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954 results on '"Song, Haiyan"'

5. A CLT for the LSS of large dimensional sample covariance matrices with diverging spikes

Author

Liu, Zhijun, Hu, Jiang, Bai, Zhidong, and Song, Haiyan

Subjects
Mathematics - Statistics Theory
Abstract

In this paper, we establish the central limit theorem (CLT) for linear spectral statistics (LSSs) of a large-dimensional sample covariance matrix when the population covariance matrices are involved with diverging spikes. This constitutes a nontrivial extension of the Bai-Silverstein theorem (BST) (Ann Probab 32(1):553--605, 2004), a theorem that has strongly influenced the development of high-dimensional statistics, especially in the applications of random matrix theory to statistics. Recently, there has been a growing realization that the assumption of uniform boundedness of the population covariance matrices in the BST is not satisfied in some fields, such as economics, where the variances of principal components may diverge as the dimension tends to infinity. Therefore, in this paper, we aim to eliminate this obstacle to applications of the BST. Our new CLT accommodates spiked eigenvalues, which may either be bounded or tend to infinity. A distinguishing feature of our result is that the variance in the new CLT is related to both spiked eigenvalues and bulk eigenvalues, with dominance being determined by the divergence rate of the largest spiked eigenvalues. The new CLT for LSS is then applied to test the hypothesis that the population covariance matrix is the identity matrix or a generalized spiked model. The asymptotic distributions of the corrected likelihood ratio test statistic and the corrected Nagao's trace test statistic are derived under the alternative hypothesis. Moreover, we present power comparisons between these two LSSs and Roy's largest root test. In particular, we demonstrate that except for the case in which the number of spikes is equal to one, the LSSs could exhibit higher asymptotic power than Roy's largest root test., Comment: It is an update version of arXiv:2212.05896

Published
2022

7. Effect of Vent Mode on the Differential Pressure Pre-cooling Efficiency of Layered Peaches

Author

CHEN Yingmin, ZHAO Luxi, LINGHU Boxiang, SONG Haiyan

Subjects
peach, differential pressure precooling, vent mode, precooling performance, numerical simulation, computational fluid dynamics, Food processing and manufacture, TP368-456
Abstract

The objective of this study was to explore the effect of the vent mode of corrugated boxes universally used in the market on the precooling performance of layered peaches and to determine the functional relationship between the precooling environmental parameters and the precooling efficiency and the optimal vent mode under different differential pressure pre-cooling working conditions in order to realize the rapid energy-saving precooling of peaches after harvest. A numerical model of heat and mass transfer during differential pressure precooling with circular and rectangular vents (abbreviated as CV and RV, respectively) was established based on computational fluid dynamics. By comparing and analyzing the experimental and simulated data, it was found that the maximum root mean square error and mean absolute percentage error between the two vent designs were 0.799 ℃ and 6.6%, respectively, which fully verified that this numerical model had high prediction accuracy. Through in-depth exploration of the temperature and flow field distribution in different vent modes, it was found that CV exhibited inferior precooling uniformity when compared with RV. Nevertheless, CV demonstrated a notable reduction in precooling time by 30%–40% and a decrease in fan energy consumption by 50%. Additionally, their relationships with differential pressure were described by. Based on these obtained results, the precooling quality of peaches could be improved by using RV, and the precooling cost could be reduced by using CV. To simultaneously achieve these two goals, the diameter of CV should be greater than 35 mm. This study provides a theoretical reference for the reasonable selection of vent parameters and accurate monitoring of fruit precooling performance in small and medium-sized orchards.

Published
2024
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8. A CLT for the LSS of large dimensional sample covariance matrices with unbounded dispersions

Author

Liu, Zhijun, Hu, Jiang, Bai, Zhidong, and Song, Haiyan

Subjects
Mathematics - Statistics Theory, Mathematics - Probability
Abstract

In this paper, we establish the central limit theorem (CLT) for linear spectral statistics (LSS) of large-dimensional sample covariance matrix when the population covariance matrices are not uniformly bounded, which is a nontrivial extension of the Bai-Silverstein theorem (BST) (2004). The latter has strongly stimulated the development of high-dimensional statistics, especially the application of random matrix theory to statistics. However, the assumption of uniform boundedness of the population covariance matrices is found strongly limited to the applications of BST. The aim of this paper is to remove the blockages to the applications of BST. The new CLT, allows the spiked eigenvalues to exist and tend to infinity. It is interesting to note that the roles of either spiked eigenvalues or the bulk eigenvalues or both of the two are dominating in the CLT. Moreover, the results are checked by simulation studies with various population settings. The CLT for LSS is then applied for testing the hypothesis that a covariance matrix $ \bSi $ is equal to an identity matrix. For this, the asymptotic distributions for the corrected likelihood ratio test (LRT) and Nagao's trace test (NT) under alternative are derived, and we also propose the asymptotic power of LRT and NT under certain alternatives.

Published
2022

45. An Introduction to the Research on Profit Models

Author

Song, HaiYan, Jiang, YiPing, Appolloni, Andrea, Series Editor, Caracciolo, Francesco, Series Editor, Ding, Zhuoqi, Series Editor, Gogas, Periklis, Series Editor, Huang, Gordon, Series Editor, Nartea, Gilbert, Series Editor, Ngo, Thanh, Series Editor, Striełkowski, Wadim, Series Editor, Jiang, Yushi, editor, Shvets, Yuriy, editor, and Mallick, Hrushikesh, editor

Published
2022
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