We propose a novel and efficient iterative two-stage variable selection approach for multivariate sparse GLARMA models, which can be used for modelling multivariate discrete-valued time series. Our approach consists in iteratively combining two steps: the estimation of the autoregressive moving average (ARMA) coefficients of multivariate GLARMA models and the variable selection in the coefficients of the Generalized Linear Model (GLM) part of the model performed by regularized methods. We explain how to implement our approach efficiently. Then we assess the performance of our methodology using synthetic data and compare it with alternative methods. Finally, we illustrate it on RNA-Seq data resulting from polyribosome profiling to determine translational status for all mRNAs in germinating seeds. Our approach, which is implemented in the MultiGlarmaVarSel R package and available on the CRAN, is very attractive since it benefits from a low computational load and is able to outperform the other methods for recovering the null and non-null coefficients. 

/pdf/variable-selection-in-sparse-multivariate-glarma-models-23b87iih.pdf

Variable selection in sparse multivariate GLARMA models: Application to
  germination control by environment

. We propose a novel and eﬃcient iterative two-stage variable selection approach for multivariate sparse GLARMA models, which can be used for modelling multivariate discrete-valued time series. Our approach consists in iteratively combining two steps: the estimation of the autoregressive moving average (ARMA) coeﬃcients of multivariate GLARMA models and the variable selection in the coeﬃcients of the Generalized Linear Model (GLM) part of the model performed by regularized methods. We explain how to implement our approach eﬃciently. Then we assess the performance of our methodology using synthetic data and compare it with alternative methods. Finally, we illustrate it on RNA-Seq data resulting from polyribosome proﬁling to determine translational status for all mRNAs in germinating seeds. Our approach, which is implemented in the MultiGlarmaVarSel R package and available on the CRAN, is very attractive since it beneﬁts from a low computational load and is able to outperform the other methods for recovering the null and non-null coeﬃcients.

Variable selection in sparse multivariate GLARMA models: Application to germination control by environment

Conditional parametric bootstrap in GLARMA models

1 Elements of Stochastic Processes.- 1.1 Introduction.- 1.2 Stochastic Processes.- 1.3 Limit Theorems.- Problems.- 2 Local Asymptotic Normality for Stochastic Processes.- 2.1 General Results for Local Asymptotic Normality.- 2.2 Local Asymptotic Normality for Linear Processes.- Problems.- 3 Asymptotic Theory of Estimation and Testing for Stochastic Processes.- 3.1 Asymptotic Theory of Estimation and Testing for Linear Processes.- 3.1.1 Asymptotic Theory Based on a Gaussian Likelihood.- 3.1.2 Asymptotic Theory of Estimation and Testing Based on LAN Results.- 3.2 Asymptotic Theory for Nonlinear Stochastic Models.- 3.2.1 Nonlinear Models.- 3.2.2 Probability Structure of Nonlinear Models.- 3.2.3 Statistical Testing and Estimation Theory for Nonlinear Models.- 3.2.4 Asymptotic Theory Based on the LAN Property.- 3.2.5 Model Selection Problems.- 3.2.6 Nonergodic Models.- 3.3 Asymptotic Theory for Continuous Time Processes.- 3.3.1 Stochastic Integrals and Diffusion Processes.- 3.3.2 Asymptotic Theory for Diffusion Processes.- 3.3.3 Diffusion Processes and Autoregressions with Roots.- Near Unity.- 3.3.4 Continuous Time ARMA Processes.- 3.3.5 Asymptotic Theory for Point Processes.- Problems.- 4 Higher Order Asymptotic Theory for Stochastic Processes.- 4.1 Introduction to Higher Order Asymptotic Theory.- 4.2 Valid Asymptotic Expansions.- 4.3 Higher Order Asymptotic Estimation Theory for Discrete Time Processes in View of Statistical Differential Geometry.- 4.4 Higher Order Asymptotic Theory for Continuous Time Processes.- 4.5 Higher Order Asymptotic Theory for Testing Problems.- 4.6 Higher Order Asymptotic Theory for Normalizing Transformations.- 4.7 Generalization of LeCam's Third Lemma and Higher Order Asymptotics of Iterative Methods.- Problems.- 5 Asymptotic Theory for Long-Memory Processes.- 5.1 Some Elements of Long-Memory Processes.- 5.2 Limit Theorems for Fundamental Statistics.- 5.3 Estimation and Testing Theory for Long-Memory Processes.- 5.4 Regression Models with Long-Memory Disturbances.- 5.5 Semiparametric Analysis and the LAN Approach.- Problems.- 6 Statistical Analysis Based on Functionals of Spectra.- 6.1 Estimation of Nonlinear Functionals of Spectra.- 6.2 Application to Parameter Estimation for Stationary Processes.- 6.3 Asymptotically Efficient Nonparametric Estimation of Functionals of Spectra in Gaussian Stationary Processes.- 6.4 Robustness in the Frequency Domain Approach.- 6.4.1 Robustness to Small Trends of Linear Functionals of a Periodogram.- 6.4.2 Peak-Insensitive Spectrum Estimation.- 6.5 Numerical Examples.- Problems.- 7 Discriminant Analysis for Stationary Time Series.- 7.1 Basic Formulation.- 7.2 Standard Methods for Gaussian Stationary Processes.- 7.2.1 Time Domain Methods.- 7.2.2 Frequency Domain Methods.- 7.2.3 Admissible Linear Procedure: Case of Unequal Mean Vectors and Covariance Matrices.- 7.3 Discriminant Analysis for Non-Gaussian Linear Processes.- 7.4 Nonparametric Approach for Discriminant Analysis.- 7.5 Parametric Approach for Discriminant Analysis.- 7.6 Derivation of Spectral Expressions to Divergence Measures Between Gaussian Stationary Processes.- 7.7 Miscellany.- Problems.- 8 Large Deviation Theory and Saddlepoint Approximation for Stochastic Processes.- 8.1 Large Deviation Theorem 538 8.2 Asymptotic Efficiency for Gaussian Stationary Processes:Large Deviation Approach.- 8.2.1 Asymptotic Theory of Neyman-Pearson Tests.- 8.2.2 Bahadur Efficiency of Estimator.- 8.2.3 Stochastic Comparison of Tests.- 8.3 Large Deviation Results for an Ornstein-Uhlenbeck Process.- 8.4 Saddlepoint Approximations for Stochastic Processes.- Problems.- A.1 Mathematics.- A.2 Probability.- A.3 Statistics.

Asymptotic theory of statistical inference for time series

In this paper, we propose a novel and efficient two-stage variable selection approach for sparse GLARMA models, which are pervasive for modeling discrete-valued time series. Our approach consists in iteratively combining the estimation of the autoregressive moving average (ARMA) coefficients of GLARMA models with regularized methods designed for performing variable selection in regression coefficients of Generalized Linear Models (GLM). We first establish the consistency of the ARMA part coefficient estimators in a specific case. Then, we explain how to efficiently implement our approach. Finally, we assess the performance of our methodology using synthetic data and compare it with alternative methods. Our approach is very attractive since it benefits from a low computational load and is able to outperform the other methods in terms of coefficient estimation, particularly in recovering the non null regression coefficients.

Variable selection in sparse GLARMA models

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Variable selection in sparse GLARMA models