Tail asymptotic of discounted aggregate claims with compound dependence under risky investment

This paper considers the tail asymptotic of discounted aggregate claims with compound dependence under risky investment. The price of risky investment is modeled by a geometric Lévy process, while claims are modeled by a one-sided linear process whose innovations further obeying a so-called upper tail asymptotic independence. When the innovations are heavy tailed, we derive some uniform asymptotic formulas. The results show that the linear dependence has significant impact on the tail asymptotic of discounted aggregate claims but the upper tail asymptotic independence is negligible.     

Large sample behavior of the Bernstein copula estimator

Bernstein polynomial estimators have been used as smooth estimators for density functions and distribution functions. The idea of using them for copula estimation has been given in Sancetta and Satchell (2004). In the present paper we study the asymptotic properties of this estimator: almost sure consistency rates and asymptotic normality. We also obtain explicit expressions for the asymptotic bias and asymptotic variance and show the improvement of the asymptotic mean squared error compared to that of the classical empirical copula estimator. A small simulation study illustrates this superior behavior in small samples.     

Asymptotic distributions of functions of a sample covariance matrix under the elliptical distribution

This paper is concerned with asymptotic distributions of functions of a sample covariance matrix under the elliptical model. Simple but useful formulae for calculating asymptotic variances and covariances of the functions are derived. Also, an asymptotic expansion formula for the expectation of a function of a sample covariance matrix is derived; it is given up to the second-order term with respect to the inverse of the sample size. Two examples are given: one of calculating the asymptotic variances and covariances of the stepdown multiple correlation coefficients, and the other of obtaining the asymptotic expansion formula for the moments of sample generalized variance.     

Higher Order Asymptotic Cumulants of Studentized Estimators in Covariance Structures

In covariance structure analysis, the Studentized pivotal statistic of a parameter estimator is often used since the statistic is asymptotically normally distributed with mean zero and unit variance. For more accurate asymptotic distribution, the first and third asymptotic cumulants can be used to have the single-term Edgeworth, Cornish-Fisher, and Hall type asymptotic expansions. In this paper, the higher order asymptotic variance and the fourth asymptotic cumulant of the statistic are obtained under nonnormality when the partial derivatives of a parameter estimator with respect to sample variances and covariances up to the third order and the moments of the associated observed variables up to the eighth order are available. The result can be used to have the two-term Edgeworth expansion. Simulations are performed to see the accuracy of the asymptotic results in finite samples.     

Power Variations and Testing for Co‐Jumps: The Small Noise Approach

In this paper, we study the effects of noise on bipower variation, realized volatility (RV) and testing for co‐jumps in high‐frequency data under the small noise framework. We first establish asymptotic properties of bipower variation in this framework. In the presence of the small noise, RV is asymptotically biased, and the additional asymptotic conditional variance term appears in its limit distribution. We also propose consistent estimators for the asymptotic variances of RV. Second, we derive the asymptotic distribution of the test statistic proposed in (Ann. Stat. 37, 1792‐1838) under the presence of small noise for testing the presence of co‐jumps in a two‐dimensional Itô semimartingale. In contrast to the setting in (Ann. Stat. 37, 1792‐1838), we show that the additional asymptotic variance terms appear and propose consistent estimators for the asymptotic variances in order to make the test feasible. Simulation experiments show that our asymptotic results give reasonable approximations in the finite sample cases.     

The Asymptotic Covariance Matrix of the Least Squares Estimator in the Stochastic Linear Regression Model: The Case of Elliptically Symmetric Distribution

This article considers the unconditional asymptotic covariance matrix of the least squares estimator in the linear regression model with stochastic explanatory variables. The asymptotic covariance matrix of the least squares estimator of regression parameters is evaluated relative to the standard asymptotic covariance matrix when the joint distribution of the dependent and explanatory variables is in the class of elliptically symmetric distributions. An empirical example using financial data is presented. Numerical examples and simulation experiments are given to illustrate the difference of the two asymptotic covariance matrices.     

Testing asymptotic independence in bivariate extremes

Bivariate extreme value condition (see (1.1) below) includes the marginal extreme value conditions and the existence of the (extreme) dependence function. Two cases are of interest: asymptotic independence and asymptotic dependence. In this paper, we investigate testing the existence of the dependence function under the null hypothesis of asymptotic independence and present two suitable test statistics. Small simulations are studied and the application for a real data is shown. The other case with the null hypothesis of asymptotic dependence is already investigated.     

Comparisons of asymptotic biases and variances of m-estimators of scale under asymmetric contamination

We study robustness properties of two types of M-estimators of scale when both location and scale parameters are unknown: (i) the scale estimator arising from simultaneous M-estimation of location and scale; and (ii) its symmetrization about the sample median. The robustness criteria considered are maximal asymptotic bias and maximal asymptotic variance when the known symmetric unimodal error distribution is subject to unknown, possibly asymmetric, £-con-tamination. Influence functions and asymptotic variance functionals are derived, and computations of asymptotic biases and variances, under the normal distribution with ε-contamination at oo, are presented for the special subclass arising from Huber's Proposal 2 and its symmetrized version. Symmetrization is seen to reduce both asymptotic bias and variance. Some complementary theoretical results are obtained, and the tradeoff between asymptotic bias and variance is discussed.     

Approximate Marginal Posterior Distributions Using Asymptotic Modes

This article gives asymptotic expansions for marginal posterior distributions with asymptotic modes of order n ^?2, and shows their validity. In addition, by using the asymptotic expansion, an approximate central posterior credible interval is derived.     

