A hybrid estimator for generalized pareto and extreme-value distributions

The methods of moments and probability-weighted moments are the most commonly used methods for estimating the parameters of the generalized Pareto distribution and generalized extreme-value distributions. These methods, however, frequently lead to nonfeasible estimates in the sense that the supports inferred from the estimates fail to contain all observations. In this paper, we propose a hybrid estimator which is derived by incorporating a simple auxiliary constraint on feasibility into the estimates. The hybrid estimator is very easy to use, always feasible, and also has smaller bias and mean square error in many cases. Its advantages are further illustrated through the analyses of two real data sets.     

A comparison of some robust,adaptive, and partially adaptive estimators of regression models

Numerous estimation techniques for regression models have been proposed. These procedures differ in how sample information is used in the estimation procedure. The efficiency of least squares (OLS) estimators implicity assumes normally distributed residuals and is very sensitive to departures from normality, particularly to "outliers" and thick-tailed distributions. Lead absolute deviation (LAD) estimators are less sensitive to outliers and are optimal for laplace random disturbances, but not for normal errors. This paper reports monte carlo comparisons of OLS,LAD, two robust estimators discussed by huber, three partially adaptiveestimators, newey's generalized method of moments estimator, and an adaptive maximum likelihood estimator based on a normal kernal studied by manski. This paper is the first to compare the relative performance of some adaptive robust estimators (partially adaptive and adaptive procedures) with some common nonadaptive robust estimators. The partially adaptive estimators are based on three flxible parametric distributions for the errors. These include the power exponential (Box-Tiao) and generalized t distributions, as well as a distribution for the errors, which is not necessarily symmetric. The adaptive procedures are "fully iterative" rather than one step estimators. The adaptive estimators have desirable large sample properties, but these properties do not necessarily carry over to the small sample case.

The monte carlo comparisons of the alternative estimators are based on four different specifications for the error distribution: a normal, a mixture of normals (or variance-contaminated normal), a bimodal mixture of normals, and a lognormal. Five hundred samples of 50 are used. The adaptive and partially adaptive estimators perform very well relative to the other estimation procedures considered, and preliminary results suggest that in some important cases they can perform much better than OLS with 50 to 80% reductions in standard errors.

     

Bayesian Analysis of Stochastic Volatility Models

New techniques for the analysis of stochastic volatility models in which the logarithm of conditional variance follows an autoregressive model are developed. A cyclic Metropolis algorithm is used to construct a Markov-chain simulation tool. Simulations from this Markov chain converge in distribution to draws from the posterior distribution enabling exact finite-sample inference. The exact solution to the filtering/smoothing problem of inferring about the unobserved variance states is a by-product of our Markov-chain method. In addition, multistep-ahead predictive densities can be constructed that reflect both inherent model variability and parameter uncertainty. We illustrate our method by analyzing both daily and weekly data on stock returns and exchange rates. Sampling experiments are conducted to compare the performance of Bayes estimators to method of moments and quasi-maximum likelihood estimators proposed in the literature. In both parameter estimation and filtering, the Bayes estimators outperform these other approaches.     

