Lasso and probabilistic inequalities for multivariate point processes

DOI10.3150/13-BEJ562zbMath1375.60092arXiv1208.0570OpenAlexW3104587455WikidataQ98839763 ScholiaQ98839763MaRDI QIDQ2345116

Vincent Rivoirard, Niels Richard Hansen, Patricia Reynaud-Bouret

Publication date: 19 May 2015

Published in: Bernoulli (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1208.0570

zbMATH Keywords

multivariate point processesmultivariate Hawkes processesBernstein-type inequalitiesLasso procedure\(\ell_{1}\)-penalization

Mathematics Subject Classification ID

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Cites Work

• Unnamed Item
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• The Adaptive Lasso and Its Oracle Properties
• Penalized projection estimators of the Aalen multiplicative intensity
• Statistics for high-dimensional data. Methods, theory and applications.
• Adaptive estimation for Hawkes processes; application to genome analysis
• Adaptive Dantzig density estimation
• Nuclear-norm penalization and optimal rates for noisy low-rank matrix completion
• Exponential inequalities for self-normalized martingales with applications
• Stochastic kinetic models: dynamic independence, modularity and graphs
• Some non asymptotic tail estimates for Hawkes processes
• Relaxed Lasso
• Maximum likelihood identification of neural point process systems
• Wavelets, approximation, and statistical applications
• Adaptive estimation of the intensity of inhomogeneous Poisson processes via concentration inequalities
• A general class of exponential inequalities for martingales and ratios
• On Bernstein-type inequalities for martingales.
• Exponential inequalities for martingales, with application to maximum likelihood estimation for counting processes
• Adaptive estimation of the conditional intensity of marker-dependent counting processes
• High-dimensional additive hazards models and the lasso
• Near optimal thresholding estimation of a Poisson intensity on the real line
• The adaptive and the thresholded Lasso for potentially misspecified models (and a lower bound for the Lasso)
• Deviation probability bound for martingales with applications to statistical estimation
• Goodness-of-fit tests and nonparametric adaptive estimation for spike train analysis
• Simultaneous analysis of Lasso and Dantzig selector
• High-dimensional generalized linear models and the lasso
• Sparsity oracle inequalities for the Lasso
• Some limit theorems for Hawkes processes and application to financial statistics
• Aggregation for Gaussian regression
• The Dantzig selector: statistical estimation when \(p\) is much larger than \(n\). (With discussions and rejoinder).
• Covariate selection for semiparametric hazard function regression models
• Stability of nonlinear Hawkes processes
• Non-asymptotic theory of random matrices: extreme singular values
• On sparse reconstruction from Fourier and Gaussian measurements
• Self-Normalized Processes
• Multiscale Poisson Intensity and Density Estimation
• Adaptive Estimation of Hazard Rate with Censored Data
• Smallest singular value of a random rectangular matrix
• An Introduction to the Theory of Point Processes
• Adaptive Warped Kernel Estimators
• Aggregation and Sparsity Via ℓ1 Penalized Least Squares
• Sparse Density Estimation with ℓ1 Penalties
• FADO: A Statistical Method to Detect Favored or Avoided Distances between Occurrences of Motifs using the Hawkes' Model
• Statistical models based on counting processes

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