L-Moments and TL-Moments as an Alternative Tool of Statistical Data Analysis

Moments and cumulants are commonly used to characterize the probability distribution or observed data set. The use of the moment method of parameter estimation is also common in the construction of an appropriate parametric distribution for a certain data set. The moment method does not always produce satisfactory results. It is difficult to determine exactly what information concerning the shape of the distribution is expressed by its moments of the third and higher order. In the case of small samples in particular, numerical values of sample moments can be very different from the corresponding values of theoretical moments of the relevant probability distribution from which the random sample comes. Parameter estimations of the probability distribution made by the moment method are often considerably less accurate than those obtained using other methods, particularly in the case of small samples. The present paper deals with an alternative approach to the construction of an appropriate parametric distribution for the considered data set using order statistics.

Feature selection of ultrahigh-dimensional covariates with survival outcomes:a selective review

Many modern biomedical studies have yielded survival data with high-throughput predictors.The goals of scientific research often lie in identifying predictive biomarkers,understanding biological mechanisms and making accurate and precise predictions.Variable screening is a crucial first step in achieving these goals.This work conducts a selective review of feature screening procedures for survival data with ultrahigh dimensional covariates.We present the main methodologies,along with the key conditions that ensure sure screening properties.The practical utility of these methods is examined via extensive simulations.We conclude the review with some future opportunities in this field.

ASYMPTOTICS OF THE CROSS-VARIATION OF YOUNG INTEGRALS WITH RESPECT TO A GENERAL SELF-SIMILAR GAUSSIAN PROCESS

We show in this work that the limit in law of the cross-variation of processes having the form of Young integral with respect to a general self-similar centered Gaussian process of orderβ∈(1/2,3/4]is normal according to the values ofβ.We apply our results to two self-similar Gaussian processes:the subfractional Brownian motion and the bifractional Brownian motion.

WAVELET-BASED ESTIMATORS OF MEAN REGRESSION FUNCTION WITH LONG MEMORY DATA

This paper provides an asymptotic expansion for the mean integrated squared error （MISE） of nonlinear wavelet-based mean regression function estimators with long memory data. This MISE expansion, when the underlying mean regression function is only piecewise smooth, is the same as analogous expansion for the kernel estimators.However, for the kernel estimators, this MISE expansion generally fails if the additional smoothness assumption is absent.

基于进入过程带扰动风险模型的破产概率

在风险市场中,索赔过程是受保单过程驱动的,基于此思想,学者们提出了一类新的基于进入过程的非寿险保险风险模型。在简化上述模型的基础上,考虑了一类带布朗运动干扰的风险保险模型,利用鞅方法给出了该模型破产概率的显式表达式以及它的一个上界估计。

On intersections of independent anisotropic Gaussian random fields

Let XH = {XH(s),s ∈RN1} and X K = {XK(t),t ∈R N2} be two independent anisotropic Gaussian random fields with values in R d with indices H =(H1,...,HN1) ∈(0,1)N1,K =(K1,...,KN2) ∈(0,1) N2,respectively.Existence of intersections of the sample paths of X H and X K is studied.More generally,let E1■RN1,E2■RN2 and FRd be Borel sets.A necessary condition and a sufficient condition for P{(XH(E1)∩XK(E2))∩F≠Ф}>0 in terms of the Bessel-Riesz type capacity and Hausdorff measure of E1×E2×F in the metric space(RN1+N2+d,) are proved,where is a metric defined in terms of H and K.These results are applicable to solutions of stochastic heat equations driven by space-time Gaussian noise and fractional Brownian sheets.

Smoothness of local times and self-intersection local times of Gaussian random fields

这份报纸涉及光滑(在 Meyer-Watanabe 的意义) Gaussian 随机的地的本地时间。为时间，碰撞本地人时间，和本地的自我交叉预定的本地人的存在和光滑的足够、必要的条件为 Gaussian 随机的域的一个大类被建立，包括部分 Brownian 运动，部分 Brownian 表和时空 Gaussian 噪音驾驶的随机的热方程的解决方案。

Almost sure, L1-and L2-growth behavior of supercritical multi-type continuous state and continuous time branching processes with immigration

Under a first order moment condition on the immigration mechanism,we show that an appropriately scaled supercritical and irreducible multi-type continuous state and continuous time branching process with immigration(CBI process)converges almost surely.If an x log(x)moment condition on the branching mechanism does not hold,then the limit is zero.If this x log(x)moment condition holds,then we prove L1 convergence as well.The projection of the limit on any left non-Perron eigenvector of the branching mean matrix is vanishing.If,in addition,a suitable extra power moment condition on the branching mechanism holds,then we provide the correct scaling for the projection of a CBI process on certain left non-Perron eigenvectors of the branching mean matrix in order to have almost sure and L1 limit.Moreover,under a second order moment condition on the branching and immigration mechanisms,we prove L2 convergence of an appropriately scaled process and the above-mentioned projections as well.A representation of the limits is also provided under the same moment conditions.

