Nonparametric maximum likelihood estimation in a non locally compact setting

Maximum likelihood estimation is considered in the context of infinite dimensional parameter spaces. It is shown that in some locally convex parameter spaces sequential compactness of the bounded sets ensures the existence of minimizers of objective functions and the consistency of maximum likelihood estimators in an appropriate topology. The theory is applied to revisit some classical problems of nonparametric maximum likelihood estimation, to study location parameters in Banach spaces, and finally to obtain Varadarajan’s theorem on the convergence of empirical measures in the form of a consistency result for a sequence of maximum likelihood estimators. Several parameter spaces sharing the crucial compactness property are identified. This research was supported by grants from the National Sciences and Engineering Research Council of Canada and the Fonds FCAR de la Province de Québec.     

Longitudinal LISREL model estimation from incomplete panel data using the EM algorithm and the Kalman smoother

Longitudinal data sets with the structure T (time points) × N (subjects) are often incomplete because of data missing for certain subjects at certain time points. The EM algorithm is applied in conjunction with the Kalman smoother for computing maximum likelihood estimates of longitudinal LISREL models from varying missing data patterns. The iterative procedure uses the LISREL program in the M-step and the Kalman smoother in the E-step. The application of the method is illustrated by simulating missing data on a data set from educational research.     

An EM algorithm for the estimation of parametric and nonparametric hierarchical nonlinear models

It is shown how to implement an EM algorithm for maximum likelihood estimation of hierarchical nonlinear models for data sets consisting of more than two levels of nesting. This upward–downward algorithm makes use of the conditional independence assumptions implied by the hierarchical model. It cannot only be used for the estimation of models with a parametric specification of the random effects, but also to extend the two-level nonparametric approach – sometimes referred to as latent class regression – to three or more levels. The proposed approach is illustrated with an empirical application.     

Small sample properties of maximum likelihood versus generalized method of moments based tests for spatially autocorrelated errors

Many applied researchers have to deal with spatially autocorrelated residuals (SAR). Available tests that identify spatial spillovers as captured by a significant SAR parameter, are either based on maximum likelihood (MLE) or generalized method of moments (GMM) estimates. This paper illustrates the properties of various tests for the null hypothesis of a zero SAR parameter in a comprehensive Monte Carlo study. The main finding is that Wald tests generally perform well regarding both size and power even in small samples. The GMM-based Wald test is correctly sized even for non-normally distributed disturbances and small samples, and it exhibits a similar power as its MLE-based counterpart. Hence, for the applied researcher the GMM Wald test can be recommended, because it is easy to implement.     

On generalized maximum likelihood estimation in the proportional hazards model with partially informative censoring

The generalized maximum likelihood estimator (GMLE) is derived and some of its variants are compared with the partial Abdushukurov-Cheng-Lin (PACL) and Kaplan-Meier (KM) estimators under the proportional hazards model with partially informative censoring. A comparison of small sample properties is conducted based on a simulation study. The results show that the GMLEs perform competitively with the PACL estimator.Acknowledgements.The authors are very much thankful to the referee for perceptive and illuminating comments. A substantial credit goes to the referee for an overall improvement of the paper.     

A note on estimation based on record data

In data-processing standpoint, an efficient algorithm for identifying the minimum value among a set of measurements are record statistics. From a sequence of n independent identically distributed continuous random variables only about log(n) records are expected, so we expect to have little data, hence any prior information is welcome (Houchens, Record value theory and inference, Ph.D. thesis, University of California, Riverside, 1984). In this paper, non-Bayesian and Bayesian estimates are derived for the two parameters of the Exponential distribution based on record statistics with respect to the squared error and Linear-Exponential loss functions and then compared with together. The admissibility of some estimators is discussed.     

A note on the covariance matrix of the maximum likelihood estimator in constrained multivariate linear regression

A useful result concerning variances and covariances of a linear function of a random matrix is applied to find the variance–covariance matrix of the maximum likelihood estimator in multivariate linear regression subject to zero constraints.     

