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COBE has provided us with a whole-sky map of the CBR anisotropies. However, even if the noise level is negligible when the four year COBE data are available, the cosmic variance will prevent us from obtaining information about the Gaussian…
Anomalies arising from nonplanar triangle diagrams of noncommutative gauge theory are studied. Local chiral gauge anomalies for both noncommutative U(1) and U(N) gauge theories with adjoint matter fields are shown to vanish. For…
We discuss the requirements of good statistics for quantifying non-Gaussianity in the Cosmic Microwave Background. The importance of rotational invariance and statistical independence is stressed, but we show that these are sometimes…
Change point detection in covariance structures is a fundamental and crucial problem for sequential data. Under the high-dimensional setting, most of the existing research has focused on identifying change points in historical data.…
In this paper we study the asymptotic behavior of the angular bispectrum of spherical random fields. Here, the asymptotic theory is developed in the framework of fixed-radius fields, which are observed with increasing resolution as the…
Gaussian cosmic microwave background skies are fully specified by the power spectrum. The conventional method of characterizing non-Gaussian skies is to evaluate higher order moments, the n-point functions and their Fourier transforms. We…
Balancing square and rectangular tables by rotation has been a interesting way to illustrate the intermediate value theorem. The aim of this note is to show that the balancing act but with non-rectangular tables can be a nice application of…
In this article, we propose a new nonparametric data analysis tool, which we call nonparametric modal regression, to investigate the relationship among interested variables based on estimating the mode of the conditional density of a…
Circular biomarkers arise naturally in many biomedical applications, particularly in ophthalmology, where angular measurements such as astigmatism are routinely recorded. Similar directional variables also occur in the study of human body…
Strong mixing property holds for a broad class of linear and nonlinear time series models such as ARMA and GARCH models. In this article we study correlation structure of strong mixing sequences, and some asymptotic properties are…
Observations of non-random distribution of galaxies with opposite spin directions have recently attracted considerable attention. Here, a method for identifying cosine-dependence in a dataset of galaxies annotated by their spin directions…
We introduce the notion of angular values for deterministic linear difference equations and random linear cocycles. We measure the principal angles between subspaces of fixed dimension as they evolve under nonautonomous or random linear…
We consider the sequential change-point detection problem of detecting changes that are characterized by a subspace structure. Such changes are frequent in high-dimensional streaming data altering the form of the corresponding covariance…
Multimodal regression estimation methods are introduced for regression models involving circular response and/or covariate. The regression estimators are based on the maximization of the conditional densities of the response variable over…
Change point analysis has applications in a wide variety of fields. The general problem concerns the inference of a change in distribution for a set of time-ordered observations. Sequential detection is an online version in which new data…
This paper investigates change-point of variance in panel data models with time series of $\alpha$-mixing. Based on the cumulative sum (CUSUM) method and the individual differences, we construct a CUSUM test for panel data models to detect…
Many experiments record sequential trajectories where each trajectory consists of oscillations and fluctuations around zero. Such trajectories can be viewed as zero-mean functional data. When there are structural breaks (on the sequence of…
We introduce nonparametric tests of independence for bivariate circular data based on trigonometric moments. Our contributions lie in (i) proposing nonparametric tests that are locally and asymptotically optimal against bivariate cosine von…
Angular observations, or observations lying on the unit circle, arise in many disciplines and require special care in their description, analysis, interpretation and visualization. We provide methods to construct concentric circular boxplot…
The q-weighted CUSUM and their corresponding estimator are well known statistics for change-point detection and estimation. They have the difficulty that the performance is highly dependent on the location of the change. An adaptive…