Related papers: Bootstrapping Max Statistics in High Dimensions: N…
For more than $50$ years the {\it Mean Measure of Divergence} (MMD) has been one of the most prominent tools used in anthropology for the study of non-metric traits. However, one of the problems, in anthropology including palaeoanthropology…
Inference for functional linear models in the presence of heteroscedastic errors has received insufficient attention given its practical importance; in fact, even a central limit theorem has not been studied in this case. At issue,…
In this paper, we establish a high-dimensional CLT for the sample mean of $p$-dimensional spatial data observed over irregularly spaced sampling sites in $\mathbb{R}^d$, allowing the dimension $p$ to be much larger than the sample size $n$.…
In this chapter, we discuss recent work on learning sparse approximations to high-dimensional functions on data, where the target functions may be scalar-, vector- or even Hilbert space-valued. Our main objective is to study how the…
Strict stationarity is a common assumption used in the time series literature in order to derive asymptotic distributional results for second-order statistics, like sample autocovariances and sample autocorrelations. Focusing on weak…
We propose a high dimensional mean test framework for shrinking random variables, where the underlying random variables shrink to zero as the sample size increases. By pooling observations across overlapping subsets of dimensions, we…
This paper is an attempt to set a justification for making use of some dicrepancy indexes, starting from the classical Maximum Likelihood definition, and adapting the corresponding basic principle of inference to situations where…
Precision matrix, which is the inverse of covariance matrix, plays an important role in statistics, as it captures the partial correlation between variables. Testing the equality of two precision matrices in high dimensional setting is a…
In this paper we introduce a novel approach for an important problem of break detection. Specifically, we are interested in detection of an abrupt change in the covariance structure of a high-dimensional random process -- a problem, which…
Cumulative sum (CUSUM) statistics are widely used in the change point inference and identification. For the problem of testing for existence of a change point in an independent sample generated from the mean-shift model, we introduce a…
High dimensional hypothesis test deals with models in which the number of parameters is significantly larger than the sample size. Existing literature develops a variety of individual tests. Some of them are sensitive to the dense and small…
In this paper we propose a new test of heteroscedasticity for parametric regression models and partial linear regression models in high dimensional settings. When the dimension of covariates is large, existing tests of heteroscedasticity…
This article presents a bootstrap approximation to the Lp_statistics of kernel density estimator in length-biased model. Length-biased data arise in many situations, such as survival analysis, renewal processes and physics. The article…
An algorithm is described that enables efficient deterministic approximate computation of the bootstrap distribution for any linear bootstrap method $T_n^*$, alleviating the need for repeated resampling from observations (resp.…
Estimates of the approximate factor model are increasingly used in empirical work. Their theoretical properties, studied some twenty years ago, also laid the ground work for analysis on large dimensional panel data models with cross-section…
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…
Motivated by the widely used geometric median-of-means estimator in machine learning, this paper studies statistical inference for ultrahigh dimensionality location parameter based on the sample spatial median under a general multivariate…
The bootstrap, based on resampling, has, for several decades, been a widely used method for computing confidence intervals for applications where no exact method is available and when sample sizes are not large enough to be able to rely on…
While widely used as a general method for uncertainty quantification, the bootstrap method encounters difficulties that raise concerns about its validity in practical applications. This paper introduces a new resampling-based method, termed…
Robust statistics aims to compute quantities to represent data where a fraction of it may be arbitrarily corrupted. The most essential statistic is the mean, and in recent years, there has been a flurry of theoretical advancement for…