On Global and Local Properties of the Trajectories of Gaussian Random Fields——A Look Through the Set of Limit Points

This paper studies the global and local properties of the trajectories of Gaussian random fields with stationary increments and proves sufficient conditions for Strassen's functional laws of the iterated logarithm at zero and infinity respectively.The sets of limit points of those Gaussian random fields are obtained.The main results are applied to fractional Riesz-Bessel processes and the sets of limit points of this field are obtained.

Uniform dimension results for Gaussian random fields

Let X = {X(t),t ∈ RN} be a Gaussian random field with values in Rd defined by X(t) =(X1(t),...,Xd(t)), t ∈ RN.(1) The properties of space and time anisotropy of X and their connections to uniform Hausdorff dimension results are discussed.It is shown that in general the uniform Hausdorff dimension result does not hold for the image sets of a space-anisotropic Gaussian random field X.When X is an(N,d)-Gaussian random field as in(1),where X1,...,Xd are independent copies of a real valued,centered Gaussian random field X0 which is anisotropic in the time variable.We establish uniform Hausdorff dimension results for the image sets of X.These results extend the corresponding results on one-dimensional Brownian motion,fractional Brownian motion and the Brownian sheet.

Association between N-terminal proB-type Natriuretic Peptide and Depressive Symptoms in Patients with Acute Myocardial Infarction

Background： While depression and certain cardiac biomarkers are associated with acute myocardial infarction （AM1）, the relationship between them remains largely unexplored. We examined the association between depressive symptoms and biomarkers in patients with AMI. Methods： We performed a cross-sectional study using data from 103 patients with AM1 between March 2013 and September 2014. The levels of depression, N-terminal proB-type natriuretic peptide （NT-proBNP）, and troponin 1 （Tnl） were measured at baseline. The patients were divided into two groups： those with depressive symptolns and those without depressive symptoms according to Zung Self-rating Depression Scale （SDS） score. Baseline comparisons between two groups were made using Student＇s t-test for continuous variables, Chi-square or Fisher＇s exact test for categorical variables, and Wilcoxon test for variables in skewed distribution. Binomial logistic regression and multivariate linear regression were performed to assess the association between depressive symptoms and biomarkers while adjusting for demographic and clinical variables. Results： Patients with depressive symptoms had significantly higher NT-proBNP levels as compared to patients without depressive symptoms （ 1135.0 [131.5, 2474.0] vs. 384.0 [ 133.0, 990.0], Z = -2.470, P 0.013）. Depressive symptoms were associated with higher NT-proBNP levels （odds ratio [OR] 2.348, 95% CI： 1.344 to 4.103, P= 0.003） and higher body mass index （OR = 1.169, 95% confidence interval [CI]： 1.016 to 1.345, P = 0.029）. The total SDS score was associated with the NT-proBNP level （[3 ： 0.327, 95% CI：1.674 to 6.119, P = 0.001） after multivariable adjustment. In particular, NT-proBNP was associated with three of the depressive dimensions, including core depression （β = 0.299, 95% CI：0.551 to 2.428, P=0.002）, cognitive depression （β= 0.320, 95% CI：0.476 to 1.811, P=0.001）, and somatic depression （β= 0.333, 95% CI： 0.240 to 0.847, P = 0.001）. Neither the overall depressive symptomatology nor the individual depressive dimensions were associated with TnI levels. Conclusions： Depressive symptoms, especially core depression, cognitive depression, and somatic depression, were related to high NT-proBNP levels in patients with AMI.

Finite sample breakdown point of Tukey＇s halfspace median

Tukey's halfspace median(HM), servicing as the multivariate counterpart of the univariate median,has been introduced and extensively studied in the literature. It is supposed and expected to preserve robustness property(the most outstanding property) of the univariate median. One of prevalent quantitative assessments of robustness is finite sample breakdown point(FSBP). Indeed, the FSBP of many multivariate medians have been identified, except for the most prevailing one—the Tukey's halfspace median. This paper presents a precise result on FSBP for Tukey's halfspace median. The result here depicts the complete prospect of the global robustness of HM in the finite sample practical scenario, revealing the dimension effect on the breakdown point robustness and complimenting the existing asymptotic breakdown point result.

