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Non-stationary nonparametric inference of river-to-groundwater travel-time distributions

JOURNAL OF HYDROLOGY 2014年第PartD期519卷 3386-3399页

作者： Liao, Zijie Osenbrueck, Karsten Cirpka, Olaf A. Univ Tubingen Ctr Appl Geosci D-72074 Tubingen Germany Univ Tubingen Water & Earth Syst Sci WESS Competence Cluster D-72074 Tubingen Germany

The travel-time distribution between rivers and groundwater observation points and the mixing of freshly infiltrated river water with groundwater of other origin is of high relevance in riverbank filtration. These characteristics usually are inferred from the analysis of natural-tracer time series, typically relying on a stationary input-output relationship. However, non-stationarity is a significant feature of the riparian zone causing time-varying river-to-groundwater transfer functions. We present a non-stationary extension of nonparametric deconvolution by performing stationary deconvolution with windowed time series, enforcing smoothness of the determined transfer function in time and travel time. The nonparametric approach facilitates the identification of unconventional features in travel-time distributions, such as broad peaks, and the sliding-window approach is an easy way to accommodate the method to dynamic changes of the system under consideration. By this, we obtain time-varying signal-recovery rates and travel-time distributions, from which we derive the mean travel time and the spread of the distribution as function of time. We apply our method to electric-conductivity data collected at River Thur, Switzerland, and adjacent piezometers. The non-stationary approach reproduces the groundwater observations significantly better than the stationary one, both in terms of overall metrics and in matching individual peaks. We compare characteristics of the transient transfer function to base flow which indicates shorter travel times at higher river stages. (C) 2014 Elsevier B.V. All rights reserved.

关键词： Travel-time distribution Bank filtration Non-stationarity nonparametric inference

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The kernel Kalman rule Efficient nonparametric inference by recursive least-squares and subspace projections

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MACHINE LEARNING 2019年第12期108卷 2113-2157页

作者： Gebhardt, Gregor H. W. Kupcsik, Andras Neumann, Gerhard Tech Univ Darmstadt Computat Learning Autonomous Syst Hsch Str 10 D-64285 Darmstadt Germany Bosch Ctr Artificial Intelligence Robert Bosch Campus 1 D-71272 Renningen Germany Univ Lincoln Lincoln Ctr Autonomous Syst Lincoln LN6 7TS England

Enabling robots to act in unstructured and unknown environments requires versatile state estimation techniques. While traditional state estimation methods require known models and make strong assumptions about the dynamics, such versatile techniques should be able to deal with high dimensional observations and non-linear, unknown system dynamics. The recent framework for nonparametric inference allows to perform inference on arbitrary probability distributions. High-dimensional embeddings of distributions into reproducing kernel Hilbert spaces are manipulated by kernelized inference rules, most prominently the kernel Bayes' rule (KBR). However, the computational demands of the KBR do not scale with the number of samples. In this paper, we present two techniques to increase the computational efficiency of non-parametric inference. First, the kernel Kalman rule (KKR) is presented as an approximate alternative to the KBR that estimates the embedding of the state based on a recursive least squares objective. Based on the KKR we present the kernel Kalman filter (KKF) that updates an embedding of the belief state and learns the system and observation models from data. We further derive the kernel forward backward smoother (KFBS) based on a forward and backward KKF and a smoothing update in Hilbert space. Second, we present the subspace conditional embedding operator as a sparsification technique that still leverages from the full data set. We apply this sparsification to the KKR and derive the corresponding sparse KKF and KFBS algorithms. We show on nonlinear state estimation tasks that our approaches provide a significantly improved estimation accuracy while the computational demands are considerably decreased.

关键词： nonparametric inference Kernel methods State estimation Model learning

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Uniform nonparametric inference for spatially dependent panel data: The xtnpsreg command

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STATA JOURNAL 2023年第1期23卷 243-264页

作者： Li, Jia Liao, Zhipeng Zhou, Wenyu Singapore Management Univ Singapore Singapore UCLA Los Angeles CA USA Zhejiang Univ Hangzhou Peoples R China

In this article, we introduce a command, xtnpsreg, that implements a uniform nonparametric inference procedure for possibly unbalanced panel datasets with general forms of spatiotemporal dependence. We demonstrate how to apply this command via several examples, including 1) the nonparametric estimation of the conditional mean function and its marginal response, 2) the construction of uniform confidence bands for these nonparametric functional parameters, 3) specification tests for parametric model restrictions, and 4) the estimation and uniform inference for functional coefficients in semi-nonparametric models.

