One purpose of this article is to establish results on the rate of almost everywhere convergence of approximation processes of convolution type in L(R), where instead of a particular rate (like t, μ > 0, t → 0+) fractional moduli of smoothness are employed. An essential tool is a modified K-functional. Away from saturation orders these results are nearly optimal. A second purpose is to illustra...

One of the key identifying assumptions for regression discontinuity (RD) designs is the local independence assumption (LIA). This paper shows that LIA puts a restriction on treatment effect heterogeneity and hence may not hold in many empirical applications. This paper then shows that LATE in both sharp and fuzzy designs can be identified under alternative smoothness conditions, and that the re...

We address the problem of estimating the value of a linear functional h f , xi from random noisy observations of y 1⁄4 Ax in Hilbert scales. Both the white noise and density observation models are considered. We propose an estimation procedure that adapts to unknown smoothness of x, of f , and of the noise covariance operator. It is shown that accuracy of this adaptive estimator is worse only b...

We consider a non-local operator L associated to a Markov process with jumps, we stop this process when it quits a domain D, and we study the C smoothness on D of the functions which are harmonic for the stopped process. A previous work was devoted to the existence of a C∞ transition density; here, the smoothness of harmonic functions is deduced by applying a duality method and by estimating th...

The statistics of failure of the hydraulic-burst (HB) test were compared with those of the ball-on-ring (BOR) test. Polycrystalline Al2O3 tape-cast specimens, both square and circular, in two different sizes, were tested. Both the mean strengths and the Weibull moduli from the BOR tests were approximately twice the values from the HB tests. The area (volume) under stress is much larger for the ...

Via a random construction we establish necessary conditions for L(l) inequalities for certain families of operators arising in harmonic analysis. In particular we consider dilates of a convolution kernel with compactly supported Fourier transform, vector maximal functions acting on classes of entire functions of exponential type, and a characterization of Sobolev spaces by square functions and ...

In this paper, we summarize results on convergence rates of various kernel based non- and semiparametric estimators, focusing the impact insufficient distributional smoothness, possibly unknown smoothness even non-existence density. presence a possible lack uncertainty about methods safeguarding against are surveyed with emphasis nonconvex model averaging. This approach can be implemented via c...