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In this paper, we focus on the BDS test, which is a nonparametric test of independence. Specifically, the null hypothesis H0 of it is that {ut} is i.i.d. (independent and identically distributed), where {ut} is a random sequence. The BDS test is widely used in economics and finance, but it has a weakness that cannot be ignored: over-rejecting H0 even if the length T of {ut} is as large as (100, 2000). To improve the over-rejection problem of BDS test, considering that the correlation integral is the foundation of this test, we not only accurately describe the expectation of the correlation integral under H0, but also calculate all terms of the asymptotic variance of the correlation integral whose order is O(T−1) and O(T−2), which is essential to improve the finite sample performance of BDS test. Based on this, we propose a revised BDS (RBDS) test and prove its asymptotic normality under H0. The RBDS test not only inherits all the advantages of BDS test, but also effectively corrects the over-rejection problem of it, which can be fully confirmed by the simulation results we presented. Moreover, based on the simulation results, we find that similar to BDS test, RBDS test would also be affected by the parameter estimations of the ARCH-type model, resulting in size distortion, but this phenomenon can be alleviated by the logarithmic transformation preprocessing of the estimate residuals of the model. Besides, through some actual datasets that have been demonstrated to fit well with ARCH-type models, we also compared the performance of BDS test and RBDS test in evaluating the goodness-of-fit of the model in empirical problem, and the results reflect that, under the same condition, the performance of the RBDS test is more encouraging. [ABSTRACT FROM AUTHOR]

In real data analysis, the underlying model is frequently unknown. Hence, the modeling strategy plays a key role in the success of data analysis. Inspired by the idea of model averaging, we propose a novel semiparametric modeling strategy for the conditional quantile prediction, without assuming that the underlying model is any specific parametric or semiparametric model. Due to the optimality of the weights selected by leave-one-out cross-validation, the proposed modeling strategy provides a more precise prediction than those based on some commonly used semiparametric models such as the varying coefficient and additive models. Asymptotic properties are established in the proposed modeling strategy along with its estimation procedure. We conducted extensive simulations to compare our method with alternatives across various scenarios. The results show that our method provides more accurate predictions. Finally, we applied our approach to the Boston housing data, yielding more precise quantile predictions of house prices compared with commonly used methods, and thus offering a clearer picture of the Boston housing market. [ABSTRACT FROM AUTHOR]

This work focuses on dimension-reduction techniques for modelling conditional extreme values. Specifically, we investigate the idea that extreme values of a response variable can be explained by nonlinear functions derived from linear projections of an input random vector. In this context, the estimation of projection directions is examined, as approached by the extreme partial least squares (EPLS) method—an adaptation of the original partial least squares (PLS) method tailored to the extreme-value framework. Further, a novel interpretation of EPLS directions as maximum likelihood estimators is introduced, utilizing the von Mises–Fisher distribution applied to hyperballs. The dimension reduction process is enhanced through the Bayesian paradigm, enabling the incorporation of prior information into the projection direction estimation. The maximum a posteriori estimator is derived in two specific cases, elucidating it as a regularization or shrinkage of the EPLS estimator. We also establish its asymptotic behavior as the sample size approaches infinity. A simulation data study is conducted in order to assess the practical utility of our proposed method. This clearly demonstrates its effectiveness even in moderate data problems within high-dimensional settings. Furthermore, we provide an illustrative example of the method’s applicability using French farm income data, highlighting its efficacy in real-world scenarios. [ABSTRACT FROM AUTHOR]

Consider an insurance risk model with constant force of interest under the assumption that an immediate claim is accompanied by a random number of delayed claims. In the presence of heavy tails on claim distributions and dependence structures among modelling components, we study the uniform asymptotics for an insurer's ruin-related quantities, where the uniformity holds for all time horizons varying in a relevant interval. [ABSTRACT FROM AUTHOR]