关键词： st0707 xtnpsreg series estimation spatiotemporal dependence panel data nonparametric inference uniform confidence band

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Consistency of Bayesian nonparametric inference for discretely observed jump diffusions

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BERNOULLI 2019年第3期25卷 2183-2205页

作者： Koskela, Jere Spano, Dario Jenkins, Paul A. Univ Warwick Dept Stat Coventry CV4 7AL W Midlands England Univ Warwick Dept Comp Sci Coventry CV4 7AL W Midlands England

We introduce verifiable criteria for weak posterior consistency of Bayesian nonparametric inference for jump diffusions with unit diffusion coefficient and uniformly Lipschitz drift and jump coefficients in arbitrary dimension. The criteria are expressed in terms of coefficients of the SDEs describing the process, and do not depend on intractable quantities such as transition densities. We also show that priors built from discrete nets, wavelet expansions, and Dirichlet mixture models satisfy our conditions. This generalises known results by incorporating jumps into previous work on unit diffusions with uniformly Lipschitz drift coefficients.

关键词： Bayesian statistics Dirichlet mixture model prior discrete net prior jump diffusion nonparametric inference posterior consistency

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nonparametric inference under b-bits quantization

The Journal of Machine Learning Research

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The Journal of Machine Learning Research 2024年第1期25卷 967-1034页

作者： Kexuan Li Ruiqi Liu Ganggang Xu Zuofeng Shang Global Biometrics and Data Sciences Bristol Myers Squibb Princeton Pike NJ Department of Mathematics and Statistics Texas Tech University Lubbock TX Department of Management Science University of Miami Coral Gables FL Department of Mathematical Sciences New Jersey Institute of Technology Newark NJ

Statistical inference based on lossy or incomplete samples is often needed in research areas such as signal/image processing, medical image storage, remote sensing, signal transmission. In this paper, we propose a nonparametric testing procedure based on samples quantized to B bits through a computationally efficient algorithm. Under mild technical conditions, we establish the asymptotic properties of the proposed test statistic and investigate how the testing power changes as B increases. In particular, we show that if B exceeds a certain threshold, the proposed nonparametric testing procedure achieves the classical minimax rate of testing (Shang and Cheng, 2015) for spline models. We further extend our theoretical investigations to a nonparametric linearity test and an adaptive nonparametric test, expanding the applicability of the proposed methods. Extensive simulation studies together with a real-data analysis are used to demonstrate the validity and effectiveness of the proposed tests.

关键词： B-bits quantization minimax rates of testing nonparametric inference smoothing splines

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nonparametric inference for covariate-adjusted model

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STATISTICS & PROBABILITY LETTERS 2020年 162卷 108766-108766页

作者： Dai, Shuang Huang, Zhensheng Nanjing Univ Sci & Technol Sch Sci Nanjing 210094 Jiangsu Peoples R China

In this paper, we provide a nonparametric test for the covariate-adjusted model where the variables are not directly observed, but are observed after being distorted by unknown functions of a commonly observable covariate in a multiplicative fashion. We estimate the distorting functions by nonparametrically regressing the response and predictors on the distorting covariate, and calculate the estimators of the unobserved variables. Based on the calibrated variables, we propose a generalized likelihood ratio (GLR) test statistic to check the adequacy for the covariate-adjusted model and establish the asymptotic property of the GLR test statistic. Moreover, we carry out some simulated and real examples to evaluate the performance of the GLR test statistic, and make comparisons with these results obtained by Zhang et al. (2015). (C) 2020 Elsevier B.V. All rights reserved.

