Cone dominance and efficiency in DEA

This paper incorporates cones on virtual multipliers of inputs and outputs into DEA analysis. Cone DEA models are developed to generalize the dual of the BCC models as well as congestion models. Input-output data and/or numbers of DMUs for BCC models are inadequate to capture many aspects where judgments, expert opinions, and other external information should be taken into analysis. Cone DEA models, on the other hand, offer improved definitions of efficiency over general cone and polyhedral cone structures. The relationships between cone models and BCC models as well as those between cone models and congestion models are discussed in the development. Two numerical examples are provided to illustrate our findings.     

Diagnostic Measures for Censored Linear Models based on Empirical Likelihood Method

In this paper, the diagnostic measures for censored linear models are studied based on the empirical likelihood method. First, the diagnostic measures for linear models are studied; Then, the censored linear models are converted to linear models, and the diagnostic measures for converted models are studied; Last, simulation studies and real data analysis are given to illustrate the validity of statistical diagnostic measures.     

NEW DEVELOPMENTS IN FOREST MODELING: CONVERGENCE BETWEEN APPLIED AND THEORETICAL APPROACHES

ABSTRACT. Additionally to simulations, a mathematical analysis of ecological models could give insights into the system behavior. However, mathematical model analysis has only been performed for simple, abstract models, because models based on biological processes are too complex. Linking simple and detailed approaches could help to obtain mathematically tractable models which are based on physiological and ecological processes. This can be achieved either by extending simpler models with components of complex ones, or by a controlled simplification of complex models. Forest models ranging from models describing processes in organs of individual tress in three-dimensional space to models averaging over all trees of an entire region, are reviewed, categorized by hierarchical level and represented in a general mathematical formulation. Possibilities and approaches of transitions between the approaches, namely linking of approaches and upscaling of individual based models are presented and discussed.     

Mathematical models of recognition and confusion in psychology

A wide range of mathematical models of recognition and confusion in psychological experiments is examined. A taxonomy for the classification of these models is proposed. This taxonomy includes discriminant models, feature-confusion models, sophisticated guessing models and choice models. Both the within-class and between-class relationships of these models are examined so as to provide a framework for the application of these models to theories of human pattern recognition. Where appropriate, specific areas of application of these models in the context of human perceptual processing are presented and discussed.     

Seasonal Space–Time Models for Climate Systems

A class of seasonal space–time models for general lattice systems is proposed. Covariance properties of spatial first-order models are studied. Estimation approaches in time series analysis are adopted and forecasting techniques using the seasonal space–time models are discussed. The models are applied to 516 consecutive fields of monthly averaged 500 mb geopotential heights over a 10 × 10 lattice in the extra-tropical northern hemisphere for the purpose of understanding the underlying statistical structure. It is found that space–time models with instantaneous spatial component give the best fit compared to other models in terms of maximizing the conditional likelihood function. The models are potentially useful for assessing the consistency of outputs from laboratory-based numerical models with field observations. Forecasting ability of the seasonal space–time models is also investigated. This revised version was published online in June 2006 with corrections to the Cover Date.     

Numerical models of wind-driven circulation in lakes

The state-of-the-art of numerical modelling of large-scale wind-driven circulation in lakes is presented. The governing equations which describe this motion are discussed along with the appropriate numerical techniques necessary to solve them in lakes. The numerical models are categorized into three large primary groups: the layered models, the Ekman-type models, and the other three-dimensional models. Discussions and comparison of models are given and future research directions are suggested.     