In this article, some general results on the rates of strong consistency for the least squares estimators and weighted least squares estimators in heteroscedastic partially linear errors-in-variables model based on widely orthant dependent random errors are presented. The results can deduce strong consistency and convergence rates under some mild conditions. Some numerical simulations are also provided to support the theoretical results. [ABSTRACT FROM AUTHOR]

Panel count regression is often required in recurrent event studies, where the interest is to model the event rate. Existing rate models are unable to handle time-varying covariate effects due to theoretical and computational difficulties. Mean models provide a viable alternative but are subject to the constraints of the monotonicity assumption, which tends to be violated when covariates fluctuate over time. In this paper, we present a new semiparametric rate model for panel count data along with related theoretical results. For model fitting, we present an efficient EM algorithm with three different methods for variance estimation. The algorithm allows us to sidestep the challenges of numerical integration and difficulties with the iterative convex minorant algorithm. We showed that the estimators are consistent and asymptotically normally distributed. Simulation studies confirmed an excellent finite sample performance. To illustrate, we analyzed data from a real clinical study of behavioral risk factors for sexually transmitted infections. [ABSTRACT FROM AUTHOR]

The trend change point is the point at which the trend (or slope) in time series data changes. How to detect such change point is one of the key issues in statistical analysis. This paper proposes for a new gradual change point model for time series trend terms based on the existing abrupt change point model. Secondly, inspired by existing studies, a ratio statistic is constructed for the gradual trend change point in heavy–tailed AR(p) series. The theoretical results indicate that the asymptotic distribution of the statistic under the null hypothesis is a functional of the Lévy process. Meanwhile, this paper proves its consistency under the alternative hypothesis. In addition, due to the heavy tailed characteristics of the sequence, in order to avoid estimating the tail index and reduce the impact of extreme values on the critical values of the statistic, this paper reconstructs the test statistic based on the subsampling method and compares it with the original method. It is found that the subsampling method has a significant improvement on the test power when the change point is located later. Finally, the method is applied to the change point problem of Google stock closing price, and the trend change point is successfully detected. [ABSTRACT FROM AUTHOR]

In this paper, we investigate hypothesis testing for the linear combination of mean vectors across multiple populations through the method of random integration. We have established the asymptotic distributions of the test statistics under both null and alternative hypotheses. Additionally, we provide a theoretical explanation for the special use of our test statistics in situations when the nonzero signals in the linear combination of the true mean vectors are weakly dense and nearly the same sign. Moreover, Monte Carlo simulations are presented to evaluate the suggested test against existing high-dimensional tests. The findings from these simulations reveal that our test not only aligns with the performance of other tests in terms of size but also exhibits superior power. [ABSTRACT FROM AUTHOR]

In this paper, we considered partially linear single-index quantile regression with longitudinal data. By using Bayesian techniques, quasi-posterior distributions of the linear and single-index parameters were constructed based on a quasi-likelihood function. Under suitable assumptions, we derived asymptotic normality of posterior estimators of the parameters, and established asymptotic relationship between the posterior estimators and their corresponding frequency estimators. Meanwhile, we used a stochastic search hierarchical model with spike-slab priors to perform variable selection and study consistency of the variable selection. Finite sample performance of the proposed methods was analyzed via simulation and real data too. [ABSTRACT FROM AUTHOR]

The Bradley-Terry model is a common model for analyzing paired comparison data. Under differential private mechanism, there is a lack of asymptotic properties for the parameter estimator of parameters in this model. In this article, we show that the moment estimators of the parameters based on the differential private degree sequence with Laplace noise is uniformly consistent and asymptotically normal. Simulations are provided to illustrate asymptotic results. [ABSTRACT FROM AUTHOR]

There is a growing literature on design-based (DB) methods to estimate average treatment effects (ATEs) for randomized controlled trials (RCTs) for full sample analyses. This article extends these methods to estimate ATEs for discrete subgroups defined by pre-treatment variables, with an application to an RCT testing subgroup effects for a school voucher experiment in New York City. We consider ratio estimators for subgroup effects using regression methods, allowing for model covariates to improve precision, and prove a new finite population central limit theorem. We discuss extensions to blocked and clustered RCT designs, and to other common estimators with random treatment-control sample sizes or summed weights: post-stratification estimators, weighted estimators that adjust for data nonresponse, and estimators for Bernoulli trials. We also develop simple variance estimators that share features with robust estimators. Simulations show that the DB subgroup estimators yield confidence interval coverage near nominal levels, even for small subgroups.

