Completeness and optimality of marginal likelihood estimating equations

A counter-example shows that the proof of optimality of the marginal likelihood estimating function for parameter of interest, under the conditions assumed in Lloyd (1987), contains a gap and is, thus, invalid. The same comment applies to the generalized version of Lloyd’s Theorem given by Bhapkar and Srinivasan (1993). In the light of known results concerning Fisher information for parameter of interest and partial sufficiency of a suitable statistic, the counter-example reveals a similar gap in the proof of corollary 3.2 of Bhapkar (1991).     

The median estimate of the autoregressive location parameter

A median-based estimate of the location (i.e. intercept) parameter in an autoregressive time series is considered. Specifically, the asymptotic joint distribution of the location estimate and a location invariant estimate of the AR parameter vector is derived. Applications of this result to rank-based estimates are briefly discussed and illustrated with a numerical example.     

Estimation Under Inequality Constraints: Semiparametric Estimation of Conditional Duration Models

This article proposes a semiparametric estimator of the parameter in a conditional duration model when there are inequality constraints on some parameters and the error distribution may be unknown. We propose to estimate the parameter by a constrained version of an unrestricted semiparametrically efficient estimator. The main requirement for applying this method is that the initial unrestricted estimator converges in distribution. Apart from this, additional regularity conditions on the data generating process or the likelihood function, are not required. Hence the method is applicable to a broad range of models where the parameter space is constrained by inequality constraints, such as the conditional duration models. In a simulation study involving conditional duration models, the overall performance of the constrained estimator was better than its competitors, in terms of mean squared error. A data example is used to illustrate the method.     

Modern trends in multivariate time-series analysis 2

The paper deals with statistical tests of hypotheses about the real parameter of a homogeneous time-discrete Markov process. The power function of an asymptotically uniformly most powerful unbiased sequence of tests is approximately calculated and the convergence order of the remainder term is given. The essential assumption used is the uniform ergodicity of the Markov process.     

Turbo C与汇编语言混合编程研究

高级语言具有编程容易、方便且调试速度快的特点，汇编语言则具有运行速度快、占用内存小、能够直接访问计算机所有硬件等特点，将二者结合起来进行混合编程是解决某些程序设计问题的有效方法．介绍了Turboc与汇编语言的接口技术，其中包括用Turboc调用汇编子程序和TurboC行间嵌入汇编语句等内容，并给出了具体实例．     

Dynamic Probabilities of Restrictions in State Space Models: An Application to the Phillips Curve

Using the Savage–Dickey density ratio and an alternative approach that uses more relaxed assumptions, we develop methods to calculate the probability that a restriction holds at a point in time without assuming that the restriction holds at any other points in time. Both approaches use MCMC output only from the unrestricted model to compute the time-varying posterior probabilities for all models of interest. Using U.S. data, we find the probability that the long-run Phillips curve is vertical to be fairly high, but decreases over time. The probability that the NAIRU is not identified fluctuates over time, but increases after 1990.     

Multiscale Gaussian convolution algorithm for estimate of Gaussian mixture model

Abstract

This paper introduces a multiscale Gaussian convolution model of Gaussian mixture (MGC-GMM) via the convolution of the GMM and a multiscale Gaussian window function. It is found that the MGC-GMM is still a Gaussian mixture model, and its parameters can be mapped back to the parameters of the GMM. Meanwhile, the multiscale probability density function (MPDF) of the MGC-GMM can be viewed as the mathematical expectation of a random process induced by the Gaussian window function and the GMM, which can be directly estimated by the use of sample data. Based on the estimated MPDF, a novel algorithm denoted by the MGC is proposed for the selection of model and the parameter estimates of the GMM, where the component number and the means of the GMM are respectively determined by the number and the locations of the maximum points of the MPDF, and the numerical algorithms for the weight and variance parameters of the GMM are derived. The MGC is suitable for the GMM with diagonal covariance matrices. A MGC-EM algorithm is also presented for the generalized GMM, where the GMM is estimated using the EM algorithm by taking the estimates from the MGC as initial parameters of the GMM model. The proposed algorithms are tested via a series of simulated sample sets from the given GMM models, and the results show that the proposed algorithms can effectively estimate the GMM model.     

Estimation op parameters in finite mixtures of exponential families from censored data

A general successive substitutions' scheme is developed to estimate parameters in a finite mixture of distributions from the exponential family, based on censored data. It is assumed that the data can be grouped in the first class and the number of observations in each of the remaining classes are known Examples from Poisson Exponential and Normal distributions are given A small simulation exercise has also been carried out for the mixture of two one parameter exponential population.     

Estimating the Hurst parameter in financial time series via heuristic approaches

This research investigates long memory financial equity markets using three heuristic methodologies namely a proposed modified variance time-aggregated plot, modified rescaled-range plot and periodogram approaches. The intensity of the long memory process is quantified in terms of Hurst parameter (H). Five Malaysian equity market indices are selected in the empirical studies with the inclusion of pre- and post-drastic economic events. Our empirical results evidenced dissimilar long memory behaviours in the different regimes of significant economic events. It is also found that after the short-memory adjustment, all the equity markets exhibited substantial reductions in long memory estimations.     

Bayesian forecasting with changing linear models

This investigation considers a general linear model which changes parameters exactly once during the observation period. Assuming all the parameters are unknown and a proper prior distribution, the Bayesian predictive distribution of the future observations is derived.

It is shown that the predictive distribution is a mixture of multivariate t distributions and that the mixing distribution is the marginal posterior mass function of the change point parameter.