Related papers: Hypotheses tests in boundary regression models
Traditional methods for linear regression generally assume that the underlying error distribution, equivalently the distribution of the responses, is normal. Yet, sometimes real life response data may exhibit a skewed pattern, and assuming…
We consider linear regression in the high-dimensional regime where the number of observations $n$ is smaller than the number of parameters $p$. A very successful approach in this setting uses $\ell_1$-penalized least squares (a.k.a. the…
Our main focus is on the generalization bound, which serves as an upper limit for the generalization error. Our analysis delves into regression and classification tasks separately to ensure a thorough examination. We assume the target…
We consider the asymptotic behavior of posterior distributions and Bayes estimators based on observations which are required to be neither independent nor identically distributed. We give general results on the rate of convergence of the…
This paper discusses two goodness-of-fit testing problems. The first problem pertains to fitting an error distribution to an assumed nonlinear parametric regression model, while the second pertains to fitting a parametric regression model…
When we use the normal mixture model, the optimal number of the components describing the data should be determined. Testing homogeneity is good for this purpose; however, to construct its theory is challenging, since the test statistic…
In the context of nonparametric regression, we study conditions under which the consistency (and rates of convergence) of estimators built from discretely sampled curves can be derived from the consistency of estimators based on the…
This paper studies probabilistic rates of convergence for consensus+innovations type of algorithms in random, generic networks. For each node, we find a lower and also a family of upper bounds on the large deviations rate function, thus…
A nonparametric anomalous hypothesis testing problem is investigated, in which there are totally n sequences with s anomalous sequences to be detected. Each typical sequence contains m independent and identically distributed (i.i.d.)…
There is a substantial literature on testing for the equality of the cumulative incidence functions associated with one specific cause in a competing risks setting across several populations against specific or all alternatives. In this…
We study the problem of robustly estimating the mean or location parameter without moment assumptions. We show that for a large class of symmetric distributions, the same error as in the Gaussian setting can be achieved efficiently. The…
Consider a Poisson point process with unknown support boundary curve $g$, which forms a prototype of an irregular statistical model. We address the problem of estimating non-linear functionals of the form $\int \Phi(g(x))\,dx$. Following a…
We propose an iterative estimating equations procedure for analysis of longitudinal data. We show that, under very mild conditions, the probability that the procedure converges at an exponential rate tends to one as the sample size…
The problem of error density estimation for a functional single index model with dependent errors is studied. A Bayesian method is utilized to simultaneously estimate the bandwidths in the kernel-form error density and regression function,…
Randomization tests are based on a re-randomization of existing data to gain data-dependent critical values that lead to exact hypothesis tests under special circumstances. However, it is not always possible to re-randomize data in…
We study optimal procedures for estimating a linear functional based on observational data. In many problems of this kind, a widely used assumption is strict overlap, i.e., uniform boundedness of the importance ratio, which measures how…
We consider the problem of uncertainty assessment for low dimensional components in high dimensional models. Specifically, we propose a decorrelated score function to handle the impact of high dimensional nuisance parameters. We consider…
The paper introduces robust independence tests with non-asymptotically guaranteed significance levels for stochastic linear time-invariant systems, assuming that the observed outputs are synchronous, which means that the systems are driven…
Motivated by real-world machine learning applications, we analyze approximations to the non-asymptotic fundamental limits of statistical classification. In the binary version of this problem, given two training sequences generated according…
This paper investigates improved testing inferences under a general multivariate elliptical regression model. The model is very flexible in terms of the specification of the mean vector and the dispersion matrix, and of the choice of the…