In this article, the primary aim is to introduce a new flexible family of circular distributions, namely the wrapped Linnik family which possesses the flexibility to model the inflection points and tail behavior often better than the existing popular flexible symmetric unimodal circular models. The second objective of this article is to obtain a simple and efficient estimator of the index parameter α of symmetric Linnik distribution exploiting the fact that it is preserved in the wrapped Linnik family. This is an interesting problem for highly volatile financial data as has been studied by several authors. Our final aim is to analytically derive the asymptotic distribution of our estimator, not available for other estimator. This estimator is shown to outperform the existing estimator over the range of the parameter for all sample sizes. The proposed wrapped Linnik distribution is applied to some real-life data. A measure of goodness of fit proposed in one of the authors' previous works is used for the above family of distributions. The wrapped Linnik family was found to be preferable as it gave better fit to those data sets rather than the popular von-Mises distribution or the wrapped stable family of distributions. [ABSTRACT FROM AUTHOR]

Estimation and hypothesis test for varying coefficient single-index multiplicative models are considered in this paper. To estimate an unknown single-index parameter, a profile product relative error estimation is proposed for the single-index parameter with a leave-one-component-out estimation method. A Wald-type test statistic is proposed to test a linear hypothesis test of the single-index. We employ the smoothly clipped absolute deviation penalty to simultaneously select variables and estimate regression coefficients. To study the model checking problem, we propose a variant of the integrated conditional moment test statistic by using a linear projection weighting function, and we also suggest a bootstrap procedure for calculating critical values. Simulation studies are conducted to demonstrate the performance of the proposed procedure and a real example is analysed for illustration. [ABSTRACT FROM AUTHOR]

AbstractWe, in this article, focus on functional partially linear quantile regression, where the observations are missing at random, which allows the response or covariates or response and covariates simultaneously missing. Estimation of the unknown function is done based on reproducing kernel method. Under suitable assumptions, we discuss consistency with rates of the estimators, and establish asymptotic normality of the estimator for the parameter. At the same time, we study hypothesis test of the parameter, and prove asymptotic distributions of restricted estimators of the parameter and test statistic under null hypothesis and local alternative hypothesis, respectively. Also, we study variable selection of the linear part of the model. By simulation and real data, finite sample performance of the proposed methods is analyzed. [ABSTRACT FROM AUTHOR]

A hypothesis related to the block structure of a covariance matrix under the doubly multivariate normal model is studied. It is assumed that the block structure of the covariance matrix belongs to a quadratic subspace, and under the null hypothesis, each block of the covariance matrix also has a structure belonging to some quadratic subspace. The Rao score and the likelihood ratio test statistics are derived, and the exact distribution of the likelihood ratio test is determined. Simulation studies show the advantage of the Rao score test over the likelihood ratio test in terms of speed of convergence to the limiting chi-square distribution, while both proposed tests are competitive in terms of their power. The results are applied to both simulated and real-life example data. [ABSTRACT FROM AUTHOR]

