Related papers: Inference for Multi-Dimensional High-Frequency Dat…
Many high-dimensional hypothesis tests aim to globally examine marginal or low-dimensional features of a high-dimensional joint distribution, such as testing of mean vectors, covariance matrices and regression coefficients. This paper…
We propose a class of nonparametric two-sample tests with a cost linear in the sample size. Two tests are given, both based on an ensemble of distances between analytic functions representing each of the distributions. The first test uses…
Dette, Siburg, and Stoimenov (2013) introduced a copula-based measure of dependence, which implies independence if it vanishes and is equal to 1 if one variable is a measurable function of the other. For continuous distributions, the…
Conditional independence is a fundamental concept in many areas of statistical research, including, for example, sufficient dimension reduction, causal inference, and statistical graphical models. In many modern applications, data arise in…
Estimating the innovation probability density is an important issue in any regression analysis. This paper focuses on functional autoregressive models. A residual-based kernel estimator is proposed for the innovation density. Asymptotic…
One of the central objectives of modern risk management is to find a set of risks where the probability of multiple simultaneous catastrophic events is negligible. That is, risks are taken only when their joint behavior seems sufficiently…
This paper is concerned with estimation and inference for ultrahigh dimensional partially linear single-index models. The presence of high dimensional nuisance parameter and nuisance unknown function makes the estimation and inference…
In many practical applications of numerical methods a substantial increase in efficiency can be obtained by using local grid refinement, since the solution is generally smooth in large parts of the domain and large gradients occur only…
High-dimensional linear models with endogenous variables play an increasingly important role in recent econometric literature. In this work we allow for models with many endogenous variables and many instrument variables to achieve…
We develop an asymptotic theory for $L^2$ norms of sample mean vectors of high-dimensional data. An invariance principle for the $L^2$ norms is derived under conditions that involve a delicate interplay between the dimension $p$, the sample…
It is established that the linear spectral statistics (LSS) of the smoothed periodogram estimate of the spectral coherence matrix of a complex Gaussian high-dimensional times series (yn) n$\in$Z with independent components satisfy at each…
We propose a framework for hypothesis testing on conditional probability distributions, which we then use to construct statistical tests of functionals of conditional distributions. These tests identify the inputs where the functionals…
A distributed estimation scheme where the sensors transmit with constant modulus signals over a multiple access channel is considered. The proposed estimator is shown to be strongly consistent for any sensing noise distribution in the…
Confidence sequences are anytime-valid analogues of classical confidence intervals that do not suffer from multiplicity issues under optional continuation of the data collection. As in classical statistics, asymptotic confidence sequences…
We consider the problem of testing the mean of high-dimensional data when the dimension may grow without explicit rate restrictions relative to the sample size. The proposed procedure is based on the statistic V_n = n||Xn||^2, which avoids…
Nonparametric regression problems with qualitative constraints such as monotonicity or convexity are ubiquitous in applications. For example, in predicting the yield of a factory in terms of the number of labor hours, the monotonicity of…
A long-standing problem in the construction of asymptotically correct confidence bands for a regression function $m(x)=E[Y|X=x]$, where $Y$ is the response variable influenced by the covariate $X$, involves the situation where $Y$ values…
The paper studies the problem of distributed parameter estimation in multi-agent networks with exponential family observation statistics. A certainty-equivalence type distributed estimator of the consensus + innovations form is proposed in…
As modern machine learning models continue to advance the computational frontier, it has become increasingly important to develop precise estimates for expected performance improvements under different model and data scaling regimes.…
Consider a nonparametric regression model with one-sided errors and regression function in a general H\"older class. We estimate the regression function via minimization of the local integral of a polynomial approximation. We show uniform…