Concepedia

Publication | Closed Access

On the Strong Mixing Property for Linear Sequences

211

Citations

4

References

1978

Year

Abstract

Previous article Next article On the Strong Mixing Property for Linear SequencesV. V. GorodetskiiV. V. Gorodetskiihttps://doi.org/10.1137/1122049PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] K. C. Chanda, Strong mixing properties of linear stochastic processes, J. Appl. Probability, 11 (1974), 401–408 MR0358951 0281.60033 CrossrefGoogle Scholar[2] I. A. Ibragimov and , Yu. A. Rozanov, Gaussian Random Processes, Nauka, Moscow, 1970, (In Russian.) Google Scholar[3] K. Yosida, Functional analysis, Die Grundlehren der Mathematischen Wissenschaften, Band 123, Academic Press Inc., New York, 1965xi+458 MR0180824 0126.11504 CrossrefGoogle Scholar[4] Bengt von Bahr and , Carl-Gustav Esseen, Inequalities for the rth absolute moment of a sum of random variables, $1\leq r\leq 2$, Ann. Math. Statist, 36 (1965), 299–303 MR0170407 0134.36902 CrossrefGoogle Scholar[5] S. V. Nagaev and , A. Kh. Fuk, Probability inequalities for sums of independent random variables, Theory Prob. Applications, 16 (1971), 643–660 10.1137/1116071 0259.60024 LinkGoogle Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails A Wasserstein-based measure of conditional dependenceBehaviormetrika, Vol. 49, No. 2 | 25 June 2022 Cross Ref Journal of Applied Statistics | 2022 Cross Ref The rate of complete consistency for recursive probability density estimator under strong mixing samplesStatistics & Probability Letters, Vol. vol. 85 | 1 Apr 2021 Cross Ref On the integral modulus of continuity of infinitely divisible distributions, especially of stochastic integralsJournal of Mathematical Analysis and Applications, Vol. 486, No. 1 | 1 Jun 2020 Cross Ref Minimum distance estimation in linear regression with strong mixing errorsCommunications in Statistics - Theory and Methods, Vol. 49, No. 6 | 23 January 2019 Cross Ref Berry-Esseen type bounds of the estimators in a semiparametric model under linear process errors with α -mixing dependent innovationsStatistics, Vol. 53, No. 5 | 10 June 2019 Cross Ref A rate of consistency for nonparametric estimators of the distribution function based on censored dependent dataStatistical Methods & Applications, Vol. 28, No. 2 | 13 November 2018 Cross Ref Hurwicz Estimator for Autoregressive Model with Generalized Error Distributed InnovationsJournal of the Indian Society for Probability and Statistics, Vol. 19, No. 2 | 23 May 2018 Cross Ref Uniformly strong consistency and Berry-Esseen bound of frequency polygons for α-mixing samplesCommunications in Statistics - Simulation and Computation, Vol. 11 | 3 October 2017 Cross Ref CONVERGENCE RATES OF SUMS OF α -MIXING TRIANGULAR ARRAYS: WITH AN APPLICATION TO NONPARAMETRIC DRIFT FUNCTION ESTIMATION OF CONTINUOUS-TIME PROCESSESEconometric Theory, Vol. 33, No. 5 | 3 October 2016 Cross Ref Asymptotic normality of numbers of observations near order statistics from stationary processesStatistics & Probability Letters, Vol. 119 | 1 Dec 2016 Cross Ref Functional coefficient seasonal time series models with an application of Hawaii tourism dataComputational Statistics, Vol. 30, No. 3 | 5 April 2015 Cross Ref Uniform Estimation and Inference of Time-Heterogeneous Panel Data Models with Interactive Fixed EffectsSSRN Electronic Journal | 1 Jan 2015 Cross Ref Bootstrapping the empirical distribution of a linear processStatistics & Probability Letters, Vol. 93 | 1 Oct 2014 Cross Ref Trimmed stable AR(1) processesStochastic Processes and their Applications, Vol. 124, No. 10 | 1 Oct 2014 Cross Ref Nonparametric regression ‐ TheoryWiley StatsRef: Statistics Reference Online | 29 