Linear and least-squares estimation of point processes

September 21, 2016 — May 29, 2017

branching

spatial

Berman-turner device. K-function. 🏗

1 References

Aalen, Odd O. 1978. “Nonparametric Inference for a Family of Counting Processes.” The Annals of Statistics.

Aalen, Odd O. 1989. “A Linear Regression Model for the Analysis of Life Times.” Statistics in Medicine.

Adams, Murray, and MacKay. 2009. “Tractable Nonparametric Bayesian Inference in Poisson Processes with Gaussian Process Intensities.” In.

Andersen, Borgan, Gill, et al. 1997. Statistical models based on counting processes. Springer series in statistics.

Baddeley, and Turner. 2000. “Practical Maximum Pseudolikelihood for Spatial Point Patterns.” Australian & New Zealand Journal of Statistics.

Barbieri, Quirk, Frank, et al. 2001. “Construction and Analysis of Non-Poisson Stimulus-Response Models of Neural Spiking Activity.” Journal of Neuroscience Methods.

Barron, and Cover. 1991. “Minimum Complexity Density Estimation.” IEEE Transactions on Information Theory.

Benichoux, Vincent, and Gribonval. 2013. “A Fundamental Pitfall in Blind Deconvolution with Sparse and Shift-Invariant Priors.” In ICASSP-38th International Conference on Acoustics, Speech, and Signal Processing-2013.

Berman, and Turner. 1992. “Approximating Point Process Likelihoods with GLIM.” Journal of the Royal Statistical Society. Series C (Applied Statistics).

Besag. 1977. “Efficiency of Pseudolikelihood Estimation for Simple Gaussian Fields.” Biometrika.

Brémaud, Massoulié, and Ridolfi. 2005. “Power Spectra of Random Spike Fields and Related Processes.” Advances in Applied Probability.

Buckley, Eagleson, and Silverman. 1988. “The Estimation of Residual Variance in Nonparametric Regression.” Biometrika.

Chaudhuri. 1991. “Nonparametric Estimates of Regression Quantiles and Their Local Bahadur Representation.” The Annals of Statistics.

Cox, and O’Sullivan. 1990. “Asymptotic Analysis of Penalized Likelihood and Related Estimators.” The Annals of Statistics.

Cucala. 2008. “Intensity Estimation for Spatial Point Processes Observed with Noise.” Scandinavian Journal of Statistics.

Diaconis, and Freedman. 1984. “Asymptotics of Graphical Projection Pursuit.” The Annals of Statistics.

Diggle. 1979. “On Parameter Estimation and Goodness-of-Fit Testing for Spatial Point Patterns.” Biometrics.

Eden, Frank, Barbieri, et al. 2004. “Dynamic Analysis of Neural Encoding by Point Process Adaptive Filtering.” Neural Computation.

Eichler, Dahlhaus, and Dueck. 2016. “Graphical Modeling for Multivariate Hawkes Processes with Nonparametric Link Functions.” Journal of Time Series Analysis.

Ellis. 1991. “Density Estimation for Point Processes.” Stochastic Processes and Their Applications.

Fatalov. 2012. “Integral Functionals for the Exponential of the Wiener Process and the Brownian Bridge: Exact Asymptotics and Legendre Functions.” Mathematical Notes.

Gaïffas, and Guilloux. 2012. “High-Dimensional Additive Hazards Models and the Lasso.” Electronic Journal of Statistics.

Green. 1987. “Penalized Likelihood for General Semi-Parametric Regression Models.” International Statistical Review / Revue Internationale de Statistique.

Guan. 2008a. “Variance Estimation for Statistics Computed from Inhomogeneous Spatial Point Processes.” Journal of the Royal Statistical Society: Series B (Statistical Methodology).

———. 2008b. “A Goodness-of-Fit Test for Inhomogeneous Spatial Poisson Processes.” Biometrika.

Guan, and Sherman. 2007. “On Least Squares Fitting for Stationary Spatial Point Processes.” Journal of the Royal Statistical Society: Series B (Statistical Methodology).

Hansen. 2010. “Penalized Maximum Likelihood Estimation for Generalized Linear Point Processes.” arXiv:1003.0848 [Math, Stat].

Hawe, Kleinsteuber, and Diepold. 2013. “Analysis Operator Learning and Its Application to Image Reconstruction.” IEEE Transactions on Image Processing.

Helmers, and Mangku. 1999. “Statistical Estimation of Poisson Intensity Functions.” ANN. INST. STAT. MATH.

Hurvich, Simonoff, and Tsai. 1998. “Smoothing Parameter Selection in Nonparametric Regression Using an Improved Akaike Information Criterion.” Journal of the Royal Statistical Society. Series B (Statistical Methodology).