Markov interest rate models

A general procedure for creating Markovian interest rate models is presented. The models created by this procedure automatically fit within the HJM framework and fit the initial term structure exactly. Therefore they are arbitrage free. Because the models created by this procedure have only one state variable per factor, twoand even three-factor models can be computed efficiently, without resorting to Monte Carlo techniques. This computational efficiency makes calibration of the new models to market prices straightforward. Extended Hull- White, extended CIR, Black-Karasinski, Jamshidian's Brownian path independent models, and Flesaker and Hughston's rational log normal models are one-state variable models which fit naturally within this theoretical framework. The ‘separable’ n-factor models of Cheyette and Li, Ritchken, and Sankarasubramanian - which require n(n + 3)/2 state variables - are degenerate members of the new class of models with n(n + 3)/2 factors. The procedure is used to create a new class of one-factor models, the ‘β-η models.’ These models can match the implied volatility smiles of swaptions and caplets, and thus enable one to eliminate smile error. The β-η models are also exactly solvable in that their transition densities can be written explicitly. For these models accurate - but not exact - formulas are presented for caplet and swaption prices, and it is indicated how these closed form expressions can be used to efficiently calibrate the models to market prices.     

Mathematical models for polygamous mating systems

In this paper, two-sex models for populations with polygamous mating systems are developed. These models depend on the mating ratio and are applicable to both polygynous and polyandrous populations. Models for the population dynamics of populations with and without competition are constructed. Also, marriage models are discussed. The models developed describe situations common to mathematical ecology and mathematical demography. All of the models developed here are based on systems of linear and nonlinear autonomous differential equations.     

我国股指期货的套期保值比率研究

本文主要运用OLS、VAR、ECM、diagonal-BEKK、full-BEKK、scalar-BEKK对沪深300股指期货仿真交易的套期保值比率进行研究,比较了静态套期模型和动态套期保值模型的效果,并研究不同参数化形式对动态套期保值模型的影响。结果表明尽管动态套期保值在样本内要优于静态套期保值模型,但样本外效果却不是很好;另外,动态模型的不同的参数化形式对结果的影响也比较大。     

Semiparametric mixtures of regressions with single-index for model based clustering

In this article, we propose two classes of semiparametric mixture regression models with single-index for model based clustering. Unlike many semiparametric/nonparametric mixture regression models that can only be applied to low dimensional predictors, the new semiparametric models can easily incorporate high dimensional predictors into the nonparametric components. The proposed models are very general, and many of the recently proposed semiparametric/nonparametric mixture regression models are indeed special cases of the new models. Backfitting estimates and the corresponding modified EM algorithms are proposed to achieve optimal convergence rates for both parametric and nonparametric parts. We establish the identifiability results of the proposed two models and investigate the asymptotic properties of the proposed estimation procedures. Simulation studies are conducted to demonstrate the finite sample performance of the proposed models. Two real data applications using the new models reveal some interesting findings.

     

Models for network evolution

This paper describes mathematical models for network evolution when ties (edges) are directed and the node set is fixed. Each of these models implies a specific type of departure from the standard null binomial model. We provide statistical tests that, in keeping with these models, are sensitive to particular types of departures from the null. Each model (and associated test) discussed follows directly from one or more socio‐cognitive theories about how individuals alter the colleagues with whom they are likely to interact. The models include triad completion models, degree variance models, polarization and balkanization models, the Holland‐Leinhardt models, metric models, and the constructural model. We find that many of these models, in their basic form, tend asymptotically towards an equilibrium distribution centered at the completely connected network (i.e., all individuals are equally likely to interact with all other individuals); a fact that can inhibit the development of satisfactory tests.     

Convexity preserving jump-diffusion models for option pricing

We investigate which jump-diffusion models are convexity preserving. The study of convexity preserving models is motivated by monotonicity results for such models in the volatility and in the jump parameters. We give a necessary condition for convexity to be preserved in several-dimensional jump-diffusion models. This necessary condition is then used to show that, within a large class of possible models, the only convexity preserving models are the ones with linear coefficients.     