A new method for fitting the complicated water level process of the lower Yellow River

With the view of effectively fitting the complicated water level process of the lower Yellow River, polynomial regression, stepwise regression, parameters by ridge estimate and so on, are logically integrated. And the progressive transformation is introduced. Then a new method is put forward. The core difference of this new method from the same kind of methods lies in that in this method the strong coupling effect of weak influencing factors which is common in a complicated water level process is considered, that many effective methods are synthetically used to reduce the fitting model error, and that the necessary progressive transformation is introduced. The advantages of many theories and methods are logically integrated in this method, and the method can be easily used. The rationality and necessity of each step in this method are ensured by sufficient theories, so this method can be widely used to effectively simulate the inherent relations in the same kind of complicated data. Furthermore, many complicated water level processes of the lower Yellow River are fitted by this method, and all the fitting precisions are markedly higher than the precision by the other existing methods. Every component term in the fitting model has clear physical meaning.

Dimensional Properties of Fractional Brownian Motion

Let B^α = {B^α（t）,t E R^N} be an （N,d）-fractional Brownian motion with Hurst index α∈ （0, 1）. By applying the strong local nondeterminism of B^α, we prove certain forms of uniform Hausdorff dimension results for the images of B^α when N 〉 αd. Our results extend those of Kaufman for one-dimensional Brownian motion.

Quantile regression for survival data in modern cancer research:expanding statistical tools for precision medicin

Quantile regression links the whole distribution of an outcome to the covariates of interest and has become an important alternative to commonly used regression models.However,the presence of censored data such as survival time,often the main endpoint in cancer studies,has hampered the use of quantile regression techniques because of the incompleteness of data.With the advent of the precision medicine era and availability of high throughput data,quantile regression with high-dimensional predictors has attracted much attention and provided added insight compared to traditional regression approaches.This paper provides a practical guide for using quantile regression for right censored outcome data with covariates of low-or highdimensionality.We frame our discussion using a dataset from the Boston Lung Cancer Survivor Cohort,a hospital-based prospective cohort study,with the goals of broadening the scope of cancer research,maximizing the utility of collected data,and offering useful statistical alternatives.We use quantile regression to identify clinical and molecular predictors,for example CpG methylation sites,associated with high-risk lung cancer patients,for example those with short survival.

Comorbid conditions related to readmissions of Chinese older patients

To the Editor:China is the most populated country,and it is aging more quickly than almost any other country in the world.According to Worldometer,[1]the population size of China,as of 2020,is around 1.4 billion,with the proportion of the 60-year olds and older being 17.30%in 2017 and expected to reach 35%in 2050.Older age tended to be closely correlated with multimorbidity.Ward and Schiller[2]reported that 65%of men and 72%of women aged>65 years in the US had at least two chronic conditions in 2010.Accordingly,older adults living with multiple chronic conditions tend to be readmitted after discharge,further leading to increased expenditure and more utilization of medical resources.Many studies have reported higher read mission rates in elderly patients.However,previous studies have focused on investigating the factors that influence read mission for a single disease,rather than for the chronic comorbid conditions in the initial hospitalization and the changes in these conditions from initial hospitalization to read mission among the elderly in China.Furthermore,most studies have focused on Caucasian patients and have been conducted in the US.Little is known about Chinese patients due to the lack of large-scale data.Identifying the common chronic comorbid conditions and the changes in these conditions from initial hospitalization to read mission among older people is important as it will help in the understanding of the chronic conditions leading to avoidable read mission and facilitate the development of efficient intervention strategies for the reduction of read missions.

The Limit of Finite Sample Breakdown Point of Tukey’s Halfspace Median for General Data

Under special conditions on data set and underlying distribution, the limit of finite sample breakdown point of Tukey＇s halfspace median （1） has been obtained in the literature. In this paper, we establish the result under weaker assumptions imposed on underlying distribution （weak smoothness） and on data set （not necessary in general position）. The refined representation of Tukey＇s sample depth regions for data set not necessary in general position is also obtained, as a by-product of our derivation.

空间各向异性Gauss场的局部时和逆像集的维数 献给余家荣教授100华诞

本文研究一类在空间R^d中具有各向异性的(N, d)-Gauss随机场,证明其局部时的正则性和逆像集的Hausdorff维数的新结果.本文也给出(N, d)-Gauss随机场的一些公开问题.