Further Results on the Limiting Distribution of GMM Sample Moment Conditions

In this article, we examine the limiting behavior of generalized method of moments (GMM) sample moment conditions and point out an important discontinuity that arises in their asymptotic distribution. We show that the part of the scaled sample moment conditions that gives rise to degeneracy in the asymptotic normal distribution is T-consistent and has a nonstandard limiting distribution. We derive the appropriate asymptotic (weighted chi-squared) distribution when this degeneracy occurs and show how to conduct asymptotically valid statistical inference. We also propose a new rank test that provides guidance on which (standard or nonstandard) asymptotic framework should be used for inference. The finite-sample properties of the proposed asymptotic approximation are demonstrated using simulated data from some popular asset pricing models.     

Asymptotics for penalised splines in generalised additive models

This paper discusses asymptotic theory for penalised spline estimators in generalised additive models. The purpose of this paper is to establish the asymptotic bias and variance as well as the asymptotic normality of the ridge-corrected penalised spline estimator. Furthermore, the asymptotics for the penalised quasi-likelihood fit in mixed models are also discussed.     

Weak convergence of functionals of stationary long memory processes to Rosenblatt-type distributions

We provide an asymptotic result for the distribution of functionals of continuous Gaussian processes with long memory. Much of the existing literature on the subject resorts to asymptotic representations based on stochastic integrals. However, the method of proof used here, based on characteristic functions, enables one to extend the class of functionals for which we are able to provide an asymptotic representation. Next, we study the properties of the asymptotic process and finally, as an application, we consider the case of continuous regression where the process of errors follows a Gamma process with long-range dependence.     

Tests for the total time on test transform order

In this paper we consider two test statistics for testing the strict TTT transform order between two life distributions of interest. We give their asymptotic distributions and compare our tests with some other related tests in terms of Pitman's asymptotic efficiency. Also we present some results to show the performance and the asymptotic normality of our tests.     

Asymptotic properties of maximum-likelihood estimators for Heston models based on continuous time observations

We study asymptotic properties of maximum-likelihood estimators for Heston models based on continuous time observations of the log-price process. We distinguish three cases: subcritical (also called ergodic), critical and supercritical. In the subcritical case, asymptotic normality is proved for all the parameters, while in the critical and supercritical cases, non-standard asymptotic behaviour is described.     

Asymptotic near admissimlity and asymptotic near optimality by the “two armed bandit” problem

The classical “Two Armed Bandit” problem with Bernoulli-distributed outcomes is being considered. First the terms “asymptotic nearly admissibility” and “asymptotic nearly optimality” are defined. A nontrivial asymptotic nearly admissible and (with respect to a certain Bayes risk) asymptotic nearly optimal strategy is presented, then these properties are shown. Finally, it is discussed how these results generalize to the non-Bernoulli cases and the “k-Armed Bandit” problem (;k≧2).     

New Confidence Intervals for the Proportion of Interest in One-Sample Correlated Binary Data

Correlated binary data is obtained in many fields of biomedical research. When constructing a confidence interval for the proportion of interest, asymptotic confidence intervals have already been developed. However, such asymptotic confidence intervals are unreliable in small samples. To improve the performance of asymptotic confidence intervals in small samples, we obtain the Edgeworth expansion of the distribution of the studentized mean of beta-binomial random variables. Then, we propose new asymptotic confidence intervals by correcting the skewness in the Edgeworth expansion in one direct and two indirect ways. New confidence intervals are compared with the existing confidence intervals in simulation studies.     

Some Properties of the Pivotal Statistic Based on the Asymptotically Distribution-Free Theory in Structural Equation Modeling

For normally distributed data, the asymptotic bias and skewness of the pivotal statistic Studentized by the asymptotically distribution-free standard error are shown to be the same as those given by the normal theory in structural equation modeling. This gives the same asymptotic null distributions of the two pivotal statistics up to the next order beyond the usual normal approximation under normality. With an alternative hypothesis, the asymptotic variances of the two statistics under normality/non normality are also derived. It is, however, shown that the asymptotic variances of the non null distributions of the statistics are generally different even under normality.     

Asymptotic expansions relating to discrimination based on two-step monotone missing samples

This paper proposes two asymptotic expansions relating to discrimination based on two-step monotone missing samples. These asymptotic expansions have been obtained by Okamoto (1963) and McLachlan (1973) for complete data under multivariate normality. This paper extends the results up to the terms of the first order in the case of two-step monotone missing samples, respectively. Especially, these asymptotic expansions play important roles in obtaining the asymptotic approximations for the probabilities of misclassification in discriminant analysis. The simulation studies have been also conducted in order to evaluate the accuracy of the approximation derived in this paper.     

Asymptotic normality of estimators for parameters of a multivariate skew-normal distribution

In this paper, asymptotic normality is established for the parameters of the multivariate skew-normal distribution under two parametrizations. Also, an analytic expression and an asymptotic normal law are derived for the skewness vector of the skew-normal distribution. The estimates are derived using the method of moments. Convergence to the asymptotic distributions is examined both computationally and in a simulation experiment.     

Some Properties of the Normalized Periodogram of a Fractionally Integrated Separable Spatial ARMA (FISSARMA) Model

In this article, we study the properties of the normalized periodogram of the Fractionally Integrated Separable Spatial ARMA (FISSARMA) models. In particular, we establish the asymptotic mean of the normalised periodogram and the asymptotic second-order moments of the normalised Fourier coefficients. We also establish the asymptotic distribution of the normalised periodogram. Some numerical results are also provided.