Related papers: Unit Root Testing with Slowly Varying Trends
This paper considers stochastic weakly convex optimization without the standard Lipschitz continuity assumption. Based on new adaptive regularization (stepsize) strategies, we show that a wide class of stochastic algorithms, including the…
Symmetry is a cornerstone of much of mathematics, and many probability distributions possess symmetries characterized by their invariance to a collection of group actions. Thus, many mathematical and statistical methods rely on such…
This paper introduces a unified framework for the detection of a source with a sensor array in the context where the noise variance and the channel between the source and the sensors are unknown at the receiver. The Generalized Maximum…
We consider the problem of performing inference on the number of common stochastic trends when data is generated by a cointegrated CKSVAR (a two-regime, piecewise affine SVAR; Mavroeidis, 2021), using a modified version of the Breitung…
We generalize the method of surrogate data of testing for nonlinearity in time series to the case that the data are sampled with uneven time intervals. The null hypothesis will be that the data have been generated by a linear stochastic…
Decomposing complex time series into trend, seasonality, and remainder components is an important task to facilitate time series anomaly detection and forecasting. Although numerous methods have been proposed, there are still many time…
In many applications common in testing for convergence the number of cross-sectional units is large and the number of time periods are few. In these situations asymptotic tests based on an omnibus null hypothesis are characterised by a…
When some treatments are ordered according to the categories of an ordinal categorical variable (e.g., extent of side effects) in a monotone order, one might be interested in knowing wether the treatments are equally effective or not. One…
Previous analysis on forecasting theory either assume knowing the true parameters or assume the stationarity of the series. Not much are known on the forecasting theory for nonstationary process with estimated parameters. This paper…
Outlier hypothesis testing is studied in a universal setting. Multiple sequences of observations are collected, a small subset of which are outliers. A sequence is considered an outlier if the observations in that sequence are distributed…
Necessary and sufficient conditions of uniform consistency are explored. A hypothesis is simple. Nonparametric sets of alternatives are bounded convex sets in $\mathbb{L}_p$, $p >1$ with "small" balls deleted. The "small" balls have the…
We consider a data-driven robust hypothesis test where the optimal test will minimize the worst-case performance regarding distributions that are close to the empirical distributions with respect to the Wasserstein distance. This leads to a…
This paper provides a variational analysis of the unconstrained formulation of the LASSO problem, ubiquitous in statistical learning, signal processing, and inverse problems. In particular, we establish smoothness results for the optimal…
We introduce a new statistical test based on the observed spacings of ordered data. The statistic is sensitive to detect non-uniformity in random samples, or short-lived features in event time series. Under some conditions, this new test…
We consider the problem of hypothesis testing in the situation where the first hypothesis is simple and the second one is local one-sided composite. We describe the choice of the thresholds and the power functions of different tests when…
We provide a continuous time limit analysis for the class of Ensemble Square Root Filter algorithms with deterministic model perturbations. In the particular linear case, we specify general conditions on the model perturbations implying…
The asymptotic properties of the variances of the spatial autoregressive model $X_{k,\ell}=\alpha X_{k-1,\ell}+\beta X_{k,\ell-1}+\gamma X_{k-1,\ell-1}+\epsilon_{k,\ell}$ are investigated in the unit root case, that is when the parameters…
While coresets have been growing in terms of their application, barring few exceptions, they have mostly been limited to unsupervised settings. We consider supervised classification problems, and non-decomposable evaluation measures in such…
A general method is presented for deriving the limiting behavior of estimators that are defined as the values of parameters optimizing an empirical criterion function. The asymptotic behavior of such estimators is typically deduced from…
The problem of linear modulation classification using likelihood based methods is considered. Asymptotic properties of most commonly used classifiers in the literature are derived. These classifiers are based on hybrid likelihood ratio test…