Article
Statistics & Probability
Omid Khademnoe, S. Mohammad E. Hosseini-Nasab
Summary: This article studies a functional linear regression model with a functional predictor and a scalar response. In the literature, a procedure based on projecting the slope function onto an arbitrary L2 basis has been introduced to test the slope function. We propose its bootstrap counterpart for testing the slope function and obtain the asymptotic null distributions of the test statistics and the asymptotic powers of the tests. Finally, a simulation study is conducted to evaluate the accuracy of the two test procedures. Using the dataset of the Export Development Bank of Iran as a practical illustration, we test the nullity of the slope function of a model predicting the total annual noncurrent balance of facilities based on the current balance of facilities.
STATISTICAL PAPERS
(2023)
Article
Economics
Bas J. M. Werker, Bo Zhou
Summary: We investigate the issue of semiparametric efficiency in the bivariate regression problem with a highly persistent predictor. By constructing invariant point-optimal tests based on the structural representation of the limit experiment and exploiting invariance relationships, we address the hypothesis testing problem for the regression coefficient of interest. Our proposed method, which uses component-wise ranks of the innovations, achieves significant power gains compared to existing tests under non-Gaussian innovation distributions. The method performs equivalently to existing tests under Gaussianity and remains robust to certain forms of conditional heteroskedasticity, as demonstrated through simulation.
JOURNAL OF ECONOMETRICS
(2022)
Article
Mathematics, Applied
Li-Xin Zhang
Summary: The central limit theorem and functional central limit theorem for martingale like random variables under the sub-linear expectation are obtained in this paper. Applications include the Lindeberg central limit theorem for independent but not necessarily identically distributed random variables, and a new proof of the Leevy characterization of a G-Brownian motion without using stochastic calculus. Rosenthal's inequality and the exponential inequality for the martingale like random variables are used to prove the results.
SCIENCE CHINA-MATHEMATICS
(2021)
Article
Statistics & Probability
Yinqiu He, Gongjun Xu, Chong Wu, Wei Pan
Summary: This paper introduces a method of using U-statistics for high-dimensional hypothesis tests, showing their asymptotic independence and normal distribution under the null hypothesis. Based on this property, an adaptive testing procedure is proposed, with high power against various alternatives.
ANNALS OF STATISTICS
(2021)
Article
Automation & Control Systems
Yibo Yan, Xiaozhou Wang, Riquan Zhang
Summary: In this study, we propose a debiased 1-SQR pound estimator by combining the debiased method with the convolution-type smoothed quantile regression (SQR) model, and establish confidence intervals and hypothesis testing in the high-dimensional setup. Theoretically, we provide non-asymptotic Bahadur representation and Berry-Esseen bound for the estimator, suggesting empirical coverage rates for the studentized confidence intervals. We also develop the theory of hypothesis testing on both a single variable and a group of variables, and demonstrate the effectiveness of our method through extensive numerical experiments.
JOURNAL OF MACHINE LEARNING RESEARCH
(2023)
Article
Statistics & Probability
Tasos C. Christofides, Charalambos Charalambous
Summary: This paper obtains the distance between U-statistics and a normal random variable using Zolotarev's ideal metric. The results are applicable to U-statistics based on i.i.d random variables and negatively associated random variables. Corresponding results are also investigated for the related class of von Mises statistics.
COMMUNICATIONS IN STATISTICS-THEORY AND METHODS
(2023)
Article
Mathematics
Li-Xin Zhang
Summary: In this paper, the functional central limit theorem is proved for martingale-like random vectors using the sub-linear expectations framework introduced by Shige Peng. As applications, the Lindeberg central limit theorem for independent random vectors is established, the sufficient and necessary conditions for the central limit theorem of independent and identically distributed random vectors are derived, and a Levy's characterization of a multi-dimensional G-Brownian motion is obtained.
COMMUNICATIONS IN MATHEMATICS AND STATISTICS
(2023)
Article
Statistics & Probability
Matthias Loewe, Sara Terveer
Summary: The text discusses the fluctuations of incomplete U-statistics over a triangular array of independent random variables, providing criteria for the Central Limit Theorem to hold and relying on a martingale CLT for proof. An application related to hitting time for random walks on random graphs is presented in Lowe and Terveer (2020).
BRAZILIAN JOURNAL OF PROBABILITY AND STATISTICS
(2021)
Article
Statistics & Probability
Hongjian Shi, Mathias Drton, Fang Han
Summary: This article introduces a distribution-free and consistent test for testing independence of two random vectors of general dimensions, by combining distance covariance with center-outward ranks and signs. The test is shown to have a limiting null distribution by exploiting the structure of distance covariance and the combinatorial nature of Hallin's ranks and signs. The results suggest that the test is accurate for moderate sample sizes and does not require permutation for implementation.
JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
(2022)
Article
Statistics & Probability
Grzegorz Rempala, Jacek Wesolowski
Summary: In this study, we derive Poisson limit theorems for the multinomial Cressie-Read goodness-of-fit statistics and some of their modifications under the assumption that the sample size increases to infinity and the number of groups increases with the sample size. Our results extend the previously reported Poisson limit theorems for the Pearson chi-square statistic.
JOURNAL OF STATISTICAL PLANNING AND INFERENCE
(2023)
Article
Mathematics
Peng Sun, Yincai Tang, Mingxiang Cao
Summary: A new test statistic based on the weighted Frobenius norm of covariance matrices is proposed in this paper to test the homogeneity of multi-group population covariance matrices. The asymptotic distributions of the proposed test under the null and alternative hypotheses are derived, respectively. Simulation results show that the proposed test procedure tends to outperform some existing test procedures.
Article
Computer Science, Theory & Methods
Juan Kuntz, Francesca R. Crucinio, Adam M. Johansen
Summary: We introduce a class of Monte Carlo estimators that exploit the target's independence structure to overcome the rapid growth of variance with dimension often observed for standard estimators. We show their superiority, establish their properties, and investigate their computational cost and efficiency when combined with other well-known Monte Carlo estimators.
STATISTICS AND COMPUTING
(2022)
Article
Computer Science, Theory & Methods
Alessandro Mastrototaro, Jimmy Olsson
Summary: We present a new approach, the ALVar estimator, for estimating the asymptotic variance in sequential Monte Carlo methods, or particle filters. The method is applicable to general distribution flows and particle filters, including auxiliary particle filters with adaptive resampling. The algorithm operates entirely online, providing real-time monitoring of the particle filter's variance with constant computational complexity and memory requirements per iteration on average. It does not require the calibration of any algorithmic parameter and only requires minor code additions to the underlying particle algorithm for variance estimation based solely on the genealogy of the propagated particle cloud. We prove that the ALVar estimator is consistent for the true asymptotic variance as the number of particles tends to infinity and demonstrate numerically its superiority to existing approaches.
STATISTICS AND COMPUTING
(2023)
Article
Automation & Control Systems
Quentin Duchemin, Yohann De Castro, Claire Lacour
Summary: This paper demonstrates the importance of non-asymptotic analysis of U-statistics in a dependent framework and applies it to three different research fields, including spectral estimation of integral operators, generalization performance of online algorithms, and goodness-of-fit test for the density of the stationary measure of a Markov chain.
JOURNAL OF MACHINE LEARNING RESEARCH
(2022)
Article
Mathematics
H. Dehling, D. Giraudo, O. Sharipov
Summary: The study examines the convergence of the empirical two-sample U-statistic with beta-mixing strictly stationary data in Skorohod spaces, and presents an application of such convergence.
ACTA MATHEMATICA HUNGARICA
(2021)
