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In this paper we propose a new test of heteroscedasticity for parametricregression models and partial linear regression models in high dimensionalsettings. When the dimension of covariates is large, existing tests ofheteroscedasticity perform badly due to the \curse of dimensionality". Toattack this problem, we construct a test of heteroscedasticity by using aprojection-based empirical process. We study the asymptotic properties of thetest statistic under the null hypothesis and alternative hypotheses. It isshown that the test can detect local alternatives departure from the nullhypothesis at the fastest possible rate in hypothesis testing. As the limitingnull distribution of the test statistic is not distribution free, we propose aresidual-based bootstrap. The validity of the bootstrap approximations isinvestigated. We present some simulation results to show the finite sampleperformances of the test. Two real data analyses are conducted forillustration.

Testing heteroscedasticity for regression models based on projections