Related papers: Moderate deviations for a nonparametric estimator …
Measurement error is a pervasive issue which renders the results of an analysis unreliable. The measurement error literature contains numerous correction techniques, which can be broadly divided into those which aim to produce exactly…
The delta method is a popular and elementary tool for deriving limiting distributions of transformed statistics, while applications of asymptotic distributions do not allow one to obtain desirable accuracy of approximation for tail…
Uniform deviation bounds limit the difference between a model's expected loss and its loss on an empirical sample uniformly for all models in a learning problem. As such, they are a critical component to empirical risk minimization. In this…
We give an improved estimate for the regularity of the conditional distribution of the empiric mean of a finite sample of IID random variables, conditional on the sample "fluctuations", extending the well-known property of Gaussian IID…
Consider the state space model (X_t,Y_t), where (X_t) is a Markov chain, and (Y_t) are the observations. In order to solve the so-called filtering problem, one has to compute L(X_t|Y_1,...,Y_t), the law of X_t given the observations…
The brilliant method due to Good and Turing allows for estimating objects not occurring in a sample. The problem, known under names "sample coverage" or "missing mass" goes back to their cryptographic work during WWII, but over years has…
In survey sampling, survey data do not necessarily represent the target population, and the samples are often biased. However, information on the survey weights aids in the elimination of selection bias. The Horvitz-Thompson estimator is a…
We consider the set M_n of all n-truncated power moment sequences of probability measures on [0,1]. We endow this set with the uniform probability. Picking randomly a point in M_n, we show that the upper canonical measure associated with…
We consider high-dimensional estimation problems where the number of parameters diverges with the sample size. General conditions are established for consistency, uniqueness, and asymptotic normality in both unpenalized and penalized…
We study the problem of robust mean estimation and introduce a novel Hamming distance-based measure of distribution shift for coordinate-level corruptions. We show that this measure yields adversary models that capture more realistic…
Recent research has shown that interval estimators with good coverage properties are achievable for some functions of quantiles, even when sample sizes are not large. Motivated by this, we consider interval estimators for the ratios of…
Variance estimation is important for statistical inference. It becomes non-trivial when observations are masked by serial dependence structures and time-varying mean structures. Existing methods either ignore or sub-optimally handle these…
This paper proposes a decorrelation-based approach to test hypotheses and construct confidence intervals for the low dimensional component of high dimensional proportional hazards models. Motivated by the geometric projection principle, we…
This paper addresses the problem of measurement errors in causal inference and highlights several algebraic and graphical methods for eliminating systematic bias induced by such errors. In particulars, the paper discusses the control of…
The problem of f-divergence estimation is important in the fields of machine learning, information theory, and statistics. While several nonparametric divergence estimators exist, relatively few have known convergence properties. In…
This note points out how confidence interval estimates for standard deviation transform into confidence interval estimates for the power of F-tests at fixed alternative means. An application is shown for the test of a two-sided hypothesis…
We develop a systematic, omnibus approach to goodness-of-fit testing for parametric distributional models when the variable of interest is only partially observed due to censoring and/or truncation. In many such designs, tests based on the…
Given additional distributional information in the form of moment restrictions, kernel density and distribution function estimators with implied generalised empirical likelihood probabilities as weights achieve a reduction in variance due…
We investigate the accuracy of the two most common estimators for the maximum expected value of a general set of random variables: a generalization of the maximum sample average, and cross validation. No unbiased estimator exists and we…
There exist some testing procedures based on the maximum mean discrepancy (MMD) to address the challenge of model specification. However, they ignore the presence of estimated parameters in the case of composite null hypotheses. In this…