Author
Yongcheng Qi
Other affiliations: Academia Sinica, Peking University, University of Georgia
Bio: Yongcheng Qi is an academic researcher from University of Minnesota. The author has contributed to research in topics: Empirical likelihood & Asymptotic distribution. The author has an hindex of 20, co-authored 97 publications receiving 1153 citations. Previous affiliations of Yongcheng Qi include Academia Sinica & Peking University.
Papers published on a yearly basis
Papers
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TL;DR: In this article, the authors defined the extreme value distributions and proved that 1(−∞,x) does not converge almost surely for any x ∈ S(G).
Abstract: Let X1, …, Xn be independent random variables with common distribution function F. Define
and let G(x) be one of the extreme-value distributions. Assume F ∈ D(G), i.e., there exist an> 0 and bn ∈ ℝ such that
.
Let l(−∞,x)(·) denote the indicator function of the set (−∞,x) and S(G) =: {x : 0 < G(x) < 1}. Obviously, 1(−∞,x)((Mn−bn)/an) does not converge almost surely for any x ∈ S(G). But we shall prove
.
88 citations
TL;DR: In this paper, Jiang and Yang showed that p goes to infinity and p can be very close to n, which is an almost sufficient and necessary condition for the central limit theorems.
Abstract: In their recent work, Jiang and Yang studied six classical Likelihood Ratio Test statistics under high-dimensional setting. Assuming that a random sample of size n is observed from a p-dimensional normal population, they derive the central limit theorems (CLTs) when p and n are proportional to each other, which are different from the classical chi-square limits as n goes to infinity, while p remains fixed. In this paper, by developing a new tool, we prove that the mentioned six CLTs hold in a more applicable setting: p goes to infinity, and p can be very close to n. This is an almost sufficient and necessary condition for the CLTs. Simulations of histograms, comparisons on sizes and powers with those in the classical chi-square approximations and discussions are presented afterwards.
69 citations
TL;DR: In this paper, a smoothed jackknife empirical likelihood method to construct confidence intervals for the receiver operating characteristic (ROC) curve is proposed and Wilks' theorem for the empirical likelihood ratio statistic is proved.
59 citations
TL;DR: In this paper, the authors studied the radii of the spherical ensemble, the truncation of the circular unitary ensemble and the product ensemble with parameters n and k, and obtained the limiting distributions of the three radii, which are not the Tracy-Widom distribution.
Abstract: By using the independence structure of points following a determinantal point process, we study the radii of the spherical ensemble, the truncation of the circular unitary ensemble and the product ensemble with parameters n and k. The limiting distributions of the three radii are obtained. They are not the Tracy–Widom distribution. In particular, for the product ensemble, we show that the limiting distribution has a transition phenomenon: When $$k/n\rightarrow 0$$
, $$k/n\rightarrow \alpha \in (0,\infty )$$
and $$k/n\rightarrow \infty $$
, the liming distribution is the Gumbel distribution, a new distribution $$\mu $$
and the logarithmic normal distribution, respectively. The cumulative distribution function (cdf) of $$\mu $$
is the infinite product of some normal distribution functions. Another new distribution $$
u $$
is also obtained for the spherical ensemble such that the cdf of $$
u $$
is the infinite product of the cdfs of some Poisson-distributed random variables.
44 citations
TL;DR: In this article, the second-order regular variation was incorporated into the censored likelihood function to derive the joint asymptotic limit for the first-and secondorder parameters under a weaker assumption, which is different from the bias reduced maximum likelihood method proposed by Feuerverger and Hall in 1999.
Abstract: Summary This paper suggests censored maximum likelihood estimators for the first- and secondorder parameters of a heavy-tailed distribution by incorporating the second-order regular variation into the censored likelihood function. This approach is different from the biasreduced maximum likelihood method proposed by Feuerverger and Hall in 1999. The paper derives the joint asymptotic limit for the first- and second-order parameters under a weaker assumption. The paper also demonstrates through a simulation study that the suggested estimator for the first-order parameter is better than the estimator proposed by Feuerverger and Hall although these two estimators have the same asymptotic variances.
44 citations
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TL;DR: Convergence of Probability Measures as mentioned in this paper is a well-known convergence of probability measures. But it does not consider the relationship between probability measures and the probability distribution of probabilities.
Abstract: Convergence of Probability Measures. By P. Billingsley. Chichester, Sussex, Wiley, 1968. xii, 253 p. 9 1/4“. 117s.
5,689 citations
TL;DR: In this article, the authors studied a random Groeth model in two dimensions closely related to the one-dimensional totally asymmetric exclusion process and showed that shape fluctuations, appropriately scaled, converges in distribution to the Tracy-Widom largest eigenvalue distribution for the Gaussian Unitary Ensemble.
Abstract: We study a certain random groeth model in two dimensions closely related to the one-dimensional totally asymmetric exclusion process. The results show that the shape fluctuations, appropriately scaled, converges in distribution to the Tracy-Widom largest eigenvalue distribution for the Gaussian Unitary Ensemble.
1,031 citations
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TL;DR: In this article, the authors generalise l'estimateur bien connu de Hill de lindice d a fonction de reparatition avec queue de variation reguliere a une estimation de l'indice of a loi de valeurs extremes.
Abstract: On generalise l'estimateur bien connu de Hill de l'indice d'une fonction de reparatition avec queue de variation reguliere a une estimation de l'indice d'une loi de valeurs extremes. On demontre la convergence et la normalite asymptotique. On utilise l'estimateur pour certaines estimations comme celle d'une quantile elevee et d'un point d'extremite
655 citations