September 2014 Cross Ref Marcinkiewicz–Zygmund and ordinary strong laws for empirical distribution functions and plug-in estimatorsStatistics, Vol. 48, No. 5 | 30 May 2013 Cross Ref ReferencesRecursive Identification and Parameter Estimation | 12 June 2014 Cross Ref Local polynomial quasi-likelihood regression with truncated and dependent dataStatistics, Vol. 47, No. 4 | 1 Aug 2013 Cross Ref BibliographyTime Series with Mixed Spectra | 20 June 2013 Cross Ref CAN Estimators from Dependent ObservationsStatistical Inference for Discrete Time Stochastic Processes | 5 October 2012 Cross Ref Asymptotic properties of conditional distribution estimator with truncated, censored and dependent dataTEST, Vol. 21, No. 4 | 19 January 2012 Cross Ref Asymptotic normality of wavelet density estimator under censored dependent observationsActa Mathematicae Applicatae Sinica, English Series, Vol. 28, No. 4 | 21 November 2012 Cross Ref On spatial processes and asymptotic inference under near-epoch dependenceJournal of Econometrics, Vol. 170, No. 1 | 1 Sep 2012 Cross Ref Asymptotic Normality of Estimators in Heteroscedastic Semi-Parametric Model with Strong Mixing ErrorsCommunications in Statistics - Theory and Methods, Vol. 41, No. 12 | 15 Jun 2012 Cross Ref Comments on “Unbiased estimates for moments and cumulants in linear regression”Journal of Statistical Planning and Inference, Vol. 142, No. 4 | 1 Apr 2012 Cross Ref Nonparametric spatial regression under near-epoch dependenceJournal of Econometrics, Vol. 167, No. 1 | 1 Mar 2012 Cross Ref A note on the Bahadur representation of sample quantiles for α-mixing random variablesMonatshefte für Mathematik, Vol. 165, No. 3-4 | 11 August 2011 Cross Ref Berry–Esseen type bounds in heteroscedastic semi-parametric modelJournal of Statistical Planning and Inference, Vol. 141, No. 11 | 1 Nov 2011 Cross Ref Local polynomial estimation of a conditional mean function with dependent truncated dataTEST, Vol. 20, No. 3 | 10 February 2011 Cross Ref Nonparametric estimation for dependent dataJournal of Nonparametric Statistics, Vol. 23, No. 3 | 1 Sep 2011 Cross Ref The estimation of the correlation coefficient of bivariate data under dependence: Convergence analysisStatistics & Probability Letters, Vol. 81, No. 8 | 1 Aug 2011 Cross Ref NONLINEAR WAVELET DENSITY ESTIMATION FOR TRUNCATED AND DEPENDENT OBSERVATIONSInternational Journal of Wavelets, Multiresolution and Information Processing, Vol. 09, No. 04 | 21 November 2011 Cross Ref Asymptotic normality of variance estimator in a heteroscedastic model with dependent errorsJournal of Nonparametric Statistics, Vol. 23, No. 2 | 1 Jun 2011 Cross Ref Asymptotic Properties of Conditional Quantile Estimator Under Left-Truncated and α-Mixing ConditionsCommunications in Statistics - Theory and Methods, Vol. 40, No. 14 | 22 Apr 2011 Cross Ref Asymptotic Normality for Regression Function Estimate Under Truncation and α-Mixing ConditionsCommunications in Statistics - Theory and Methods, Vol. 40, No. 11 | 15 Apr 2011 Cross Ref Wavelet estimation of conditional density with truncated, censored and dependent dataJournal of Multivariate Analysis, Vol. 102, No. 3 | 1 Mar 2011 Cross Ref Unbiased Efficient Estimator of the Fourth-Order Cumulant for Random Zero-Mean Non-i.i.d. Signals: Particular Case of MA Stochastic ProcessIEEE Transactions on Information Theory, Vol. 56, No. 12 | 1 Dec 2010 Cross Ref ON TAIL INDEX ESTIMATION FOR DEPENDENT, HETEROGENEOUS DATAEconometric Theory, Vol. 26, No. 5 | 17 February 2010 Cross Ref Stationarity and mixing properties of the dynamic Tobit modelEconomics Letters, Vol. 107, No. 2 | 1 May 2010 Cross Ref Asymptotic normality and Berry–Esseen results for conditional density estimator