Related papers: Asymptotics of trimmed CUSUM statistics
In this paper, we study the asymptotic behavior of supremum distribution of some classes of iterated stochastic processes $\{X(Y(t)) : t \in [0, \infty)\}$, where $\{X(t) : t \in \mathbb{R} \}$ is a centered Gaussian process and $\{Y(t): t…
We present a technique to study normalizing strategies when termination is asymptotic, that is, it appears as a limit, as opposite to reaching a normal form in a finite number of steps. Asymptotic termination occurs in several settings,…
We study the variational behavior of the total inverse mean curvature of curves with prescribed boundary in the half-plane. We characterize the existence of critical points with prescribed area. We show that such critical points are…
Recurrence quantification analysis is a method for measuring the complexity of dynamical systems. Recurrence determinism is a fundamental characteristic of it, closely related to correlation sum. In this paper, we study asymptotic behavior…
Randomization tests rely on simple data transformations and possess an appealing robustness property. In addition to being finite-sample valid if the data distribution is invariant under the transformation, these tests can be asymptotically…
Testing for change points in sequences of covariance matrices is an important and equally challenging problem in statistical methodology with applications in various fields. Motivated by the observation that even in cases where the ratio…
If multiway cluster-robust standard errors are used routinely in applied economics, surprisingly few theoretical results justify this practice. This paper aims to fill this gap. We first prove, under nearly the same conditions as with…
The least trimmed squares (LTS) estimator is a renowned robust alternative to the classic least squares estimator and is popular in location, regression, machine learning, and AI literature. Many studies exist on LTS, including its…
In this paper, we consider the structural change in a class of discrete valued time series, which the true conditional distribution of the observations is assumed to be unknown. The conditional mean of the process depends on a parameter…
We propose a general framework of sequential testing procedures based on $U$-statistics which contains as an example a sequential CUSUM test based on differences in mean but also includes a robust sequential Wilcoxon change point procedure.…
In this paper, we survey results on the asymptotic behavior of the variance of the best linear unbiased estimator (BLUE) for the mean of stationary processes. This behavior is influenced by the regularity and memory structures of the…
We study goodness-of-fit testing for non-causal autoregressive time series with non-Gaussian stable noise. To model time series exhibiting sharp spikes or occasional bursts of outlying observations, the exponent of the non-Gaussian stable…
This paper presents some asymptotic results for statistics of Brownian semi-stationary (BSS) processes. More precisely, we consider power variations of BSS processes, which are based on high frequency (possibly higher order) differences of…
We are concerned with the problem of detecting a single change point in the model parameters of time series data generated from an exponential family. In contrast to the existing literature, we allow that the true location of the change…
This paper deals with the problem of testing for dispersion parameter change in discretely observed diffusion processes when the observations are contaminated by outliers. To lessen the impact of outliers, we first calculate residuals using…
This paper investigates asymptotic behaviors of gradient descent algorithms (particularly accelerated gradient descent and stochastic gradient descent) in the context of stochastic optimization arising in statistics and machine learning…
We establish the asymptotic expansion in $\beta$ matrix models with a confining, off-critical potential, in the regime where the support of the equilibrium measure is a union of segments. We first address the case where the filling…
We propose a change detection method for the famous Cox--Ingersoll--Ross model. This model is widely used in financial mathematics and therefore detecting a change in its parameters is of crucial importance. We develop one- and two-sided…
This paper introduces a new version of the smoothly trimmed mean with a more general version of weights, which can be used as an alternative to the classical trimmed mean. We derive its asymptotic variance and to further investigate its…
We obtain results on both weak and almost sure asymptotic behaviour of power variations of a linear combination of independent Wiener process and fractional Brownian motion. These results are used to construct strongly consistent parameter…