High-breakdown-point regression estimators protect against large errors and data contamination. We generalize the concept of trimming used by many of these robust estimators, such as the least trimmed squares and maximum trimmed likelihood, and propose a general trimmed estimator, which renders...

This paper proposes a nonparametric test of Granger causality in quantile. Zheng (1998, <italic>Econometric Theory</italic> 14, 123–138) studied the idea to reduce the problem of testing a quantile restriction to a problem of testing a particular type of mean restriction in independent data. We extend...

Let (<italic>X</italic>₁, <italic>Y</italic>₁), …, (<italic>X</italic>, <italic>Y</italic>) be independent and identically distributed random variables and let <italic>l</italic>(<italic>x</italic>) be the unknown <italic>p</italic>-quantile regression curve of <italic>Y</italic> conditional on <italic>X</italic>. A quantile smoother <italic>l</italic>(<italic>x</italic>) is a localized, nonlinear estimator of <italic>l</italic>(<italic>x</italic>). The strong uniform consistency rate is established under...

This paper describes a method for testing a parametric model of the mean of a random variable <italic>Y</italic> conditional on a vector of explanatory variables <italic>X</italic> against a semiparametric alternative. The test is motivated by a conditional moment test against a parametric alternative and amounts to replacing...

Positive definiteness of income effect matrices provides a sufficient condition for the <italic>law of demand</italic> to hold. Given cross section household expenditure data, empirical evidence for the law of demand can be obtained by estimating such matrices. Härdle, Hildenbrand, and Jerison used the...