Gaussian processes using sample quantiles
• Bahadur representation of sample quantiles for a functional of Gaussian dependent sequences under a minimal assumption
• A test for additive outliers applicable to long-memory time series
• LASS: a tool for the local analysis of self-similarity
• Robust estimation of the self-similarity parameter in network traffic using wavelet transform
• Visualization and inference based on wavelet coefficients, SiZer and SiNos
• Central limit theorems for non-linear functionals of Gaussian fields
• Time series: theory and methods.
• Limit theorems for nonlinear functionals of a stationary Gaussian sequence of vectors
• The empirical process of a short-range dependent stationary sequence under Gaussian subordination
• Gaussian semiparametric estimation of long range dependence
• Estimators of long-memory: Fourier versus wavelets
• THE ESTIMATION AND APPLICATION OF LONG MEMORY TIME SERIES MODELS
• On the Spectral Density of the Wavelet Coefficients of Long-Memory Time Series with Application to the Log-Regression Estimation of the Memory Parameter
• CENTRAL LIMIT THEOREM FOR THE LOG-REGRESSION WAVELET ESTIMATION OF THE MEMORY PARAMETER IN THE GAUSSIAN SEMI-PARAMETRIC CONTEXT
• Asymptotic Statistics
• Alternatives to the Median Absolute Deviation
• Ideal spatial adaptation by wavelet shrinkage
• Wavelet analysis of long-range-dependent traffic
• Robust estimation of the scale and of the autocovariance function of Gaussian short- and long-range dependent processes
• Asymptotic self‐similarity and wavelet estimation for long‐range dependent fractional autoregressive integrated moving average time series with stable innovations