Parameter Identification for Drift Fractional Brownian Motions with Application to the Chinese Stock Markets

This article deals with the problem of estimating all the unknown parameters in the drift fractional Brownian motion with discretely sampled data. The estimation procedure is built upon the marriage of the variation method and the ergodic theory. The strong consistencies of these estimators are provided. Moreover, our method and two existing approaches are compared based on the computational running time and the accuracy of estimation via simulation studies. We also apply the proposed method to the real high-frequency financial data within a window of 4 h in the trading day from the Chinese mainland stock market.     

The two-sample problem with multivariate censored data: a new rank test family

A new rank test family is proposed to test the equality of two multivariate failure times distributions with censored observations. The tests are very simple: they are based on a transformation of the multivariate rank vectors to a univariate rank score and the resulting statistics belong to the familiar class of the weighted logrank test statistics. The new procedure is also applicable to multivariate observations in general, such as repeated measures, some of which may be missing. To investigate the performance of the proposed tests, a simulation study was conducted with bivariate exponential models for various censoring rates. The size and power of these tests against Lehmann alternatives were compared to the size and power of two other tests (Wei and Lachin, 1984 and Wei and Knuiman, 1987). In all simulations the new procedures provide a relatively good power and an accurate control over the size of the test. A real example from the National Cooperative Gallstone Study is given     

Dynamic risk control for project development

A statistical methodology for dynamic risk control is discussed. The research is aimed at constructing tools for the analysis of expert opinions within a company about the risks involved in the production of a new commercial product or service. Focus is on risk events and on the analysis of the expert assessments of probabilities, losses and correlations of such events. A rescoring loop of risk assessments and preventive actions taken by the company on the basis of these assessments is illustrated through an example on software development. Relevant literature on risk and subjective elicitations is reviewed.     

Illustration of Sampling-Based Methods for Uncertainty and Sensitivity Analysis

A sequence of linear, monotonic, and nonmonotonic test problems is used to illustrate sampling-based uncertainty and sensitivity analysis procedures. Uncertainty results obtained with replicated random and Latin hypercube samples are compared, with the Latin hypercube samples tending to produce more stable results than the random samples. Sensitivity results obtained with the following procedures and/or measures are illustrated and compared: correlation coefficients (CCs), rank correlation coefficients (RCCs), common means (CMNs), common locations (CLs), common medians (CMDs), statistical independence (SI), standardized regression coefficients (SRCs), partial correlation coefficients (PCCs), standardized rank regression coefficients (SRRCs), partial rank correlation coefficients (PRCCs), stepwise regression analysis with raw and rank-transformed data, and examination of scatter plots. The effectiveness of a given procedure and/or measure depends on the characteristics of the individual test problems, with (1) linear measures (i.e., CCs, PCCs, SRCs) performing well on the linear test problems, (2) measures based on rank transforms (i.e., RCCs, PRCCs, SRRCs) performing well on the monotonic test problems, and (3) measures predicated on searches for nonrandom patterns (i.e., CMNs, CLs, CMDs, SI) performing well on the nonmonotonic test problems.     

Efficient Covariance Estimation for Asynchronous Noisy High‐Frequency Data

Abstract. We focus on estimating the integrated covariance of log‐price processes in the presence of market microstructure noise. We construct a consistent asymptotically unbiased estimator for the quadratic covariation of two Itô processes in the case where high‐frequency asynchronous discrete returns under market microstructure noise are observed. This estimator is based on synchronization and multi‐scale methods and attains the optimal rate of convergence. A lower bound for the rate of convergence is derived from the local asymptotic normality property of the simpler parametric model with equidistant and synchronous observations. A Monte Carlo study analyses the finite sample size characteristics of our estimator.     

Small-area estimation in the presence of area-level correlated responses

The Fay-Herriot area-level model for correlated response data is augmented with a between-groups-of-domains effect. Correlated-response parameters of small-area estimates no longer need the assumption of spatial contiguity. A simulation shows that area-level correlated-response observations increase the efficiency of the estimates, but do not reduce the biases.     

Scale mixtures log-Birnbaum–Saunders regression models with censored data: a Bayesian approach

The main objective of this paper is to develop a full Bayesian analysis for the Birnbaum–Saunders (BS) regression model based on scale mixtures of the normal (SMN) distribution with right-censored survival data. The BS distributions based on SMN models are a very general approach for analysing lifetime data, which has as special cases the Student-t-BS, slash-BS and the contaminated normal-BS distributions, being a flexible alternative to the use of the corresponding BS distribution or any other well-known compatible model, such as the log-normal distribution. A Gibbs sample algorithm with Metropolis–Hastings algorithm is used to obtain the Bayesian estimates of the parameters. Moreover, some discussions on the model selection to compare the fitted models are given and case-deletion influence diagnostics are developed for the joint posterior distribution based on the Kullback–Leibler divergence. The newly developed procedures are illustrated on a real data set previously analysed under BS regression models.     

Multiple cases deletion measures in linear measurement error models

In this paper, we define a multiple cases deletion model (MCDM) in linear measurement error models (LMEMs). Then, by using the corrected score method of Nakamura (1990), the estimation of parameters is obtained. Furthermore, Based on MCDM, we provide computationally inexpensive deletion diagnostic tools for LMEMs. An example illustrates that our method is useful for diagnosing influential subsets of observations.     

Outlier detection based on extreme value theory and applications

Whether an extreme observation is an outlier or not depends strongly on the corresponding tail behavior of the underlying distribution. We develop an automatic, data-driven method rooted in the mathematical theory of extremes to identify observations that deviate from the intermediate and central characteristics. The proposed algorithm is an extension of a method previously proposed in the literature for the specific case of heavy tailed Pareto-type distributions to all max-domains of attraction. We propose some applications such as a tail-adjusted boxplot which yields a more accurate representation of possible outliers, and the identification of outliers in a multivariate context through an analysis of associated random variables such as local outlier factors. Several examples and simulation results illustrate the finite sample behavior of the algorithm and its applications.