Term structure estimation in the presence of autocorrelation

This paper assesses the effects of autocorrelation on parameter estimates of affine term structure models (ATSM) when principal components analysis is used to extract factors. In contrast to recent studies, we design and run a Monte Carlo experiment that relies on the construction of a simulation design that is consistent with the data, rather than theory or observation, and find that parameter estimation from ATSM is precise in the presence of serial correlation in the measurement error term. Our findings show that parameter estimation of ATSM with principal component based factors is robust to autocorrelation misspecification.     

Sequential decisions under uncertainty and the maximum theorem

For sequential decision problems in which the decision-maker observes a process of state variables and chooses an adapted process of action variables, the paper defines a topology on the space of measures of processes of state variables which ensures the applicability of Berge's maximum theorem to the decision-maker's optimal behavior. The topology controls for the information available to the decision-maker at each decision date. The paper also discusses the implications of the analysis for the dynamic-programming approach to sequential decision-making under uncertainty, and for equilibrium existence proof strategies in sequential-market models and games.     

A note on consistency and unbiasedness of point estimation with fuzzy data

Based on the SLLN for fuzzy random variables in uniform metric d, some asymptotical properties of point estimation with fuzzy random samples are investigated. The results of this paper establish a corresponding version on the consistency and unbiasedness of point estimation with n-dimensional fuzzy samples under considering a kind of fuzzy statistic.     

改进菱形运动估计算法研究与实现

针对目前菱形运动估计搜索算法存在的问题,对不同宏块采用相同的搜索策略,而不能根据视频序列的特性,迅速缩小搜索的范围,造成搜索冗余。文章分析了运动矢量的分布相关性,提出了基于起点预测的改进菱形运动估计算法。该算法结合提前中止准则,能改进菱形算法的搜索流程。仿真结果表明,该算法在降低计算复杂度的同时,还可有效地保证搜索精度。     

Influence analysis for Poisson inverse Gaussian regression models based on the EM algorithm

For Poisson inverse Gaussian regression models, it is very complicated to obtain the influence measures based on the traditional method, because the associated likelihood function involves intractable expressions, such as the modified Bessel function. In this paper, the EM algorithm is employed as a basis to derive diagnostic measures for the models by treating them as a mixed Poisson regression with the weights from the inverse Gaussian distributions. Several diagnostic measures are obtained in both case-deletion model and local influence analysis, based on the conditional expectation of the complete-data log-likelihood function in the EM algorithm. Two numerical examples are given to illustrate the results.     

A note on the uniform asymptotic normality of location M-estimates

In the robustness framework, the parametric model underlying the data is usually embedded in a neighborhood of other plausible distributions. Accordingly, the asymptotic properties of robust estimates should be uniform over the whole set of possible models. In this paper, we study location M-estimates calculated with a previous generalized S-scale and show that, under some regularity conditions, they are uniformly asymptotically normal over contamination neighborhoods of known size. There is a trade off between the size of the neighborhood and the breakdown point of the GS-scale, but it is possible to adjust the estimates so that they have 50% breakdown point whereas the uniform asymptotic normality is ensured over neighborhoods that contain up to 25% of contamination. Alternatively, both the breakdown point and the size of the neighborhood could be chosen to be 38%. These results represent an improvement over those obtained recently by Salibian-Barrera and Zamar (2004) J.R. Berrendero was Spanish supported by Grant BFM2001-0169 and Grand 06/0050/2003 (Comunidad De Madrid) R. H. Zamar was partially supported by the Natural Sciences and Engineering Research Council of Canada (NSERC).     

