For the Bickel-Rosenblatt goodness-of-fit test with fixed bandwidth studied by Fan (1998) we derive its Bahadur exact slopes in a neighbourhood of a simple hypothesis f = f and we use them to get a better understanding on the role played by the smoothing parameter in the detection of departures from the null hypothesis. When f is an univariate normal distribution and we take for kernel the standard normal density function, we compute these slopes for a set of Edgeworth alternatives which give us...
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