Functional CLT for nonparametric estimates of the spectrum and change- point problem for a spectral function

DOI10.1007/BF00970826zbMath0761.62123MaRDI QIDQ1174048

Liudas Giraitis, Remigijus Leipus

Publication date: 25 June 1992

Published in: Lithuanian Mathematical Journal (Search for Journal in Brave)

zbMATH Keywords

functional central limit theoremchange-point problemspectral statisticsSkorokhod space of two-parameter functionsstationary moving average sequencestatistics of Kolmogorov-Smirnov type

Mathematics Subject Classification ID

Density estimation (62G07) Inference from stochastic processes and spectral analysis (62M15) Functional limit theorems; invariance principles (60F17)

Related Items

Nonparametric functionals of spectral distributions and their applications to time series analy\-sis, The integrated periodogram for long-memory processes with finite or infinite variance, Serial rank statistics for detection of changes., Detection of multiple change-points in multivariate time series, Change in autoregressive processes, On parameter estimation for locally stationary long-memory processes, Gaussian limit fields for the integrated periodogram, Testing and estimating in the change-point problem of the spectral function

Cites Work

• A functional limit theorem for tapered empirical spectral functions
• Central limit theorems for quadratic forms in random variables having long-range dependence
• On bilinear forms in Gaussian random variables and Toeplitz matrices
• Testing that a Gaussian process is stationary
• Empirical spectral processes and their applications to time series analysis
• Nonparametric statistical procedures for the changepoint problem
• A central limit theorem for quadratic forms in strongly dependent linear variables and its application to asymptotical normality of Whittle's estimate
• Testing and estimating change-points in time series
• Retrospective and sequential tests for a change in distribution based on kolmogorov-smirnov-type statistics
• Asymptotic properties of spectral estimates of second order
• Limit Processes for Co-Spectral and Quadrature Spectral Distribution Functions
• On Weak Convergence of Stochastic Processes with Multidimensional Time Parameter
• Convergence Criteria for Multiparameter Stochastic Processes and Some Applications
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