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The vertical distance between the actual value of y and the estimated value of y. In other words, it measures the vertical distance between the actual data point and the predicted point on the line
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A Method of Trigonometric Modelling of Seasonal Variation Demonstrated with Multiple Sclerosis Relapse Data
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Local Composite Quantile Regression Smoothing for Harris Recurrent Markov Processes.

Degui Li1, Runze Li2

  • 1Department of Mathematics, University of York, York, YO10 5DD, UK. degui.li@york.ac.uk.

Journal of Econometrics
|September 27, 2016
PubMed
Summary

This study introduces a robust local polynomial composite quantile regression (CQR) method for nonlinear models, extending analysis to nonstationary Markov chains. The research establishes theoretical guarantees and proposes efficiency improvements for this advanced smoothing technique.

Keywords:
Asymptotic theoryHarris recurrent Markov processbandwidth selectioncomposite quantile regressionlocal polynomial smoothingβ-null recurrence

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Area of Science:

  • Statistics
  • Econometrics
  • Time Series Analysis

Background:

  • Local polynomial regression is a standard method for time series analysis.
  • Composite quantile regression (CQR) offers a robust alternative, particularly for stationary data.
  • Existing methods often assume stationarity, limiting applicability to more complex processes.

Purpose of the Study:

  • To extend the local polynomial composite quantile regression (CQR) method to nonlinear and nonparametric models.
  • To analyze the behavior of CQR under the general Harris recurrent Markov chain framework, including nonstationary cases.
  • To develop and evaluate robust and efficient estimation techniques for complex time series data.

Main Methods:

  • Application of local polynomial CQR smoothing.
  • Analysis within the Harris recurrent Markov chain framework.
  • Development of asymptotic theory for CQR estimators.
  • Introduction of a weighted CQR estimator and data-driven bandwidth selection.

Main Results:

  • Established asymptotic theory for the local polynomial CQR estimator under Harris recurrent Markov chains.
  • Demonstrated that convergence rates are slower for nonstationary cases compared to stationary ones.
  • Proposed a weighted CQR estimator for improved efficiency.
  • Introduced a data-driven method for optimal bandwidth selection.

Conclusions:

  • The local polynomial CQR method is effective for nonlinear models under general Markov chains.
  • The study provides a theoretical foundation for using CQR in nonstationary time series.
  • The proposed enhancements improve the practical applicability and efficiency of CQR methods.