The estimation of a certain threshold beyond which an extreme value distribution can be fitted to the tail of a data distribution remains one of the main issues in the theory of statistics of extremes. While standard Peak over Threshold (PoT) approaches determine this threshold graphically, we introduce in this paper a general framework which makes it possible for one to determine this threshold algorithmically by estimating it as a free parameter within a composite distribution. To see how this threshold point arises, we propose a general framework for generating three-component hybrid distributions which meets the need of data sets with right heavy-tail. The approach involves the combination of a distribution which can efficiently model the bulk of the data around the mean, with an heavy-tailed distribution meant to model the data observations in the tail while using another distribution as a link to connect the two. Some special examples of distributions resulting from the general framework are generated and studied. An estimation algorithm based on the maximum likelihood method is proposed for the estimation of the free parameters of the hybrid distributions. Application of the hybrid distributions to the S &P 500 index financial data set is also carried out. [ABSTRACT FROM AUTHOR]

The main aim of this work is to develop a new goodness-of-fit test for the one-sided Lévy distribution. The proposed test is based on the scale-ratio approach in which two estimators of the scale parameter of one-sided Lévy distribution are confronted. The asymptotic distribution of the test statistic is obtained under null hypotheses. The performance of the test is demonstrated using simulated observations from various known distributions. Finally, two real-world datasets are analyzed. [ABSTRACT FROM AUTHOR]

The multivariate inverse hypergeometric (MIH) distribution is an extension of the negative multinomial (NM) model that accounts for sampling without replacement in a finite population. Even though most studies on longitudinal count data with a specific number of 'failures' occur in a finite setting, the NM model is typically chosen over the more accurate MIH model. This raises the question: How much information is lost when inferring with the approximate NM model instead of the true MIH model? The loss is quantified by a measure called deficiency in statistics. In this paper, asymptotic bounds for the deficiencies between MIH and NM experiments are derived, as well as between MIH and the corresponding multivariate normal experiments with the same mean-covariance structure. The findings are supported by a local approximation for the log-ratio of the MIH and NM probability mass functions, and by Hellinger distance bounds. [ABSTRACT FROM AUTHOR]

Abstract.This study delves into the conditional mode estimation of a randomly censored scalar response variable operating within the framework of strong mixing conditions. We introduce a kernel-based estimator for the conditional mode function. The principal contribution of this investigation lies in the derivation of the asymptotic distribution and the strong rate of convergence of the newly proposed estimators. These findings are established under a set of fairly comprehensive structural assumptions governing the underlying models. Additionally, we conduct a series of simulation studies to showcase the finite sample performance characteristics of the proposed estimator. [ABSTRACT FROM AUTHOR]

AbstractIn this study, we consider the problems of testing for a mean vector and testing the equality of two mean vectors with monotone missing data. We propose new test statistics similar to the simplified Hotelling’s T2-type test statistic for one-sample and two-sample problems under general-step monotone missing data. Approximate upper percentiles of this new statistics are provided by asymptotic expansion along with transformed test statistics based on Bartlett adjustment. Approximate simultaneous confidence intervals for pairwise comparisons among mean vectors are also presented. Furthermore, we investigated the asymptotic behavior of the proposed statistics using a Monte Carlo simulation, and the approximate accuracy of the proposed approximations are provided and discussed. Finally, the numerical power for several statistics is given. [ABSTRACT FROM AUTHOR]

Estimating parameters of drift and diffusion coefficients for multidimensional stochastic delay equations with small noise are considered. The delay structure is written as an integral form with respect to a delay measure. Our contrast function is based on a local-Gauss approximation to the transition probability density of the process. We show consistency and asymptotic normality of the minimum-contrast estimator when a small dispersion coefficient ε → 0 and sample size n → ∞ simultaneously. [ABSTRACT FROM AUTHOR]

In this paper, we consider the clustering of bivariate functional data where each random surface consists of a set of curves recorded repeatedly for each subject. The k-centres surface clustering method based on marginal functional principal component analysis is proposed for the bivariate functional data, and a novel clustering criterion is presented where both the random surface and its partial derivative function in two directions are considered. In addition, we also consider two other clustering methods, k-centres surface clustering methods based on product functional principal component analysis or double functional principal component analysis. Simulation results indicate that the proposed methods have a nice performance in terms of both the correct classification rate and the adjusted rand index. The approaches are further illustrated through empirical analysis of human mortality data. [ABSTRACT FROM AUTHOR]