Relationship between DEA models without explicit inputs and DEA-R models

Data envelopment analysis (DEA) is one of often used modeling tools for efficiency and performance evaluation of decision making units. Ratio DEA (DEA-R) is a group of novel mathematical models that combines standard DEA methodology and ratio analysis. The efficiency score given by standard DEA CCR model is less than or equal to that given by DEA-R model. In case of single input or single output the efficiency scores in CCR and DEA-R models are identical. The paper deals with DEA-R models without explicit inputs, i.e. models where only pure outputs or index data are taken into account. A basic DEA-R model without explicit inputs is formulated and a relation between output-oriented DEA models without explicit inputs and output-oriented DEA-R models is analyzed. Central resource allocation and slack-based measure models within DEA-R framework are examined. Finally they are used for projections of decision making units on the efficient frontier. The results of the proposed models are applied for efficiency evaluation of 15 units (Chinese research institutes) and they are discussed.     

全时段最优套期保值模型及实证研

针对传统套期保值模型只考虑套期保值资产在套期保值期末的风险及未能充分利用样本数据所提供的信息的问题,本文提出了一类同时考虑套期保值期内不同期限风险的全时段最优套期保值比率计算模型.全时段套期保值模型通过最小化套期保值资产在套期保值期内不同期限的风险将投资者面临的风险在整个套期保值期内稳定保持在一个较低的水平,并更充分的利用了资产历史价格样本数据所提供的信息.本文基于沪深300指数及其仿真股指期货的历史价格数据,对传统形式的三种套期保值模型与本文提出的三种全时段套期保值模型的套期保值效果进行了实证分析和比较,并使用GARCH模型比较分析了这些模型套期保值的动态效果,结果表明三种全时段模型的套期保值效果都要优于相应的传统模型,能有效地缓解提前终止套期保值时投资者所面临的风险.     

A useful reparameterization for second‐order autoregressive processes

In time series analysis, autoregressive (a.r.) models are often fitted successfully to data, and such models are usually among the first to be taught. It is therefore important to understand why such models are useful in practice. An alternative parameterization for second order a.r. models, which assists understanding and interpretation, is discussed. The models are most plausible if certain restrictions are placed on the autoregressive parameters, which in turn lead to restrictions on the autocorrelation coefficients. Fitting the reparameterized model is straightforward, and the reparameterization may be extended, less usefully, to higher order a.r. models. The second‐order model is fitted to some meteorological data.     

Simple stochastic models of cracks

The stochastic Markov models describe various natural and technological processes. They are often used in rather diverse areas. The Markov models are distinguished with discrete time and relatively few states. In concrete cases, such models allow us to carry out effective calculations. In the article are considered some special models with two, four and eight states. The processes are simulated that are connected with hydraulic fracturing and wave front development.     

Integer programming models for hierarchical workforce scheduling problems including excess off-days and idle labour times

The decision problem considered in this paper is a hierarchical workforce scheduling problem in which a higher qualified worker can substitute for a lower qualified one, but not vice versa, labour requirements may vary, and each worker must receive n off-days a week. Within this context, five mathematical models are discussed. The first two of these five models are previously published. Both of them are for the case where the work is indivisible. The remaining three models are developed by the authors of this paper. One of these new models is for the case where the work is indivisible and the other two are for the case where the work is divisible. The three new models are proposed with the purpose of removing the shortcomings of the previously published two models. All of the five models are applied on the same illustrative example. Additionally, a total of 108 test problems are solved within the context of two computational experiments.     

非线性再生散度随机效应模型参数置信域的曲率表示

该文基于Laplace逼近建立了非线性再生散度随机效应模型在Euclid空间中的几何结构, 并在此基础上研究了此模型参数和子集参数的置信域, 进一步推广和发展了 Hamilton, Watts 和 Bates^[1]关于正态非线性回归模型, Wei^[2,3]关于嵌入模型和指数族非线性模型, Zhu, Tang 和 Wei^[4]关于半参数非线性模型,唐年胜、韦博成和王学仁^[5]关于非线性再生散度模型, Tang 和 Wang^[6]关于拟似然非线性模型等的结果.