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A portmanteau-type test for detecting serial correlation in locally stationary functional time series. STATISTICAL INFERENCE FOR STOCHASTIC PROCESSES 2023. [DOI: 10.1007/s11203-022-09285-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/19/2023]
Abstract
AbstractThe portmanteau test provides the vanilla method for detecting serial correlations in classical univariate time series analysis. The method is extended to the case of observations from a locally stationary functional time series. Asymptotic critical values are obtained by a suitable block multiplier bootstrap procedure. The test is shown to asymptotically hold its level and to be consistent against general alternatives.
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2
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Wu F, Wang GJ, Kong XB. Inference on volatility curve at high frequencies via functional data analysis. COMMUN STAT-THEOR M 2022. [DOI: 10.1080/03610926.2020.1864829] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
Affiliation(s)
- Fan Wu
- School of Mathematics, Southeast University, Nanjing, China
| | - Guan-jun Wang
- School of Mathematics, Southeast University, Nanjing, China
| | - Xin-bing Kong
- School of Statistics and Mathematics, Nanjing Audit University, Nanjing, China
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3
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Cameron J, Bagchi P. A test for heteroscedasticity in functional linear models. TEST-SPAIN 2022. [DOI: 10.1007/s11749-021-00786-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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Zhao F, Lin N, Hu W, Zhang B. A faster U-statistic for testing independence in the functional linear models. J Stat Plan Inference 2022. [DOI: 10.1016/j.jspi.2021.08.002] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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Mestre G, Portela J, Rice G, Muñoz San Roque A, Alonso E. Functional time series model identification and diagnosis by means of auto- and partial autocorrelation analysis. Comput Stat Data Anal 2021. [DOI: 10.1016/j.csda.2020.107108] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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7
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García‐Portugués E, Álvarez‐Liébana J, Álvarez‐Pérez G, González‐Manteiga W. A goodness‐of‐fit test for the functional linear model with functional response. Scand Stat Theory Appl 2020. [DOI: 10.1111/sjos.12486] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Eduardo García‐Portugués
- Department of Statistics Carlos III University of Madrid, Spain
- UC3M‐Santander Big Data Institute Carlos III University of Madrid, Spain
| | - Javier Álvarez‐Liébana
- Department of Statistics and Operations Research and Mathematics Didactics University of Oviedo, Spain
| | | | - Wenceslao González‐Manteiga
- Department of Statistics, Mathematical Analysis and Optimization University of Santiago de Compostela, Spain
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Abstract
Summary
We propose a new nonparametric conditional mean independence test for a response variable $Y$ and a predictor variable $X$ where either or both can be function-valued. Our test is built on a new metric, the so-called functional martingale difference divergence, which fully characterizes the conditional mean dependence of $Y$ given $X$ and extends the martingale difference divergence proposed by Shao & Zhang (2014). We define an unbiased estimator of functional martingale difference divergence by using a $\mathcal{U}$-centring approach, and we obtain its limiting null distribution under mild assumptions. Since the limiting null distribution is not pivotal, we use the wild bootstrap method to estimate the critical value and show the consistency of the bootstrap test. Our test can detect the local alternative which approaches the null at the rate of $n^{-1/2}$ with a nontrivial power, where $n$ is the sample size. Unlike the three tests developed by Kokoszka et al. (2008), Lei (2014) and Patilea et al. (2016), our test does not require a finite-dimensional projection or assume a linear model, and it does not involve any tuning parameters. Promising finite-sample performance is demonstrated via simulations, and a real-data illustration is used to compare our test with existing ones.