The Hosmer-Lemeshow (HL) test is a commonly used global goodness-of-fit (GOF) test that assesses the quality of the overall fit of a logistic regression model. In this paper, we give results from simulations showing that the type I error rate (and hence power) of the HL test decreases as model complexity grows, provided that the sample size remains fixed and binary replicates (multiple Bernoulli trials) are present in the data. We demonstrate that a generalized version of the HL test (GHL) presented in previous work can offer some protection against this power loss. These results are also supported by application of both the HL and GHL test to a real-life data set. We conclude with a brief discussion explaining the behavior of the HL test, along with some guidance on how to choose between the two tests. In particular, we suggest the GHL test to be used when there are binary replicates or clusters in the covariate space, provided that the sample size is sufficiently large. [ABSTRACT FROM AUTHOR]

We consider a functional linear regression model with functional predictor and scalar response. For this model, a procedure to test the slope function based on projecting the slope function onto an arbitrary L 2 basis has been introduced in the literature. We propose its bootstrap counterpart for testing the slope function, and obtain the asymptotic null distributions of the tests statistics and the asymptotic powers of the tests. Finally, we conduct a simulation study to evaluate the accuracy of the two tests procedures. As a practical illustration, we use the Export Development Bank of Iran dataset, and test the nullity of the slope function of a model predicting total annual noncurrent balance of facilities based on current balance of facilities. [ABSTRACT FROM AUTHOR]

Tensor eigenvectors naturally generalize matrix eigenvectors to multi-way arrays: eigenvectors of symmetric tensors of order k and dimension p are stationary points of polynomials of degree k in p variables on the unit sphere. Dominant eigenvectors of symmetric tensors maximize polynomials in several variables on the unit sphere, while base eigenvectors are roots of polynomials in several variables. In this paper, we focus on skewness-based projection pursuit and on third-order tensor eigenvectors, which provide the simplest, yet relevant connections between tensor eigenvectors and projection pursuit. Skewness-based projection pursuit finds interesting data projections using the dominant eigenvector of the sample third standardized cumulant to maximize skewness. Skewness-based projection pursuit also uses base eigenvectors of the sample third cumulant to remove skewness and facilitate the search for interesting data features other than skewness. Our contribution to the literature on tensor eigenvectors and on projection pursuit is twofold. Firstly, we show how skewness-based projection pursuit might be helpful in sequential cluster detection. Secondly, we show some asymptotic results regarding both dominant and base tensor eigenvectors of sample third cumulants. The practical relevance of the theoretical results is assessed with six well-known data sets. [ABSTRACT FROM AUTHOR]

Generalized linear models (GLMs) are very widely used, but formal goodness-of-fit (GOF) tests for the overall fit of the model seem to be in wide use only for certain classes of GLMs. We develop and apply a new goodness-of-fit test, similar to the well-known and commonly used Hosmer–Lemeshow (HL) test, that can be used with a wide variety of GLMs. The test statistic is a variant of the HL statistic, but we rigorously derive an asymptotically correct sampling distribution using methods of Stute and Zhu (Scand J Stat 29(3):535–545, 2002) and demonstrate its consistency. We compare the performance of our new test with other GOF tests for GLMs, including a naive direct application of the HL test to the Poisson problem. Our test provides competitive or comparable power in various simulation settings and we identify a situation where a naive version of the test fails to hold its size. Our generalized HL test is straightforward to implement and interpret and an R package is publicly available. [ABSTRACT FROM AUTHOR]

