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Nonparametric Inferences on Conditional Quantile Processes


  • Chuan Goh


This paper is concerned with tests of restrictions on the sample path of conditional quantile processes. These tests are tantamount to assessments of lack of fit for models of conditional quantile functions or more generally as tests of how certain covariates affect the distribution of an outcome variable of interest. This paper extends tests of the generalized likelihood ratio (GLR) type as introduced by Fan, Zhang and Zhang (2001) to nonparametric inference problems regarding conditional quantile processes. As such, the tests proposed here present viable alternatives to existing methods based on the Khmaladze (1981, 1988) martingale transformation. The range of inference problems that may be addressed by the methods proposed here is wide, and includes tests of nonparametric nulls against nonparametric alternatives as well as tests of parametric specifications against nonparametric alternatives. In particular, it is shown that a class of GLR statistics based on nonparametric additive quantile regressions have pivotal asymptotic distributions given by the suprema of squares of Bessel processes, as in Hawkins (1987) and Andrews (1993). The tests proposed here are also shown to be asymptotically rate-optimal for nonparametric hypothesis testing according to the formulations of Ingster (1993) and of Spokoiny (1996).

Suggested Citation

  • Chuan Goh, 2007. "Nonparametric Inferences on Conditional Quantile Processes," Working Papers tecipa-277, University of Toronto, Department of Economics.
  • Handle: RePEc:tor:tecipa:tecipa-277

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    quantile regression; nonparametric inference; minimax rate; additive models; local polynomials; generalized likelihood ratio;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models

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