Change-point detection for expected shortfall in time series

Expected shortfall (ES) is a popular risk measure and plays an important role in risk and portfolio management. Recently, change-point detection of risk measures has been attracting much attention in finance. Based on the self-normalized CUSUM statistic in Fan, Glynn and Pelger (2018) and the Wild Binary Segmentation (WBS) algorithm in Fryzlewicz (2014), this paper proposes a variant WBS procedure to detect and estimate change points of ES in time series. The strengthened Schwarz information criterion is also introduced to determine the number of change points. Monte Carlo simulation studies are conducted to assess the finite-sample performance of our variant WBS procedure about ES in time series. An empirical application is given to illustrate the usefulness of our procedure.     

A play-the-winner-type urn design with reduced variability

We propose a new adaptive allocation rule, the drop-the-loser, that randomizes subjects in the course of a trial comparing treatments with dichotomous outcomes. The rule tends to assign more patients to better treatments with the same limiting proportion as the randomized play-the-winner rule. The new design has significantly less variable allocation proportion than the randomized play-the-winner rule. Decrease in variability translates into a gain in statistical power. For some values of success probabilities the drop-the-loser rule has a double advantage over conventional equal allocation in that it has better power and assigns more subjects to the better treatment. Acknowledgments. I thank Stephen Durham, the associate editor, and the referees for their helpful suggestions.     

Estimation of the mean in ranked set sampling with non responses

The estimation of the population mean when ranked set sampling [rss] is used for selecting the sample and non responses [nr] are present, is studied. The nr stratum is sub sampled using simple random sampling with replacement. Two strategies are analyzed. One of them is based on the selection of a sub sample from the nr in each cycle. The other uses sub samples selected among the nr in each rank.  The accuracy of the proposed estimators is characterized by the corresponding expected variances. Simulations and real life data are used for analyzing the behavior of them. Acknowledgements: This paper was developed partially during the visit of the author to Université des Antilles et Gouyane. The author gratefully acknowledges the helpful suggestions of the referees and thanks the support of DAAD for visiting Humboldt University where a version of the paper version was made.     

Another view on optimal design for estimating the point of extremum in quadratic regression

In this paper we illustrate how certain design problems can be simplified by reparametrization of the response function. This alternative viewpoint provides further insights than the more traditional approaches, like minimax, Bayesian or sequential techniques. It will also improve a practitioner’s understanding of more general situations and their “classical” treatment.     

随机存货决策中的安全库存研究

在有短缺成本下 ,讨论了再定购点的确定 ,着重分析了安全库存的一种简易计算。     

On efficiency of the ratio estimator

Summary The exact mean square error for the ratio estimator of a finite population total based on simple random sampling without replacement is shown to have an expected value less than that of the variance of the ratio estimator based on Midzuno’s scheme, under a usual super-population model.     

Robustness issues in multilevel regression analysis

A multilevel problem concerns a population with a hierarchical structure. A sample from such a population can be described as a multistage sample. First, a sample of higher level units is drawn (e.g. schools or organizations), and next a sample of the sub‐units from the available units (e.g. pupils in schools or employees in organizations). In such samples, the individual observations are in general not completely independent. Multilevel analysis software accounts for this dependence and in recent years these programs have been widely accepted. Two problems that occur in the practice of multilevel modeling will be discussed. The first problem is the choice of the sample sizes at the different levels. What are sufficient sample sizes for accurate estimation? The second problem is the normality assumption of the level‐2 error distribution. When one wants to conduct tests of significance, the errors need to be normally distributed. What happens when this is not the case? In this paper, simulation studies are used to answer both questions. With respect to the first question, the results show that a small sample size at level two (meaning a sample of 50 or less) leads to biased estimates of the second‐level standard errors. The answer to the second question is that only the standard errors for the random effects at the second level are highly inaccurate if the distributional assumptions concerning the level‐2 errors are not fulfilled. Robust standard errors turn out to be more reliable than the asymptotic standard errors based on maximum likelihood.     

Designs for estimating an extremal point of quadratic regression models in a hyperball

This paper is devoted to studying optimal designs for estimating an extremal point of a multivariate quadratic regression model in the unit hyperball. The problem of estimating an extremal point is reduced to that of estimating certain parameters of a corresponding nonlinear (in parameters) regression model. For this reduced problem truncated locally D-optimal designs are found in an explicit form. The result is a generalization of the results of Fedorov and Müller (1997) for onedimensional quadratic regression function in the unit segment. Received February 2002     

A two-stage stratified Warner’s randomized response model using optimal allocation

This paper applies Kim and Wardes (2004) stratified Warners randomized response model to Mangat and Singhs (1990) two-stage randomized response model. The proposed stratified randomized response model has an optimal allocation and a large gain in precision. Hence, the estimator based on the proposed method is more efficient than Kim and Wardes (2004) and Mangat and Singhs (1990) estimators under the conditions presented in both the case of completely truthful reporting and that of not completely truthful reporting by the respondents.     

论检验直接成本和间接成本的平衡及平衡点的经济意义

分析了工业企业外购物品检验成本的两个组成部分:检验过程直接投入的要素成本和检验结果失准诱发的问接成本,并分析论证了二者的习性、平衡条件以及平衡点的计算方法及应用。