In this article, we consider the asymptotic distribution of residual distribution estimator in the first order autoregressive models with positively associated or negatively associated random errors. Under mild regularity assumptions, some asymptotic normality results for residual distribution estimator are obtained when the autoregressive model is a stationary process or an explosive process. In addition, some simulations of estimated curves and mean integrated square errors are illustrated, which agree with our theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we consider a transformation in a random variable which follows a bimodal Birnbaum-Saunders distribution. We propose the unit-bimodal Birnbaum-Saunders (UBBS) distribution and investigate some of its important properties, like cumulative distribution function, moments, survival function and risk function. We apply the UBBS distribution to censored data inflated at zero and one. We used the maximum likelihood approach for parameter estimation and to compare the models. Given the flexibility in UBBS distribution modes, our proposal performs best in beta regression models with zero and/or one excess. [ABSTRACT FROM AUTHOR]

AbstractWe consider multicategory extensions of binary discrimination methods via one-versus-one (OVO) or one-versus-rest (OVR) methodologies, focusing on extensions of the binary classification by linear mean difference (MD), support vector machine (SVM), maximal data piling (MDP), and distance weighted discrimination (DWD) via OVO, and the multicategory extension of MD via OVR, in the context of high-dimensional and low sample size (HDLSS) data. The asymptotic behavior of OVO-MD, OVO-SVM, OVO-MDP and OVO-DWD is described when the dimension of the data increases and the sample size is fixed, in terms of the probabilities of correct classification of a new data point, finding sufficient conditions for the correct classification probabilities to converge to one as the dimension approaches infinity. As in the binary case, OVO-MD, OVO-SVM and OVO-MDP have the same asymptotic behavior while OVO-DWD could behave differently. We also consider the asymptotic behavior of the OVR-MD methodology providing necessary and sufficient conditions for a new data point of a given class to be correctly classified with probability tending to one. A simulation experiment is conducted to further compare the methodologies, and consider the four binary methods in the OVR case. We evaluate the performance of the considered methods using a microarray data set. [ABSTRACT FROM AUTHOR]

Abstract.In this article, we study a goodness of fit test for a multiplicative distortion model under a uniformly distributed but unobserved random variable. The unobservable variable is distorted in a multiplicative fashion by an observed confounding variable. The proposed k-th power test statistic is based on logarithmic transformed observations and a correlation coefficient-based estimator without distortion measurement errors. The proper choice of k is discussed through the empirical coverage probabilities. The asymptotic null distribution of the test statistics are obtained with known asymptotic variances. Next, we proposed the conditional mean calibrated test statistic when a variable is distorted in a multiplicative fashion. We conduct Monte Carlo simulation experiments to examine the performance of the proposed test statistics. [ABSTRACT FROM AUTHOR]

Mazucheli et al. (J Appl Stat 46(4):700–714, 2019) introduced unit Lindley distribution by transforming Lindley (J Roy Stat Soc Ser B Stat Methodol 20(1):102–107, 1958) distribution for modelling proportion data. In this paper, we consider an exponential version of unit Lindley distribution. Various statistical and structural properties of the new distribution are discussed such as moments, hazard rate function, inequality measures, entropy etc. Different estimation methods are used to estimate the parameters of the model and their performances are demonstrated by Monte Carlo simulation. Finally the dominance of proposed distribution is embellished through real life data sets by comparing with some other unit distributions available in literature. [ABSTRACT FROM AUTHOR]

AbstractIn this article, we investigate the estimators for the heteroscadastic partially linear regression model under dependent errors defined by yi=xiβ+g(ti)+εi (1≤i≤n), where εi = σiei, σi2=f(ui), the design points (xi,ti,ui) are known and nonrandom, β is an unknown parameter to be estimated, the functions g(⋅) and f(⋅) are unknown, which are defined on a closed interval [0,1], and the random errors {ei} are (α, β)-mixing random variables. When the model is heteroscedastic, the unknown parameter β and the unknown function g(⋅) are approximated by the weighted least squares estimators. We derive the asymptotic normality of the weighted least squares estimators under some suitable conditions. Simulation studies are conducted to demonstrate the finite sample performance of the proposed procedure. Finally, we use real data to examine the dependence between oil prices and exchange rates. [ABSTRACT FROM AUTHOR]