A note on least squares estimation and the blue in a generalized linear regression model

In a generalized linear regression model, least squares and Gauss-Markov estimators differ, in general, if the variance-covariance matrix of the disturbances is singular. In the present note it is shown that, nevertheless, the conventional least squares procedure leads to a Gauss-Markov estimator if it is applied to a modified model which results from adding dummy constraints to the original model. These constraints reflect the effects of the singularity of the variance- convariance matrix. As a consequence, a Gauss-Markov estimate may always be obtained by standard least squares minimization, which offers considerable computational advantages.     

A note on the Robust Trend and ARARMA methodologies used in the M3 Competition

This brief note describes two of the forecasting methods used in the M3 Competition, Robust Trend and ARARMA. The origins of these methods are very different. Robust Trend was introduced to model the special features of some telecommunications time series. It was subsequently found to be competitive with Holt’s linear model for the more varied set of time series used in the M1 Competition. The ARARMA methodology was proposed by Parzen as a general time series modelling procedure, and can be thought of as an alternative to the ARIMA methodology of Box and Jenkins. This method was used in the M1 Competition and achieved the lowest mean absolute percentage error for longer forecasting horizons. These methods will be described in more detail and some comments on their use in the M3 Competition conclude this note.     

Forecasting volatility: A reality check based on option pricing, utility function, value-at-risk, and predictive likelihood

We analyze the predictive performance of various volatility models for stock returns. To compare their performance, we choose loss functions for which volatility estimation is of paramount importance. We deal with two economic loss functions (an option pricing function and an utility function) and two statistical loss functions (a goodness-of-fit measure for a value-at-risk (VaR) calculation and a predictive likelihood function). We implement the tests for superior predictive ability of White [Econometrica 68 (5) (2000) 1097] and Hansen [Hansen, P. R. (2001). An unbiased and powerful test for superior predictive ability. Brown University]. We find that, for option pricing, simple models like the Riskmetrics exponentially weighted moving average (EWMA) or a simple moving average, which do not require estimation, perform as well as other more sophisticated specifications. For a utility-based loss function, an asymmetric quadratic GARCH seems to dominate, and this result is robust to different degrees of risk aversion. For a VaR-based loss function, a stochastic volatility model is preferred. Interestingly, the Riskmetrics EWMA model, proposed to calculate VaR, seems to be the worst performer. For the predictive likelihood-based loss function, modeling the conditional standard deviation instead of the variance seems to be a dominant modeling strategy.     

A note on the determination of A-optimal type block designs under fixed and mixed effects models

In this paper, we consider the problem of estimating a selected set of contrasts between v treatments using a block design consisting of b blocks of size k. Traditionally, the construction of A-optimal block designs for such situations has been carried out assuming a fixed effects model. In this paper, we show that A-optimal designs constructed under a fixed effects model are robust in the sense that these designs have maximal minimal efficiency when considered among all available designs and under all possible mixed effects models. AMS 1991 subject classifications: Primary 62K05; Secondary 62K10     

PSO算法的改进及应用研究

文章为PSO算法提供了一种新机制,使其在陷入局部最优时,以更大概率跳出局部最优位置,进入解空间的其他区域进行搜索,可大大增强PSO算法的全局搜索能力。     

The core-periphery model: A note on the existence and uniqueness of short-run equilibrium

We consider the core-periphery model [P. Krugman, Increasing returns and economic geography, Journal of Political Economy 199 (1) (1991) 483–499]. The nature and stability of the possible steady states of the model have been made progressively precise; [M. Fujita, P. Krugman, A. Venables, The Spatial Economy. Cities, Regions and International Trade, MIT Press, Cambridge, 1999; R. Baldwin, R. Forslid, Ph. Martin, G. Ottaviano, F. Robert-Nicoud, Economic Geography and Public Policy, Princeton Univ. Press, 2003]. In that model as well as in all the new economic geography models that have been derived from it, the short-run (instantaneous) equilibrium is implicitly determined by the current labor distribution across regions. The numerical computations used so far to determine the short-run equilibrium, tend to suggest its existence. In this paper, an existence and uniqueness proof of short-run equilibrium is provided.