with censored and dependent dataJournal of Multivariate Analysis, Vol. 101, No. 5 | 1 May 2010 Cross Ref The Estimation of the Fourth-Order Cumulant for Dependent Data: Consistency and Asymptotic NormalityIEEE Transactions on Signal Processing, Vol. 58, No. 4 | 1 Apr 2010 Cross Ref On Mixing Conditions for Sequences of Moving AveragesTheory of Probability & Its Applications, Vol. 54, No. 2 | 21 May 2010AbstractPDF (175 KB)Testing for changes in the covariance structure of linear processesJournal of Statistical Planning and Inference, Vol. 139, No. 6 | 1 Jun 2009 Cross Ref Strong law of large numbers for pairwise positive quadrant dependent random variablesStatistical Inference for Stochastic Processes, Vol. 12, No. 1 | 23 April 2008 Cross Ref Estimation of a tail index based on minimum density power divergenceJournal of Multivariate Analysis, Vol. 99, No. 10 | 1 Nov 2008 Cross Ref Monitoring shifts in mean: Asymptotic normality of stopping timesTEST, Vol. 17, No. 3 | 27 February 2007 Cross Ref The notion of ψ-weak dependence and its applications to bootstrapping time seriesProbability Surveys, Vol. 5, No. none | 1 Jan 2008 Cross Ref Asymptotic distribution of the cointegrating vector estimator in error correction models with conditional heteroskedasticityJournal of Econometrics, Vol. 137, No. 1 | 1 Mar 2007 Cross Ref LOCAL LINEAR FITTING UNDER NEAR EPOCH DEPENDENCEEconometric Theory, Vol. 23, No. 01 | 6 December 2006 Cross Ref Sampling Properties of U-statistics for a Class of Stationary Nonlinear ProcessesAnnals of the Institute of Statistical Mathematics, Vol. 58, No. 3 | 11 May 2006 Cross Ref Nonparametric RegressionEncyclopedia of Statistical Sciences | 15 August 2006 Cross Ref UNIT ROOT TESTING FOR FUNCTIONALS OF LINEAR PROCESSESEconometric Theory, Vol. 22, No. 01 | 12 December 2005 Cross Ref A parametric bootstrap test for cyclesJournal of Econometrics, Vol. 129, No. 1-2 | 1 Nov 2005 Cross Ref Kernel density estimator for strong mixing processesJournal of Statistical Planning and Inference, Vol. 133, No. 2 | 1 Aug 2005 Cross Ref Nonparametric estimation of time varying parameters under shape restrictionsJournal of Econometrics, Vol. 126, No. 1 | 1 May 2005 Cross Ref Asymptotic properties of density estimates for linear processes: application of projection methodJournal of Nonparametric Statistics, Vol. 17, No. 1 | 1 Jan 2005 Cross Ref Cusum Test for Parameter Change Based on the Maximum Likelihood EstimatorSequential Analysis, Vol. 23, No. 2 | 31 Dec 2004 Cross Ref Local M-estimator for nonparametric time seriesStatistics & Probability Letters, Vol. 65, No. 4 | 1 Dec 2003 Cross Ref Deconvolving multivariate kernel density estimates from contaminated associated observationsIEEE Transactions on Information Theory, Vol. 49, No. 11 | 1 Nov 2003 Cross Ref On the cusum of squares test for variance change in nonstationary and nonparametric time series modelsAnnals of the Institute of Statistical Mathematics, Vol. 55, No. 3 | 1 Sep 2003 Cross Ref Local polynomial fitting under associationJournal of Multivariate Analysis, Vol. 86, No. 2 | 1 Aug 2003 Cross Ref An empirical likelihood goodness-of-fit test for time seriesJournal of the Royal Statistical Society: Series B (Statistical Methodology), Vol. 65, No. 3 | 8 July 2003 Cross Ref Nonparametric estimation equations for time series dataStatistics & Probability Letters, Vol. 62, No. 4 | 1 May 2003 Cross Ref The sequential estimation in stochastic regression model with random coefficientsStatistics & Probability Letters, Vol. 61, No. 1 | 1 Jan 2003 Cross Ref Geometric absolute regularity of Banach space-valued autoregressive processesStatistics & Probability Letters, Vol. 60, No. 3 | 1 Dec 2002 Cross Ref