Estimating the population proportion in modified ranked set sampling methods

In this paper, proportion estimators and associated variance estimators are proposed for a binary variable with a concomitant variable based on modified ranked set sampling methods, which are extreme ranked set sampling (ERSS), median ranked set sampling (MRSS), percentile ranked set sampling (Per-RSS) and L ranked set sampling (LRSS) methods. The Monte Carlo simulation study is performed to compare the performance of the estimators based on bias, mean squared error, and relative efficiency for different levels of correlation coefficient, set and cycle sizes under normal and log-normal distributions. Moreover, the study is supported with real data application.     

Independent attributes control chart for Markov-dependent processes

Statistical process monitoring (SPM) is a very efficient tool to maintain and to improve the quality of a product. In many industrial processes, end product has two or more attribute-type quality characteristics. Some of them are independent, but the observations are Markovian dependent. It is essential to develop a control chart for such situations. In this article, we develop an Independent Attributes Control Chart for Markov Dependent Processes based on error probabilities criterion under the assumption of one-step Markov dependency. Implementation of the chart is similar to that of Shewhart-type chart. Performance of the chart has been studied using probability of detecting shift criterion. A procedure to identify the attribute(s) responsible for out-of-control status of the process is given.     

Optional randomized response techniques for quantitative characteristics

Gupta et al. and Huang considered optional randomized response techniques where the probability of choosing the randomized (or direct) response is fixed for all the respondents. In this paper the assumption of the constant probability of choosing the option has been relaxed by dividing respondents into two groups: one group provides direct response and the second a randomized response. The method of estimation of the population mean and variances under the modified assumption are obtained. Relative efficiencies of the proposed techniques are compared theoretically and empirically.     

Estimating ordered quantiles of two exponential populations with a common minimum guarantee time

The problem of estimating ordered quantiles of two exponential populations is considered, assuming equality of location parameters (minimum guarantee times), using the quadratic loss function. Under order restrictions, we propose new estimators which are the isotonized version of the MLEs, call it, restricted MLE. A sufficient condition for improving equivariant estimators is derived under order restrictions on the quantiles. Consequently, estimators improving upon the old estimators have been derived. A detailed numerical study has been done to evaluate the performance of proposed estimators using the Monte-Carlo simulation method and recommendations have been made for the use of the estimators.     

Systemic risk statistics with scenario analysis

In this paper, we introduce two new classes of risk statistics, named convex and positively homogeneous systemic risk statistics, respectively. Structural decomposition results and representation results for them are provided. These new risk statistics can be considered as a kind of systemic risk extension of risk statistics introduced by Kou, Peng, and Heyde, and also empirical versions of system risk measures introduced by Cehn, Iyengar, and Mollemi and Kromer, Overbeck, and Zich. Finally, some examples are also given.     

煤矿瓦斯爆炸事故单危险源风险度量模型研究

本文研究了煤矿瓦斯爆炸事故危险源的分类,把危险源划分为人的不安全行为、机器设备不安全状态、环境不安全特征和管理缺陷四大类,并根据煤矿现场调查各类危险源的数据以及相应数学方法的特点,提出煤矿瓦斯爆炸事故人、机器设备(物)、环境、管理四类危险源的风险度量方法,在此基础上构建四类危险源的风险度量模型。研究表明,危险源的风险度量模型由风险发生的可能性、危险源重要度以及事故导致的损失构成;危险源风险发生的可能性,在具体应用中可以采用各类危险源的不可靠度、故障率等来衡量;危险源在事故中的重要度可以通过分析事故故障树种要素结构重要性获取。根据风险评价的结果,可以对危险源进行分级排序,从而为煤矿事故单危险源的控制提供依据。     

Local composite quantile regression estimation of time-varying parameter vector for multidimensional time-inhomogeneous diffusion models

This paper is dedicated to the study of the composite quantile regression (CQR) estimations of time-varying parameter vectors for multidimensional diffusion models. Based on the local linear fitting for parameter vectors, we propose the local linear CQR estimations of the drift parameter vectors, and verify their asymptotic biases, asymptotic variances and asymptotic normality. Moreover, we discuss the asymptotic relative efficiency (ARE) of the local linear CQR estimations with respect to the local linear least-squares estimations. We obtain that the local estimations that we proposed are much more efficient than the local linear least-squares estimations. Simulation studies are constructed to show the performance of the estimations proposed.     

Asymptotics of the Finite-time Ruin Probability for the Sparre Andersen Risk Model Perturbed by an Inflated Stationary Chi-process

In this article, we consider the Sparre Andersen risk model that is perturbed by an inflated chi-process with non-negative random inflator R. Under some conditions on the perturbation and the random inflator, which allow for both small and large fluctuations, exact asymptotic behaviour of the finite-time ruin probability is obtained when initial reserve tends to infinity.     

Detecting structural breaks in multivariate financial time series: evidence from hedge fund investment strategies

This paper extends the class of asset-based style factor models with multiple structural breaks to the multivariate setting. We propose a model that allows for the presence of common breaks in a system of factor models for individual hedge fund investment strategies, which share common investment characteristics. We develop a Bayesian approach to inference for the unknown number and positions of the structural breaks, based on a set of filtering recursions similar to those of the forward–backward algorithm. Furthermore, we identify relevant risk factors, common among the series of hedge funds, using a Bayesian model comparison approach. We apply our method to a set of correlated hedge fund strategies, which are mainly characterized by equity related bets. Multiple common breaks are identified, consistent with well-known market events, which reveal evidence for structural changes in the risk exposures as well as in the correlation structure of the analysed series.     

The matched pair sign test using bivariate ranked set sampling for different ranking based schemes

Bivariate rank set sample (BVRSS) matched pair sign test is introduced and investigated for different ranking based schemes. We show that this test is asymptotically more efficient and more powerful than its counterpart sign test based on a bivariate simple random sample (BVSRS) for different ranking schemes. The asymptotic null distribution and the efficiency of the test are derived. Pitman’s asymptotic relative efficiency is used to compare the asymptotic performance of the matched pair sign test using BVRSS versus using BVSRS in all ranking cases. For small sample sizes, the bootstrap method is used to estimate P-values. Numerical comparisons are used to gain insight about the efficiency of the BVRSS sign test compared to the BVSRS sign test. Our numerical and theoretical results indicate that using any ranking scheme of BVRSS for the matched pair sign test is more efficient than using BVSRS.