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Affiliation(s)
- C E Lee
- Department of Business Analytics and Statistics, University of Tennessee, Knoxville, 916 Volunteer Blvd, Knoxville, Tennessee 37996, USA
| | - X Zhang
- Department of Statistics, Texas A&M University, 155 Ireland St, College Station, Texas 77843, USA
| | - X Shao
- Department of Statistics, University of Illinois at Urbana Champaign, 725 South Wright St, Champaign, Illinois 61820, USA
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Li Q, Tan X, Wang L. Testing for error correlation in partially functional linear regression models. COMMUN STAT-THEOR M 2019. [DOI: 10.1080/03610926.2019.1642492] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
Affiliation(s)
- Qian Li
- School of Statistics and Management, Shanghai University of Finance and Economics, Shanghai, China
| | - Xiangyong Tan
- School of Statistics and Management, Shanghai University of Finance and Economics, Shanghai, China
| | - Liming Wang
- School of Statistics and Management, Shanghai University of Finance and Economics, Shanghai, China
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11
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Procrustes Metrics on Covariance Operators and Optimal Transportation of Gaussian Processes. SANKHYA A 2019. [DOI: 10.1007/s13171-018-0130-1] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/16/2022]
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12
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Maeng H, Fryzlewicz P. Regularised forecasting via smooth-rough partitioning of the regression coefficients. Electron J Stat 2019. [DOI: 10.1214/19-ejs1573] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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13
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Davenport CA, Maity A, Baladandayuthapani V. Functional interaction-based nonlinear models with application to multiplatform genomics data. Stat Med 2018; 37:2715-2733. [PMID: 29737021 DOI: 10.1002/sim.7671] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/22/2017] [Revised: 02/05/2018] [Accepted: 03/09/2018] [Indexed: 11/11/2022]
Abstract
Functional regression allows for a scalar response to be dependent on a functional predictor; however, not much work has been done when a scalar exposure that interacts with the functional covariate is introduced. In this paper, we present 2 functional regression models that account for this interaction and propose 2 novel estimation procedures for the parameters in these models. These estimation methods allow for a noisy and/or sparsely observed functional covariate and are easily extended to generalized exponential family responses. We compute standard errors of our estimators, which allows for further statistical inference and hypothesis testing. We compare the performance of the proposed estimators to each other and to one found in the literature via simulation and demonstrate our methods using a real data example.
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Affiliation(s)
- Clemontina A Davenport
- Department of Biostatistics and Bioinformatics, Duke University Medical Center, Durham, NC, 27705, USA
| | - Arnab Maity
- Department of Statistics, North Carolina State University, Raleigh, NC, 27695, USA
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Reimherr M, Sriperumbudur B, Taoufik B. Optimal prediction for additive function-on-function regression. Electron J Stat 2018. [DOI: 10.1214/18-ejs1505] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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15
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Patilea V, Sánchez-Sellero C, Saumard M. Testing the Predictor Effect on a Functional Response. J Am Stat Assoc 2017. [DOI: 10.1080/01621459.2015.1110031] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
Affiliation(s)
- Valentin Patilea
- CREST (Ensai), Campus de Ker-Lann, Bruz, France, and Bucharest University of Economic Studies, Bucharest, Romania
| | - César Sánchez-Sellero
- Department of Statistics and O.R., Universidad de Santiago de Compostela, Santiago de Compostela, Spain
| | - Matthieu Saumard
- Pontificia Universidad Catolica de Valparaiso, Valparaiso, Chile
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Zhu T, Politis DN. Kernel estimates of nonparametric functional autoregression models and their bootstrap approximation. Electron J Stat 2017. [DOI: 10.1214/17-ejs1303] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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17
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A simultaneous confidence corridor for varying coefficient regression with sparse functional data. TEST-SPAIN 2014. [DOI: 10.1007/s11749-014-0392-4] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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18
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Bayesian bandwidth estimation for a semi-functional partial linear regression model with unknown error density. Comput Stat 2013. [DOI: 10.1007/s00180-013-0463-0] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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19
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Hörmann S, Kokoszka P. Consistency of the mean and the principal components of spatially distributed functional data. BERNOULLI 2013. [DOI: 10.3150/12-bej418] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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21
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Kokoszka P, Reimherr M. Asymptotic normality of the principal components of functional time series. Stoch Process Their Appl 2013. [DOI: 10.1016/j.spa.2012.12.011] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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Horváth L, Kokoszka P, Reeder R. Estimation of the mean of functional time series and a two-sample problem. J R Stat Soc Series B Stat Methodol 2012. [DOI: 10.1111/j.1467-9868.2012.01032.x] [Citation(s) in RCA: 89] [Impact Index Per Article: 7.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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FREMDT STEFAN, STEINEBACH JOSEFG, HORVÁTH LAJOS, KOKOSZKA PIOTR. Testing the Equality of Covariance Operators in Functional Samples. Scand Stat Theory Appl 2012. [DOI: 10.1111/j.1467-9469.2012.00796.x] [Citation(s) in RCA: 50] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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25
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Lian H. Convergence of nonparametric functional regression estimates with functional responses. Electron J Stat 2012. [DOI: 10.1214/12-ejs716] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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