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A simple consistent test of conditional symmetry in symmetrically trimmed tobit models


  • Tao Chen

    () (Department of Economics, University of Waterloo, Ontario, Canada)

  • Gautam Tripathi

    () (CREA, Université du Luxembourg)


We propose a "weighted and sample-size adjusted" Kolmogorov-Smirnov type statistic to test the assumption of conditional symmetry maintained in the symmetrically trimmed least-squares (STLS) approach of Powell (1986b), which is widely used to estimate censored or truncated regression models without making distributional assumptions. The statistic proposed here is consistent and computationally easy to implement because, unlike traditional Kolmogorov-Smirnov statistics, it is not optimized over an uncountable set. Moreover, it does not require any nonparametric smoothing, although we test the validity of a conditional feature. We also propose a bootstrap procedure to obtain the p-values and critical values that are required to carry out the test in practical applications. Results from a simulation study suggest that our test can work very well even in small to moderately sized samples. As an empirical illustration, we apply our test to two datasets that have been used in the literature to estimate censored regression models using Powell's STLS approach, to check whether the assumption of conditional symmetry is supported by these datasets.

Suggested Citation

  • Tao Chen & Gautam Tripathi, 2014. "A simple consistent test of conditional symmetry in symmetrically trimmed tobit models," CREA Discussion Paper Series 14-04, Center for Research in Economic Analysis, University of Luxembourg.
  • Handle: RePEc:luc:wpaper:14-04

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    4. Tao Chen & Gautam Tripathi, 2013. "Testing conditional symmetry without smoothing," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 25(2), pages 273-313, June.
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    11. Santos Silva, J M C, 2001. "Influence Diagnostics and Estimation Algorithms for Powell's SCLS," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(1), pages 55-62, January.
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