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Quantifying the urbanization effect on trends in climate extremes is important both for detection and attribution studies and for human adaptation; however, a fundamental problem is how to accurately estimate a trend and its statistical significance, especially for non-Gaussian and serially dependent data. In this paper, the choice of trend estimation and significance testing method is suggested as important for these kinds of studies, as illustrated by quantifying the urbanization effect on trends in seven hot-extreme indices for the megacity of Shanghai during 1961-2013. Both linear and nonlinear trend estimation methods were used. The trends and corresponding statistical significances were estimated by taking into account potential non-Gaussian and serial dependence in the extreme indices. A new method based on adaptive surrogate data is proposed to test the statistical significance of the ensemble empirical mode decomposition (EEMD) nonlinear trend. The urbanization contribution was found to be approximately 34 % (43 %) for the trend in the non-Gaussian distributed heat wave index based on nonparametric linear trend (EEMD nonlinear trend) estimation. For some of the other six hot-extreme indices analyzed, the urbanization contributions estimated based on linear and nonlinear trends varied greatly, with as much as a twofold difference between them. For the linear trend estimation itself, the ordinary least squares fit can give a substantially biased estimation of the urbanization contribution for some of the non-Gaussian extreme indices. [ABSTRACT FROM AUTHOR]