9 problems

Let the conditions of the stability theorem hold, but now for block sizes $n_i$ that are not necessarily equal. Define the mean block size and variance by … If the relative standar…

Let $f$ be a density on the sphere, and let $n$ denote the sample size. A bandwidth is non-degenerate if it is strictly positive and minimizes the mean integrated squared error. No…

Li–Racine conjecture. The associated optimal bandwidth should diverge to infinity.

The setting is local polynomial regression for spatial data on $\mathbb{R}^d$, with bandwidths chosen for estimating the regression function and its derivatives from spatially depe…

Let ${\rm CL}$ denote the cross-validation criterion used for bandwidth selection, let $p$ be the moment parameter in the assumptions, and let asymptotic optimality (a.o.) mean the…

Let $k$ denote the bandwidth parameter, let $\widehat{d}_j^{(k)}$ be the estimated residual variance associated with bandwidth $k$, and consider the prior…

Bandwidth-normality conjecture. The normalized bandwidth error

Honesty conjecture. For any $M$, the resulting confidence interval is asymptotically honest over the intersection of $\mathcal{F}({M})$ and that appropriately defined set of regres…

The paper studies kernel estimators for a time-varying regression function with locally stationary covariates. In particular, its asymptotic theory gives bias and variance expressi…