Nonparametric test for the form of parametric regression with time series errors

Lan Wang, Ingrid Van Keilegom

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

Abstract

We propose a new nonparametric method for testing the parametric form of a regression function in the presence of time series errors. The test is motivated by recent advancement in the theory of ANOVA with large number of factor levels and also utilizes a new difference-based estimation method in nonparametric regression with time-series errors proposed by Hall and Van Keilegom (2003). The test statistic is asymptotically normal under the null and local alternative hypotheses. We also propose a bootstrap method to calculate the critical values and prove its consistency. In a Monte Carlo study, we demonstrate that this bootstrap procedure has good properties for moderate sample size.

Original languageEnglish (US)
Pages (from-to)369-386
Number of pages18
JournalStatistica Sinica
Volume17
Issue number1
StatePublished - Jan 1 2007

Keywords

  • Bootstrap
  • Correlated errors
  • Goodness-of-fit test
  • Lack-of-fit test
  • Nearest-neighbor windows
  • Nonparametric regression
  • Residual
  • Time-series errors
  • Trend

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