Kernel density estimation under negative superadditive dependence and its application for real data

In this paper, the kernel density estimator for negatively superadditive dependent random variables is studied. The exponential inequalities and the exponential rate for the kernel estimator of density function with a uniform version, over compact sets are investigated. Also, the optimal bandwidth rate of the estimator is obtained using mean integrated squared error. The results are generalized and used to improve the ones obtained for the case of associated sequences. As an application, FGM sequences that fulfil our assumptions are investigated. Also, the convergence rate of the kernel density estimator is illustrated via a simulation study. Moreover, a real data analysis is presented.     

Multivariate Return Decomposition: Theory and Implications

In this paper, we propose a model based on multivariate decomposition of multiplicative – absolute values and signs – components of asset returns. In the m-variate case, the marginals for the m absolute values and the binary marginals for the m directions are linked through a 2m-dimensional copula. The approach is detailed in the case of a bivariate decomposition. We outline the construction of the likelihood function and the computation of different conditional measures. The finite-sample properties of the maximum likelihood estimator are assessed by simulation. An application to predicting bond returns illustrates the usefulness of the proposed method.     

Max‐infinitely divisible models and inference for spatial extremes

For many environmental processes, recent studies have shown that the dependence strength is decreasing when quantile levels increase. This implies that the popular max‐stable models are inadequate to capture the rate of joint tail decay, and to estimate joint extremal probabilities beyond observed levels. We here develop a more flexible modeling framework based on the class of max‐infinitely divisible processes, which extend max‐stable processes while retaining dependence properties that are natural for maxima. We propose two parametric constructions for max‐infinitely divisible models, which relax the max‐stability property but remain close to some popular max‐stable models obtained as special cases. The first model considers maxima over a finite, random number of independent observations, while the second model generalizes the spectral representation of max‐stable processes. Inference is performed using a pairwise likelihood. We illustrate the benefits of our new modeling framework on Dutch wind gust maxima calculated over different time units. Results strongly suggest that our proposed models outperform other natural models, such as the Student‐t copula process and its max‐stable limit, even for large block sizes.     

Uniform consistency rate of kNN regression estimation for functional time series data

In this paper, we investigate the k-nearest neighbours (kNN) estimation of nonparametric regression model for strong mixing functional time series data. More precisely, we establish the uniform almost complete convergence rate of the kNN estimator under some mild conditions. Furthermore, a simulation study and an empirical application to the real data analysis of sea surface temperature (SST) are carried out to illustrate the finite sample performances and the usefulness of the kNN approach.     

Nonparametric beta kernel estimator for long and short memory time series

In this article we introduce a nonparametric estimator of the spectral density by smoothing the periodogram using beta kernel density. The estimator is proved to be bounded for short memory data and diverges at the origin for long memory data. The convergence in probability of the relative error and Monte Carlo simulations show that the proposed estimator automatically adapts to the long- and the short-range dependency of the process. A cross-validation procedure is studied in order to select the nuisance parameter of the estimator. Illustrations on historical as well as most recent returns and absolute returns of the S&P500 index show the performance of the beta kernel estimator. The Canadian Journal of Statistics 48: 582–595; 2020 © 2020 Statistical Society of Canada     

Elementary renewal theorems for widely dependent random variables with applications to precise large deviations

Abstract

On the basis of Wang and Cheng (J. Math. Anal. Appl. 384 (2011) 597–606), this paper further investigates elementary renewal theorems for counting processes generated by random walks with widely orthant dependent increments. The obtained results improve the corresponding ones of the above-mentioned paper mainly in the sense of weakening the moment conditions on the positive parts of the increments. Meanwhile, a revised version of strong law of large numbers for random walks with widely orthant dependent increments is established, which improves Theorem 1.4 of Wang and Cheng (2011 Wang, Y., and D. Cheng. 2011. Basic renewal theorems for a random walk with widely dependent increments and their applications. Journal of Mathematical Analysis and Applications 384 (2):597–606. doi:10.1016/j.jmaa.2011.06.010.[Crossref], [Web of Science ®] , [Google Scholar]) by enlarging the regions of dominating coefficients. Finally, by using the above results, some precise large deviation results for a nonstandard renewal risk model are established, in which the innovations are widely orthant dependent random variables with common heavy tails, and the inter-arrival times are also widely orthant dependent.     

Estimation of the marginal expected shortfall under asymptotic independence

We study the asymptotic behavior of the marginal expected shortfall when the two random variables are asymptotic independent but positively associated, which is modeled by the so-called tail dependent coefficient. We construct an estimator of the marginal expected shortfall, which is shown to be asymptotically normal. The finite sample performance of the estimator is investigated in a small simulation study. The method is also applied to estimate the expected amount of rainfall at a weather station given that there is a once every 100 years rainfall at another weather station nearby.     

Copula representation of bivariate L-moments: a new estimation method for multiparameter two-dimensional copula models

Serfling and Xiao [A contribution to multivariate L-moments, L-comoment matrices. J Multivariate Anal. 2007;98:1765–1781] extended the L-moment theory to the multivariate setting. In the present paper, we focus on the two-dimensional random vectors to establish a link between the bivariate L-moments (BLM) and the underlying bivariate copula functions. This connection provides a new estimate of dependence parameters of bivariate statistical data. Extensive simulation study is carried out to compare estimators based on the BLM, the maximum likelihood, the minimum distance and a rank approximate Z-estimation. The obtained results show that, when the sample size increases, BLM-based estimation performs better as far as the bias and computation time are concerned. Moreover, the root-mean-squared error is quite reasonable and less sensitive in general to outliers than those of the above cited methods. Further, the proposed BLM method is an easy-to-use tool for the estimation of multiparameter copula models. A generalization of the BLM estimation method to the multivariate case is discussed.     

初中起点幼师大学生历史课过度教学现象探析

一般而言，历史课及其任课教师是比较受初中起点幼师大学生欢迎的。与此同时，历史课教学中也时常不经意间在教学内容安排、教学方法运用和教学观点表达等方面出现过度教学现象。学生主体地位的异化，教学过程把控失当和教学反思的缺位，是造成过度教学的主要原因。消除过度教学现象的对策主要是坚持教学过程中学生的主体地位，掌握教学有度的艺术和重视教学反思。     

Local Estimation of the Conditional Stable Tail Dependence Function

We consider the local estimation of the stable tail dependence function when a random covariate is observed together with the variables of main interest. Our estimator is a weighted version of the empirical estimator adapted to the covariate framework. We provide the main asymptotic properties of our estimator, when properly normalized, in particular the convergence of the empirical process towards a tight centred Gaussian process. The finite sample performance of our estimator is illustrated on a small simulation study and on a dataset of air pollution measurements.