Entropy-Based Moment Selection in the Presence of Weak Identification

Hall et al. (2007 Hall , A. R. , Inoue , A. , Jana , K. , Shin , C. (2007). Information in generalized method of moments estimation and entropy based moment selection. Journal of Econometrics 138:488–512.[Crossref] , [Google Scholar]) propose a method for moment selection based on an information criterion that is a function of the entropy of the limiting distribution of the Generalized Method of Moments (GMM) estimator. They establish the consistency of the method subject to certain conditions that include the identification of the parameter vector by at least one of the moment conditions being considered. In this article, we examine the limiting behavior of this moment selection method when the parameter vector is weakly identified by all the moment conditions being considered. It is shown that the selected moment condition is random and hence not consistent in any meaningful sense. As a result, we propose a two-step procedure for moment selection in which identification is first tested using a statistic proposed by Stock and Yogo (2003 Stock , J. H. , Yogo , M. ( 2003 ). Testing for weak instruments in linear IV regression . Discussion paper, Kennedy School of Government, Harvard University, Cambridge, MA . [Google Scholar]) and then only if this statistic indicates identification does the researcher proceed to the second step in which the aforementioned information criterion is used to select moments. The properties of this two-step procedure are contrasted with those of strategies based on either using all available moments or using the information criterion without the identification pre-test. The performances of these strategies are compared via an evaluation of the finite sample behavior of various methods for inference about the parameter vector. The inference methods considered are based on the Wald statistic, Anderson and Rubin's (1949 Anderson , T. W. , Rubin , H. ( 1949 ). Estimation of the parameters of a single equation in a complete system of stochastic equations . Annals of Mathematical Statistics 20 : 46 – 63 .[Crossref] , [Google Scholar]) statistic, Kleibergen (2002 Kleibergen , F. ( 2002 ). Pivotal statistics for testing structural parameters in instrumenatl variables regression . Econometrica 70 : 1781 – 1803 .[Crossref], [Web of Science ®] , [Google Scholar]) K statistic, and combinations thereof in which the choice is based on the outcome of the test for weak identification.     

Inverse moments of discrete distributions

In this paper an expression for the inverse moment of order r is given for the truncated binomial and Poisson distributions. This enables one to obtain inverse moments in a finite series. Some applications and multivariate generalizations are also given. The method also enables one to obtain relations between inverse moments and factorial moments and distributions of sums of variables.     

广义希尔伯特变换及其数字实现

基于广义Hilbert变换将传统的Hilbert变换由整数阶向分数阶的推广,其应用领域也得到了扩展。首先,在频域定义广义Hilbert变换,利用广义Hilbert变换来构造新的广义解析信号。然后从数字信号处理角度来考察理想的广义数字Hilbert变换器的基本性质及其数字实现。文中利用窗函数法和频率采样法设计了FIR广义数字Hilbert变换器,并分析了设计误差。     

Comments on zacks' recent paper on one-sided cusum procedures

The goal of this paper is to propose approximations for the cdf and the inverse cdf of the normal sample median. The presented methodology, which seems to not have been investigated before, suggests to fit the normal sample median distribution with a symmetrical Johnson S_U: distribution having ap-proximatively the same second and fourth moments. The results obtained with this approach, compared with the normal approximation, are very impressive, especially for the inverse cdf. One important application of the inverse cdf approximation of the normal sample median is the computation of accurate α‐level median/range control limits for any value of α (and not only for the popular value α = 0.0027). This paper can be also viewed as an homage to Professor N.L. Johnson's works by making a link between two of his major papers.     

The three-parameter two-piece normal family of distributions and its fitting

This note introduces a family of skew and symmetric distributions containing the normal family and indexed by three parameters with clear meanings. Another respect in which this family compares favourably with families like the Pearson family, the Bessel-Gram-Charlier family and the Johnson family is ease of maximum likelihood fitting. Fitting by the method of moments is also considered. Asymptotic distributions of maximum likelihood and moment estimators are worked out. A test of symmetry and normality is suggested.     

Some robust designs for polynomial regression models

The author identifies static optimal designs for polynomial regression models with or without intercept. His optimality criterion is an average between the D‐optimality criterion for the estimation of low‐degree terms and the D₈‐optimality criterion for testing the significance of higher degree terms. His work relies on classical results concerning canonical moments and the theory of continued fractions.     

Some results for multidimensional stationary independent increment processes

The characteristic function, cumulants and moments of vector-valued multidimensional processes, satisfying properties similar to stationary independent increments, are derived. By considering a set of additional postulates for such processes, it is shown that the marginal distribution of such processes is multivariate Poisson. Some of the results in this paper are extensions of the properties of the first two moments of a univariate one-dimensional process with stationary independent increments.