Related papers: Exponential bounds for minimum contrast estimators
Strip-plot designs are very useful when the treatments have a factorial structure and the factors levels are hard-to-change. We develop a randomization-based theory of causal inference from such designs in a potential outcomes framework.…
We obtain non-asymptotic Gaussian concentration bounds for the difference between the invariant measure $\nu$ of an ergodic Brownian diffusion process and the empirical distribution of an approximating scheme with decreasing time step along…
This paper develops nonasymptotic information inequalities for the estimation of the eigenspaces of a covariance operator. These results generalize previous lower bounds for the spiked covariance model, and they show that recent upper…
We consider the problem of estimating the structural function in nonparametric instrumental regression, where in the presence of an instrument W a response Y is modeled in dependence of an endogenous explanatory variable Z. The proposed…
Bounds on the exchange-correlation energy of many-electron systems are derived and tested. By using universal scaling properties of the electron-electron interaction, we obtain the exponent of the bounds in three, two, one, and quasi-one…
The reconstruction problem in electrical impedance tomography is highly ill-posed, and it is often observed numerically that reconstructions have poor resolution far away from the measurement boundary but better resolution near the…
We develop novel empirical Bernstein inequalities for the variance of bounded random variables. Our inequalities hold under constant conditional variance and mean, without further assumptions like independence or identical distribution of…
We survey a few concentration inequalities for submodular and fractionally subadditive functions of independent random variables, implied by the entropy method for self-bounding functions. The power of these concentration bounds is that…
The ill-posedness of the inverse problem of recovering a regression function in a nonparametric instrumental variable model leads to estimators that may suffer from a very slow, logarithmic rate of convergence. In this paper, we show that…
Unmeasured confounding, selection bias, and measurement error are well-known sources of bias in epidemiologic research. Methods for assessing these biases have their own limitations. Many quantitative sensitivity analysis approaches…
Weighting methods are widely used to adjust for covariates in observational studies, sample surveys, and regression settings. In this paper, we study a class of recently proposed weighting methods which find the weights of minimum…
We establish some new non-asymptotical lower bounds for deviation of regular unbiased estimation of unknown parameter from its true value in different norms, alike the classical Rao-Kramer's inequality. We show that if the new norm is…
In extreme value theory and other related risk analysis fields, probability weighted moments (PWM) have been frequently used to estimate the parameters of classical extreme value distributions. This method-of-moment technique can be applied…
We provide new non-asymptotic false discovery proportion (FDP) confidence envelopes in several multiple testing settings relevant for modern high dimensional-data methods. We revisit the multiple testing scenarios considered in the recent…
Many recent works have shown that adversarial examples that fool classifiers can be found by minimally perturbing a normal input. Recent theoretical results, starting with Gilmer et al. (2018b), show that if the inputs are drawn from a…
We study the behavior of linear discriminant functions for binary classification in the infinite-imbalance limit, where the sample size of one class grows without bound while the sample size of the other remains fixed. The coefficients of…
Biased stochastic estimators, such as finite-differences for noisy gradient estimation, often contain parameters that need to be properly chosen to balance impacts from the bias and the variance. While the optimal order of these parameters…
We provide an upper bound as a random variable for the functions of estimators in high dimensions. This upper bound may help establish the rate of convergence of functions in high dimensions. The upper bound random variable may converge…
Estimates are constructed for the deviation of the concentration functions of sums of independent random variables with finite variances from the folded normal distribution function without any assumptions concerning the existence of the…
In this paper, we consider the nonparametric regression problem with multivariate predictors. We provide a characterization of the degrees of freedom and divergence for estimators of the unknown regression function, which are obtained as…