Kernel density estimation for linear processesThe Annals of Statistics, Vol. 30, No. 5 | 1 Oct 2002 Cross Ref Some Aspects of Statistical Inference in a Markovian and Mixing FrameworkModeling Uncertainty | 1 Jan 2002 Cross Ref Estimating a Distribution Function for Censored Time Series DataJournal of Multivariate Analysis, Vol. 78, No. 2 | 1 Aug 2001 Cross Ref Propriétés de mélanges des processus autorégressifs banachiquesComptes Rendus de l'Académie des Sciences - Series I - Mathematics, Vol. 333, No. 4 | 1 Aug 2001 Cross Ref Average Regression Surface for Dependent DataJournal of Multivariate Analysis, Vol. 75, No. 1 | 1 Oct 2000 Cross Ref Functional-Coefficient Regression Models for Nonlinear Time SeriesJournal of the American Statistical Association, Vol. 95, No. 451 | 1 Sep 2000 Cross Ref On the Asymptotic Distributions of Partial Sums of Functionals of Infinite-Variance Moving AveragesThe Annals of Probability, Vol. 27, No. 3 | 1 Jul 1999 Cross Ref A consistent nonparametric test for serial independenceJournal of Econometrics, Vol. 84, No. 2 | 1 Jun 1998 Cross Ref Functional estimation for time series: Uniform convergence propertiesJournal of Statistical Planning and Inference, Vol. 68, No. 1 | 1 May 1998 Cross Ref The asymptotic behavior of the empirical process based on a linear process under some contiguous alternativesJournal of Statistical Planning and Inference, Vol. 67, No. 1 | 1 Mar 1998 Cross Ref Limit theorems for functionals of moving averagesThe Annals of Probability, Vol. 25, No. 4 | 1 Oct 1997 Cross Ref Nonparametric estimation of density derivatives of dependent dataJournal of Statistical Planning and Inference, Vol. 61, No. 1 | 1 May 1997 Cross Ref Frequency polygons for weakly dependent processesStatistics & Probability Letters, Vol. 33, No. 1 | 1 Apr 1997 Cross Ref Asymptotic behavior of hill's estimator for autoregressive dataCommunications in Statistics. Stochastic Models, Vol. 13, No. 4 | 1 Jan 1997 Cross Ref An outlier test for linear processes — II. Large contaminationMetrika, Vol. 43, No. 1 | 1 Dec 1996 Cross Ref Kernel density estimation for linear processes: Asymptotic normality and optimal bandwidth derivationAnnals of the Institute of Statistical Mathematics, Vol. 48, No. 3 | 1 Sep 1996 Cross Ref On histograms for linear processesJournal of Statistical Planning and Inference, Vol. 53, No. 3 | 1 Aug 1996 Cross Ref Fixed-design regression for linear time seriesThe Annals of Statistics, Vol. 24, No. 3 | 1 Jun 1996 Cross Ref Nuisance parameter free properties of correlation integral based statisticsEconometric Reviews, Vol. 15, No. 3 | 1 Jan 1996 Cross Ref Kernel density estimation for random fields: The L1 TheoryJournal of Nonparametric Statistics, Vol. 6, No. 2-3 | 1 Jan 1996 Cross Ref Strong approximation for cross-covariances of linear variables with long-range dependenceStochastic Processes and their Applications, Vol. 60, No. 2 | 1 Dec 1995 Cross Ref A trimmed mean of location of an AR(∞) stationary processJournal of Statistical Planning and Inference, Vol. 48, No. 2 | 1 Nov 1995 Cross Ref SEMIPARAMETRIC TIME SERIES REGRESSIONJournal of Time Series Analysis, Vol. 15, No. 4 | 1 Jul 1994 Cross Ref Conditional empirical, quantile and difference processes for a large class of time series with applicationsJournal of Statistical Planning and Inference, Vol. 40, No. 1 | 1 Jun 1994 Cross Ref Nonparametric time series regressionAnnals of the Institute of Statistical Mathematics, Vol. 46, No. 2 | 1 Jun 1994 Cross Ref Nonparametric prediction for random fieldsStochastic Processes and their Applications, Vol. 48, No. 1 | 1 Oct 1993 Cross Ref Kernel density estimation for linear processesStochastic Processes and their Applications, Vol. 