Inference on Time Series Nonparametric Conditional Moment Restrictions Using General Sieves

• URL: http://arxiv.org/abs/2301.00092v2
• Date: Tue, 3 Jan 2023 02:37:07 GMT
• Title: Inference on Time Series Nonparametric Conditional Moment Restrictions Using General Sieves
• Authors: Xiaohong Chen, Yuan Liao, Weichen Wang
• Abstract summary: This paper considers general nonlinear sieve quasi-likelihood ratio (GN-QLR) based on expectation inferences of time series data. While the normality of the estimated functionals depends on some unknown Riesz representer of the functional space, we show that the optimally weighted GN-QLR statistic is Chi-square distributed.
• Score: 4.065100518793487
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: General nonlinear sieve learnings are classes of nonlinear sieves that can approximate nonlinear functions of high dimensional variables much more flexibly than various linear sieves (or series). This paper considers general nonlinear sieve quasi-likelihood ratio (GN-QLR) based inference on expectation functionals of time series data, where the functionals of interest are based on some nonparametric function that satisfy conditional moment restrictions and are learned using multilayer neural networks. While the asymptotic normality of the estimated functionals depends on some unknown Riesz representer of the functional space, we show that the optimally weighted GN-QLR statistic is asymptotically Chi-square distributed, regardless whether the expectation functional is regular (root-$n$ estimable) or not. This holds when the data are weakly dependent beta-mixing condition. We apply our method to the off-policy evaluation in reinforcement learning, by formulating the Bellman equation into the conditional moment restriction framework, so that we can make inference about the state-specific value functional using the proposed GN-QLR method with time series data. In addition, estimating the averaged partial means and averaged partial derivatives of nonparametric instrumental variables and quantile IV models are also presented as leading examples. Finally, a Monte Carlo study shows the finite sample performance of the procedure

Related papers

• Kernel-based off-policy estimation without overlap: Instance optimality beyond semiparametric efficiency [53.90687548731265]
  We study optimal procedures for estimating a linear functional based on observational data. For any convex and symmetric function class $mathcalF$, we derive a non-asymptotic local minimax bound on the mean-squared error.
  arXiv  Detail & Related papers  (2023-01-16T02:57:37Z)
• MP-GELU Bayesian Neural Networks: Moment Propagation by GELU Nonlinearity [0.0]
  We propose a novel nonlinear function named moment propagating-Gaussian error linear unit (MP-GELU) that enables the fast derivation of first and second moments in BNNs. MP-GELU provides higher prediction accuracy and better quality of uncertainty with faster execution than those of ReLU-based BNNs.
  arXiv  Detail & Related papers  (2022-11-24T03:37:29Z)
• Off-policy estimation of linear functionals: Non-asymptotic theory for semi-parametric efficiency [59.48096489854697]
  The problem of estimating a linear functional based on observational data is canonical in both the causal inference and bandit literatures. We prove non-asymptotic upper bounds on the mean-squared error of such procedures. We establish its instance-dependent optimality in finite samples via matching non-asymptotic local minimax lower bounds.
  arXiv  Detail & Related papers  (2022-09-26T23:50:55Z)
• Inference on Strongly Identified Functionals of Weakly Identified Functions [71.42652863687117]
  We study a novel condition for the functional to be strongly identified even when the nuisance function is not. We propose penalized minimax estimators for both the primary and debiasing nuisance functions.
  arXiv  Detail & Related papers  (2022-08-17T13:38:31Z)
• Functional Nonlinear Learning [0.0]
  We propose a functional nonlinear learning (FunNoL) method to represent multivariate functional data in a lower-dimensional feature space. We show that FunNoL provides satisfactory curve classification and reconstruction regardless of data sparsity.
  arXiv  Detail & Related papers  (2022-06-22T23:47:45Z)
• Experimental Design for Linear Functionals in Reproducing Kernel Hilbert Spaces [102.08678737900541]
  We provide algorithms for constructing bias-aware designs for linear functionals. We derive non-asymptotic confidence sets for fixed and adaptive designs under sub-Gaussian noise.
  arXiv  Detail & Related papers  (2022-05-26T20:56:25Z)
• Convergence bounds for nonlinear least squares and applications to tensor recovery [0.0]
  We consider the problem of approximating a function in general nonlinear subsets of $L2$ when only a weighted Monte Carlo estimate of the $L2$-norm can be computed. A critical analysis of our results allows us to derive a sample efficient algorithm for the model set of low-rank tensors.
  arXiv  Detail & Related papers  (2021-08-11T14:14:02Z)
• Meta-Learning for Koopman Spectral Analysis with Short Time-series [49.41640137945938]
  Existing methods require long time-series for training neural networks. We propose a meta-learning method for estimating embedding functions from unseen short time-series. We experimentally demonstrate that the proposed method achieves better performance in terms of eigenvalue estimation and future prediction.
  arXiv  Detail & Related papers  (2021-02-09T07:19:19Z)
• SLEIPNIR: Deterministic and Provably Accurate Feature Expansion for Gaussian Process Regression with Derivatives [86.01677297601624]
  We propose a novel approach for scaling GP regression with derivatives based on quadrature Fourier features. We prove deterministic, non-asymptotic and exponentially fast decaying error bounds which apply for both the approximated kernel as well as the approximated posterior.
  arXiv  Detail & Related papers  (2020-03-05T14:33:20Z)
• Sequential Gaussian Processes for Online Learning of Nonstationary Functions [9.997259201098602]
  We propose a sequential Monte Carlo algorithm to fit infinite mixtures of GPs that capture non-stationary behavior while allowing for online, distributed inference. Our approach empirically improves performance over state-of-the-art methods for online GP estimation in the presence of non-stationarity in time-series data.
  arXiv  Detail & Related papers  (2019-05-24T02:29:49Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.