We study minimax estimation rates for a class of non-linear statistical inverse problems motivated by various applications, including density estimation, binary regression and spectral density estimation. We derive matching upper and lower bounds for pointwise loss using function-dependent rates that capture spatial heterogeneity of the function. The upper bound is obtained via a two-step procedure, where the first step inverts the non-linearity and is based on wavelet thresholding. The procedure is fully adaptive, both spatially and over modified Holder smoothness classes that are natural in this setting. This is joint work with Johannes Schmidt-Hieber.

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