41, No. 2 | 1 Jun 1992 Cross Ref KERNEL REGRESSION SMOOTHING OF TIME SERIESJournal of Time Series Analysis, Vol. 13, No. 3 | 1 May 1992 Cross Ref Fixed design regression for time series: Asymptotic normalityJournal of Multivariate Analysis, Vol. 40, No. 2 | 1 Feb 1992 Cross Ref Joint asymptotic normality of kernel estimates under dependence conditions, with application to hazard rateJournal of Nonparametric Statistics, Vol. 1, No. 4 | 1 Jan 1992 Cross Ref On multivariate variable-kernel density estimates for time seriesCanadian Journal of Statistics, Vol. 19, No. 4 | 1 Dec 1991 Cross Ref Study of Risks of Kernel EstimatorsTheory of Probability & Its Applications, Vol. 35, No. 3 | 17 July 2006AbstractPDF (808 KB)Basic structure of the asymptotic theory in dynamic nonlineaerco nometric models, part i: consistency and approximation conceptsEconometric Reviews, Vol. 10, No. 2 | 21 March 2007 Cross Ref Kernel Density Estimation under a Locally Mixing ConditionNonparametric Functional Estimation and Related Topics | 1 Jan 1991 Cross Ref L1 Strong Consistency for Density Estimates in Dependent SamplesNonparametric Functional Estimation and Related Topics | 1 Jan 1991 Cross Ref Some stochastic inequalities and asymptotic normality of serial rank statistics in general linear processesJournal of Statistical Planning and Inference, Vol. 25, No. 1 | 1 May 1990 Cross Ref GENERAL LINEAR PROCESSES:A PROPERTY OF THE EMPIRICAL PROCESS APPLIED TO DENSITY AND MODE ESTIMATIONJournal of Time Series Analysis, Vol. 11, No. 3 | 1 May 1990 Cross Ref Rank statistics for serial dependenceJournal of Statistical Planning and Inference, Vol. 24, No. 2 | 1 Feb 1990 Cross Ref Kernel estimation of the survival function and hazard rate under weak dependenceJournal of Statistical Planning and Inference, Vol. 24, No. 2 | 1 Feb 1990 Cross Ref Strong representations for LAD estimators in linear modelsProbability Theory and Related Fields, Vol. 83, No. 4 | 1 Dec 1989 Cross Ref Recursive density estimation under dependenceIEEE Transactions on Information Theory, Vol. 35, No. 5 | 1 Sep 1989 Cross Ref Recursive estimators for stationary, strong mixing processes—a representation theorem and asymptotic distributionsStochastic Processes and their Applications, Vol. 31, No. 2 | 1 Apr 1989 Cross Ref Mixing properties of ARMA processesStochastic Processes and their Applications, Vol. 29, No. 2 | 1 Sep 1988 Cross Ref Least Squares Regression with Integrated or Dynamic Regressors under Weak Error AssumptionsEconometric Theory, Vol. 3, No. 1 | 11 February 2009 Cross Ref Moment inequalities for mixing sequences of random variablesStochastic Analysis and Applications, Vol. 5, No. 1 | 1 Jan 1987 Cross Ref Some mixing properties of time series modelsStochastic Processes and their Applications, Vol. 19, No. 2 | 1 Apr 1985 Cross Ref Central Limit Theorems for dependent variables. IZeitschrift f�r Wahrscheinlichkeitstheorie und Verwandte Gebiete, Vol. 57, No. 4 | 1 Dec 1981 Cross Ref Conditions for linear processes to be strong-mixingZeitschrift f�r Wahrscheinlichkeitstheorie und Verwandte Gebiete, Vol. 57, No. 4 | 1 Dec 1981 Cross Ref Chi-Square Goodness-of-Fit Tests Based on Dependent ObservationsStatistical Distributions in Scientific Work | 1 Jan 1981 Cross Ref Flexible Seasonal Time Series ModelsEconometric Analysis of Financial and Economic Time Series Cross Ref Volume 22, Issue 2| 1978Theory of Probability & Its Applications203-432 History Submitted:12 June 1975Published online:17 July 2006 InformationCopyright © 1978 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1122049Article page range:pp. 411-413ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics

References

YearCitations

Page 1