The DOI matches its Crossref record; 25 of the 25 references it cites were found in a registry or an index.
Nonlinear system theory: Another look at dependence
Open accessAbstract
Based on the nonlinear system theory, we introduce previously undescribed dependence measures for stationary causal processes. Our physical and predictive dependence measures quantify the degree of dependence of outputs on inputs in physical systems. The proposed dependence measures provide a natural framework for a limit theory for stationary processes. In particular, under conditions with quite simple forms, we present limit theorems for partial sums, empirical processes, and kernel density estimates. The conditions are mild and easily verifiable because they are directly related to the data-generating mechanisms.
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Cites
An introduction to probability theory and its applications
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Engle, R. F. (1982) · Econometrica · doi:10.2307/1912773 · Cited by 20,795
Time Series Analysis: Forecasting and Control
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Remarks on Some Nonparametric Estimates of a Density Function
Rosenblatt, M. (1956) · The Annals of Mathematical Statistics · doi:10.1214/aoms/1177728190 · Cited by 4,547
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Non-linear time series. A dynamical system approach
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Non-linear Time Series: A Dynamical System Approach
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A CENTRAL LIMIT THEOREM AND A STRONG MIXING CONDITION
Rosenblatt, M. (1956) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.42.1.43 · Cited by 1,365
Cited by
Fairness in Criminal Justice Risk Assessments: The State of the Art
Berk, R., Heidari, H., Jabbari, S., Kearns, M., & Roth, A. (2021) · Sociological Methods & Research · doi:10.1177/0049124118782533 · Cited by 988
“The IID requirement can be relaxed somewhat (Rosenblatt 1956; Wu 2005).”
BackgroundRegularized estimation in sparse high-dimensional time series models
Basu, S., & Michailidis, G. (2015) · The Annals of Statistics · doi:10.1214/15-aos1315 · Cited by 345
Metadata
- Authors
- Wu, W. B.
- Venue
- Proceedings of the National Academy of Sciences
- Published
- 2005-09-22
- Volume
- 102
- Issue
- 40
- Pages
- 14150-14154
- ISSN
- 0027-8424 (ISSN-L)
- 1091-6490
- OpenAlex
- W2068019718
- Cited by
- 572
- References
- 25
- FWCI
- 11.13
- Type
- journal article
- Language
- en
- Open access
- green
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