关键词： Covariate-adjusted model nonparametric inference Generalized likelihood ratio test Bootstrap method

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Parametric embedding of nonparametric inference problems

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JOURNAL OF STATISTICAL THEORY AND PRACTICE 2018年第1期12卷 151-164页

作者： Alvo, Mayer Lai, Tze Leung Yu, Philip L. H. Univ Ottawa Dept Math & Stat Ottawa ON Canada Stanford Univ Dept Stat Stanford CA 94305 USA Univ Hong Kong Dept Stat & Actuarial Sci Pokfulam Rd Hong Kong Hong Kong Peoples R China

In 1937, Neyman introduced the notion of smooth tests of the null hypothesis that the sample data come from a uniform distribution on the interval (0,1) against alternatives in a smooth parametric family. This idea can be used to embed various nonparametric inference problems in a parametric family. Focusing on nonparametric rank tests, we show how to derive traditional rank tests by applying this approach. We also show how to use it to obtain simplifying insights and optimality results in complicated settings that involve censored and truncated data, for which it is more convenient to use hazard functions to define the embedded family. We describe an application of the embedding approach to the problem of testing for trend in environmental studies.

关键词： Parametric embedding nonparametric inference smooth tests censored and truncated data hazard rank tests

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Weighted Empirical Processes in the nonparametric inference for Levy Processes

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MATHEMATICAL METHODS OF STATISTICS 2009年第4期18卷 281-309页

作者： Buchmann, B. Monash Univ Clayton Vic Australia

Given observations of a Levy process, we provide nonparametric estimators of its Levy tail and study the asymptotic properties of the corresponding weighted empirical processes. Within a special class of weight functions, we give necessary and sufficient conditions that ensure strong consistency and asymptotic normality of the weighted empirical processes, provided that complete information on the jumps is available. To cope with infinite activity processes, we depart from this assumption and analyze the weighted empirical processes of a sampling scheme where small jumps are neglected. We establish a bootstrap principle and provide a simulation study for some prominent Levy processes.

关键词： Levy processes Levy measure nonparametric inference weighted empirical processes weighted uniform norms Levy tail Poisson fields infinite activity bootstrap confidence bounds stable process variance-gamma process

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Three essays on nonparametric inference for longitudinal data and time series data.

Three essays on nonparametric inference for longitudinal dat...

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作者： Kim, Seonjin PennState University Libraries

学位级别：Doctor of Philosophy

This thesis consists of three essays on nonparametric inference problems for dependent data, such as longitudinal data and time series data. In the literature on statistical estimation and inference, the frequently imposed independence assumption allows for technical simplicity, but it leads to serious restrictions in many applications. For example, in longitudinal data analysis and time series analysis, dependence is actually one of the main objectives of interest. The techniques developed for independent data may fail or not be efficient where dependence presents. Moreover, the traditional approach to nonparametric inference problems has some disadvantages due to the structure dependency and estimation difficulty of the limiting variance function, and there exist mathematical obstacles caused by dependence inherited in data. In order to alleviate the aforementioned problems, I have developed novel theories and methodologies for dependent data through self-normalization techniques and quantile regression. The developments involve theoretical notability as well as practical applicability for financial, medical, environmental, and social science.

关键词： Locally stationary process Longitudinal data Measurement errors nonparametric inference Quantile regression Time series

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Optimal nonparametric inference via deep neural network

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JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 2022年第2期505卷 125561-125561页

作者： Liu, Ruiqi Boukai, Ben Shang, Zuofeng Texas Tech Univ Dept Math & Stat Lubbock TX 79409 USA Indiana Univ Purdue Univ Indianapolis Dept Math Sci Indianapolis IN USA New Jersey Inst Technol Dept Math Sci Newark NJ 07102 USA

Deep neural network is a state-of-art method in modern science and technology. Much statistical literature have been devoted to understanding its performance in nonparametric estimation, whereas the results are suboptimal due to a redundant logarithmic sacrifice. In this paper, we show that such log-factors are not necessary. We derive upper bounds for the L-2 minimax risk in nonparametric estimation. Sufficient conditions on network architectures are provided such that the upper bounds become optimal (without log-sacrifice). Our proof relies on an explicitly constructed network estimator based on tensor product B-splines. We also derive asymptotic distributions for the constructed network and a relating hypothesis testing procedure. The testing procedure is further proved as minimax optimal under suitable network architectures. (C) 2021 Elsevier Inc. All rights reserved.

关键词： Deep neural network nonparametric inference Tensor product B-splines Optimal minimax risk bound Asymptotic distribution nonparametric testing

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