Jensen, and Künsch. 1994. “On Asymptotic Normality of Pseudo Likelihood Estimates for Pairwise Interaction Processes.” Annals of the Institute of Statistical Mathematics.

Jensen, and Møller. 1991. “Pseudolikelihood for Exponential Family Models of Spatial Point Processes.” The Annals of Applied Probability.

Juban, Fugon, and Kariniotakis. 2007. “Probabilistic Short-Term Wind Power Forecasting Based on Kernel Density Estimators.” In.

Koenker, and Hallock. 2001. “Quantile Regression.” The Journal of Economic Perspectives.

Koenker, and Machado. 1999. “Goodness of Fit and Related Inference Processes for Quantile Regression.” Journal of the American Statistical Association.

Mairal, Bach, Ponce, et al. 2009. “Online Dictionary Learning for Sparse Coding.” In Proceedings of the 26th Annual International Conference on Machine Learning. ICML ’09.

Marziliano, Vetterli, and Blu. 2006. “Sampling and Exact Reconstruction of Bandlimited Signals with Additive Shot Noise.” IEEE Transactions on Information Theory.

Matsumoto, and Yor. 2005. “Exponential Functionals of Brownian Motion, I: Probability Laws at Fixed Time.” Probability Surveys.

Pillow, Shlens, Paninski, et al. 2008. “Spatio-Temporal Correlations and Visual Signalling in a Complete Neuronal Population.” Nature.

Puri, and Tuan. 1986. “Maximum Likelihood Estimation for Stationary Point Processes.” Proceedings of the National Academy of Sciences of the United States of America.

Reynaud-Bouret. 2003. “Adaptive Estimation of the Intensity of Inhomogeneous Poisson Processes via Concentration Inequalities.” Probability Theory and Related Fields.

Reynaud-Bouret, Rivoirard, Grammont, et al. 2014. “Goodness-of-Fit Tests and Nonparametric Adaptive Estimation for Spike Train Analysis.” The Journal of Mathematical Neuroscience.

Reynaud-Bouret, and Roy. 2007. “Some Non Asymptotic Tail Estimates for Hawkes Processes.” Bulletin of the Belgian Mathematical Society - Simon Stevin.

Reynaud-Bouret, and Schbath. 2010. “Adaptive Estimation for Hawkes Processes; Application to Genome Analysis.” The Annals of Statistics.

Riabiz, Ardeshiri, and Godsill. 2016. “A Central Limit Theorem with Application to Inference in α-Stable Regression Models.” In.

Schelldorfer, Meier, and Bühlmann. 2014. “GLMMLasso: An Algorithm for High-Dimensional Generalized Linear Mixed Models Using ℓ1-Penalization.” Journal of Computational and Graphical Statistics.

Schoenberg. 2005. “Consistent Parametric Estimation of the Intensity of a Spatial–Temporal Point Process.” Journal of Statistical Planning and Inference.

Silverman. 1982. “On the Estimation of a Probability Density Function by the Maximum Penalized Likelihood Method.” The Annals of Statistics.

Simon, Friedman, Hastie, et al. 2011. “Regularization Paths for Cox’s Proportional Hazards Model via Coordinate Descent.” Journal of Statistical Software.

Simpson, Illian, Lindgren, et al. 2011. “Going Off Grid: Computationally Efficient Inference for Log-Gaussian Cox Processes.” arXiv:1111.0641 [Math, Stat].

Smith, and Brown. 2003. “Estimating a State-Space Model from Point Process Observations.” Neural Computation.

Stowell, Gill, and Clayton. 2016. “Detailed Temporal Structure of Communication Networks in Groups of Songbirds.” Journal of The Royal Society Interface.

Thrampoulidis, Abbasi, and Hassibi. 2015. “LASSO with Non-Linear Measurements Is Equivalent to One With Linear Measurements.” In Advances in Neural Information Processing Systems 28.

Unser, and Tafti. 2014. An Introduction to Sparse Stochastic Processes.

van de Geer, Bühlmann, Ritov, et al. 2014. “On Asymptotically Optimal Confidence Regions and Tests for High-Dimensional Models.” The Annals of Statistics.

van Lieshout. 2011. “On Estimation of the Intensity Function of a Point Process.” Methodology and Computing in Applied Probability.

Wu, Müller, and Zhang. 2013. “Functional Data Analysis for Point Processes with Rare Events.” Statistica Sinica.

Zarezade, Upadhyay, Rabiee, et al. 2017. “RedQueen: An Online Algorithm for Smart Broadcasting in Social Networks.” In Proceedings of the Tenth ACM International Conference on Web Search and Data Mining. WSDM ’17.