Related papers: Are You All Normal? It Depends!
Multivariate normal mixtures provide a flexible model for high-dimensional data. They are widely used in statistical genetics, statistical finance, and other disciplines. Due to the unboundedness of the likelihood function, classical…
When modeling directional data, that is, unit-norm multivariate vectors, a first natural question is to ask whether the directions are uniformly distributed or, on the contrary, whether there exist modes of variation significantly different…
We consider the problem of testing whether pairs of univariate random variables are associated. Few tests of independence exist that are consistent against all dependent alternatives and are distribution free. We propose novel tests that…
There has been a wide interest to extend univariate and multivariate nonparametric procedures to clustered and hierarchical data. Traditionally, parametric mixed models have been used to account for the correlation structures among the…
This paper investigates the distribution of marks obtained by students across multiple courses to explore whether the data conforms to a skew-normal distribution. Traditional methods for assessing normality, such as the Shapiro Wilk test,…
We develop large sample theory for merged data from multiple sources. Main statistical issues treated in this paper are (1) the same unit potentially appears in multiple datasets from overlapping data sources, (2) duplicated items are not…
For clinical studies with continuous outcomes, when the data are potentially skewed, researchers may choose to report the whole or part of the five-number summary (the sample median, the first and third quartiles, and the minimum and…
We introduce a new type of test for complete spatial randomness that applies to mapped point patterns in a rectangle or a cube of any dimension. This is the first test of its kind to be based on characteristic functions and utilizes a…
We formulate nonparametric and semiparametric hypothesis testing of multivariate stationary linear time series in a unified fashion and propose new test statistics based on estimators of the spectral density matrix. The limiting…
Due to the lack of a canonical ordering in ${\mathbb R}^d$ for $d>1$, defining multivariate generalizations of the classical univariate ranks has been a long-standing open problem in statistics. Optimal transport has been shown to offer a…
We give a review of recent ANOVA-like procedures for testing group differences based on data in a metric space and present a new such procedure. Our statistic is based on the classic Levene's test for detecting differences in dispersion. It…
The test of independence is a crucial component of modern data analysis. However, traditional methods often struggle with the complex dependency structures found in high-dimensional data. To overcome this challenge, we introduce a novel…
In this paper, we provide a statistical testing framework to check whether a random sample splitting in a multi-dimensional space is carried out in a valid way, which could be directly applied to A/B testing and multivariate testing to…
Spherical symmetry arguments are used to produce a general device to convert identities and inequalities for the $p$th absolute moments of real-valued random variables into the corresponding identities and inequalities for the $p$th moments…
We revisit the classical problem of comparing regression functions, a fundamental question in statistical inference with broad relevance to modern applications such as data integration, transfer learning, and causal inference. Existing…
The network data has attracted considerable attention in modern statistics. In research on complex network data, one key issue is finding its underlying connection structure given a network sample. The methods that have been proposed in…
We treat the problem of testing independence between m continuous variables when m can be larger than the available sample size n. We consider three types of test statistics that are constructed as sums or sums of squares of pairwise rank…
This paper proposes novel tests for the absence of jumps in a univariate semimartingale and for the absence of common jumps in a bivariate semimartingale. Our methods rely on ratio statistics of power variations based on irregular…
Spatial documentation is exponentially increasing given the availability of Big IoT Data, enabled by the devices miniaturization and data storage capacity. Bayesian spatial statistics is a useful statistical tool to determine the dependence…
A method for change point detection is proposed. We consider a univariate sequence of independent random variables with piecewise constant expectation and variance, apart from which the distribution may vary periodically. We aim to detect…