In this work we introduce the class of Unit-Weibull Autoregressive Moving Average models for continuous random variables taking values in (0, 1). The proposed model is an observation driven one, for which, conditionally on a set of covariates and the process' history, the random component is assumed to follow a Unit-Weibull distribution parameterized through its ρ th quantile. The systematic component prescribes an ARMA-like structure to model the conditional ρ th quantile by means of a link. Parameter estimation in the proposed model is performed using partial maximum likelihood, for which we provide closed formulas for the score vector and partial information matrix. We also discuss some inferential tools, such as the construction of confidence intervals, hypotheses testing, model selection, and forecasting. A Monte Carlo simulation study is conducted to assess the finite sample performance of the proposed partial maximum likelihood approach. Finally, we examine the prediction power by contrasting our method with others in the literature using the Manufacturing Capacity Utilization from the US. [ABSTRACT FROM AUTHOR]

We propose an estimator of the conditional tail moment (CTM) when the data are subject to random censorship. The variable of main interest and the censoring variable both follow a Pareto-type distribution. We establish the asymptotic properties of our estimator and discuss bias-reduction. Then, the CTM is used to estimate, in case of censorship, the premium principle for excess-of-loss reinsurance. The finite sample properties of the proposed estimators are investigated with a simulation study and we illustrate their practical applicability on a dataset of motor third party liability insurance. [ABSTRACT FROM AUTHOR]

We propose and analyze a permutation test of the tail dependence between two random variables whose marginal distributions are assumed to be known. Justifying the test, we show that the proposed test statistics and their permutation distribution converge to the normal distribution. The analysis is motivated by the recent results of DiCiccio and Romano (J Am Stat Assoc 112(519):1211–1220, 2017) on permutation tests for correlation between random variables. We also provide a simulation study of the size and power properties of the test and an application to financial data. [ABSTRACT FROM AUTHOR]

In this paper, we study spatial cross-sectional data models in the form of matrix exponential spatial specification (MESS), where MESS appears in both dependent and error terms. The empirical likelihood (EL) ratio statistics are established for the parameters of the MESS model. It is shown that the limiting distributions of EL ratio statistics follow chi-square distributions, which are used to construct the confidence regions of model parameters. Simulation experiments are conducted to compare the performances of confidence regions based on EL method and normal approximation method. [ABSTRACT FROM AUTHOR]

In this paper, Let Mn denote the maximum of logarithmic general error distribution with parameter v ≥ 1. Higher-order expansions for distributions of powered extremes M n p are derived under an optimal choice of normalizing constants. It is shown that M n p , when v = 1, converges to the Fréchet extreme value distribution at the rate of 1/n, and if v > 1 then M n p converges to the Gumbel extreme value distribution at the rate of . [ABSTRACT FROM AUTHOR]

Consider a nonstandard compound renewal risk model with stochastic return on investments, where the price process of investment portfolio is modeled as an exponential Lévy process. In the presence of heavy tails and dependence structures among modeling components, we study the uniform asymptotics of the tail probability of stochastic discounted aggregate claims and the finite-time ruin probability for all time varying in a relevant finite or infinite interval. [ABSTRACT FROM AUTHOR]

During extreme events such as natural or man-made disasters, it is likely that after immediate claims directly caused by the events, there are other delayed claims occurring in a certain period of future. In the classical risk model, each immediate claim is accompanied with a delayed one, but in reality each immediate claim can lead to a random number of delayed ones. To this end, we consider an insurance risk model with a random number of delayed claims as well as Brownian perturbation, dependence structures and constant interest force, and explore asymptotic estimations for an insurer's ruin-related risks exposed to the extreme events. This article provides a novel insight to model and analyze the potential risks by fully considering the ongoing impacts of heavy-tailed claims, and thus accurately assesses the insurer's operation risk in the long run. [ABSTRACT FROM AUTHOR]