Author

P. Aronow

h-index 1 View on Semantic Scholar

We have 2 of 5 papers

We haven’t gathered this author’s papers yet. Follow them and we’ll fetch their work.

Not the right person? Other researchers publish under this name.

Preprint Aug 2026

Adaptive Confidence Sets for Binary Regression without Design Smoothness

We study honest adaptive confidence sets for the regression function in random-design binary regression under $L^2(dx)$ loss. Assuming only known bounds $0<c\leq g\leq C<\infty$ on the unknown design density, we construct asymptotically honest, rate-adaptive confidence sets without requiring $g$ to be smooth. Full adaptation is possible when the range of regression-function smoothness spans at most a factor of two. Over wider smoothness ranges, adaptation is achieved on the usual separated classes at the corresponding testing rates $n^{-2s/(4s+d)}$. A lower bound under the uniform design shows that these separation rates are rate-optimal. This answers a question raised by Mukherjee and Sen (2018).

P. Aronow, P. Lopatto · 0 citations

Preprint Jul 2026

On Rates Attainable under Random Design: A Negative Answer to a Problem of Robins

We give a negative answer to a problem posed by James Robins on estimating a constant conditional variance in nonparametric regression under random design. For every $s>1$ and integer $d>4s$, when the regression function is $s$-H\"older, the unknown design density is bounded above and away from zero, and the conditional error laws may depend on the design but have mean zero, a common variance, and uniformly bounded fourth moments, we show that the minimax root-mean-square risk is bounded below by $n^{-\beta}$ with $\beta=\frac{d(3s+1)+8s}{(d+2s)(d+4)}$. Hence the conjectured rate $n^{-4s/(d+4s)}$ is not uniformly attainable. We use a similar argument to establish the minimax rate $n^{-1/2}\vee n^{-4s/(d+4s)}$ when $s \in (0,1]$.

P. Aronow, P. Lopatto · 0 citations