A distance-based statistical analysis of fuzzy number-valued data

Real-life data associated with experimental outcomes are not always real-valued. In particular, opinions, perceptions, ratings, etc., are often assumed to be vague in nature, especially when they come from human valuations. Fuzzy numbers have extensively been considered to provide us with a convenient tool to express these vague data. In analyzing fuzzy data from a statistical perspective one finds two key obstacles, namely, the nonlinearity associated with the usual arithmetic with fuzzy data and the lack of suitable models and limit results for the distribution of fuzzy-valued statistics. These obstacles can be frequently bypassed by using an appropriate metric between fuzzy data, the notion of random fuzzy set and a bootstrapped central limit theorem for general space-valued random elements. This paper aims to review these ideas and a methodology for the statistical analysis of fuzzy number data which has been developed along the last years.     

Dynamical analysis of a game network

In this paper, our purpose is to establish a direct dynamical relationship between payoffs of players in a game. A network dynamical model is first proposed to describe the direct dynamical relationship. A Markovian chain is also introduced in the given network model to show the mixed strategy property in a game. As a result, a direct dynamical relationship between payoffs of players in a game can be illustrated through a network model with a Markovian chain. In addition, a sufficient condition is addressed to guarantee that the discussed network model has a unique and stable Nash equilibrium. Finally, a numerical example is shown to illustrate the effectiveness of the obtained criterion.     

On an application of game theory to a problem of testing statistical hypothesis

Consider an-dimensional random vector with known covariance matrix. The expectation values of its single components may take arbitrary values subject to the restriction that their sum is a prescribed positive constant. Now choose a linear combination of these components, take its expectation value and divide this by the square root of its variance. This quotient, which is of importance in some problems of test theory serves as the pay-off function of a two-person zero-sum game. Player I wants to maximize the quotient by forming suitable linear combinations and player II wants to minimize it by choosing appropriate expectation values of the single components of the random vector subject to the restriction stated above. It is shown that the game possesses an essentially unique equilibrium point. In the more complicated case, when the strategies of the second player are confined to non-negative expectation values of the random vector's components, there is also an essentially unique equilibrium point of the game. It coincides with that one of the unconstrained case if and only if the row sums of the random vector's covariance matrix are all nonnegative.     

Contrarian investment strategy with data envelopment analysis concept

One of the typical issues in financial literature is that the market tends to be overly pessimistic about value stocks, many of which are past losers. Therefore, over-reactions might capture by measuring earnings surprise vary with past return levels. In this paper, we propose a new index for an effective investment strategy to capture the return-reversal effect using both Data Envelopment Analysis (DEA) and Inverted DEA in order to consider the above characteristics of the market. Our investment strategy using the new index exhibits better performance than the naive return-reversal strategy that only uses past returns or earnings surprise. In addition, the correlations between our new index and commonly used value indices are insignificant, and the value indices cannot represent the over-valued (under-valued) situations perfectly. Hence, considering both proposed and value indices like book-to-price one, we could select value stocks more effectively than by using only one of these indices.     

Finding all pure strategy Nash equilibria in a planar location game

In this paper, we deal with a planar location-price game where firms first select their locations and then set delivered prices in order to maximize their profits. If firms set the equilibrium prices in the second stage, the game is reduced to a location game for which pure strategy Nash equilibria are studied assuming that the marginal delivered cost is proportional to the distance between the customer and the facility from which it is served. We present characterizations of local and global Nash equilibria. Then an algorithm is shown in order to find all possible Nash equilibrium pairs of locations. The minimization of the social cost leads to a Nash equilibrium. An example shows that there may exist multiple Nash equilibria which are not minimizers of the social cost.     

Exploring uses of persistent homology for statistical analysis of landmark-based shape data

A method for the use of persistent homology in the statistical analysis of landmark-based shape data is given. Three-dimensional landmark configurations are used as input for separate filtrations, persistent homology is performed, and persistence diagrams are obtained. Groups of configurations are compared using distances between persistence diagrams combined with dimensionality reduction methods. A three-dimensional landmark-based data set is used from a longitudinal orthodontic study, and the persistent homology method is able to distinguish clinically relevant treatment effects. Comparisons are made with the traditional landmark-based statistical shape analysis methods of Dryden and Mardia, and Euclidean Distance Matrix Analysis.     

Understanding herding based on a co-evolutionary model for strategy and game structure

So far, there has been no conclusion on the mechanism for herding, which is often discussed in the academia. Assuming escaping behavior of individuals in emergency is rational rather than out of panic according to recent findings in social psychology, we investigate the behavioral evolution of large crowds from the perspective of evolutionary game theory. Specifically, evolution of the whole population divided into two subpopulations, namely the co-evolution of strategy and game structure, is numerically simulated based on the game theoretical models built and the evolutionary rule designed, and a series of phenomena including extinction of one subpopulation and herding effect are predicted in the proposed framework. Furthermore, if the rewarding for rational agents becomes significantly larger than that for emotional ones, herding effect will disappear. It is exciting that some phase transition points with interesting properties for the system can be found. In addition, our model framework is able to explain the fact that it is difficult for mavericks to prevail in society. The current results of this work will be helpful in understanding and restraining herding effect in real life.     

Competition analysis of a triopoly game with bounded rationality

A dynamic Cournot game characterized by three boundedly rational players is modeled by three nonlinear difference equations. The stability of the equilibria of the discrete dynamical system is analyzed. As some parameters of the model are varied, the stability of Nash equilibrium is lost and a complex chaotic behavior occurs. Numerical simulation results show that complex dynamics, such as, bifurcations and chaos are displayed when the value of speed of adjustment is high. The global complexity analysis can help players to take some measures and avoid the collapse of the output dynamic competition game.     

A methodology for sensitivity analysis of models fitted to data using statistical methods

A simple methodology is presented for sensitivity analysis ofmodels that have been fitted to data by statistical methods.Such analysis is a decision support tool that can focus theeffort of a modeller who wishes to further refine a model and/orto collect more data. A formula is given for the calculationof the proportional reduction in the variance of the model ‘output’that would be achievable with perfect knowledge of a subsetof the model parameters. This is a measure of the importanceof the set of parameters, and is shown to be asymptoticallyequal to the squared correlation between the model output andits best predictor based on the omitted parameters. The methodology is illustrated with three examples of OR problems,an age-based equipment replacement model, an ARIMA forecastingmodel and a cancer screening model. The sampling error of thecalculated percentage of variance reduction is studied theoretically,and a simulation study is then used to exemplify the accuracyof the method as a function of sample size.     

Integrated data envelopment analysis and cooperative game for evaluating energy efficiency of transportation sector: a case of Iran

Annals of Operations Research - Transportation sector with the consumption of 25% of energy play a major role in Iranian economy. This sector produces 27% of total undesirable greenhouse gases in...     

Optimization of a minimal-storage strategy for cloud amount data

A strategy is proposed which reduces the storage requirements for cloud amount information by up to 50%. Archiving only the mean cloud amount, μ, is recommended. Retrieval of most of the original data is possible if observations are made at high resolution ( 1 km) and the processing system gives rise to predominantly binary (i.e. cloud or no-cloud) information. The strategy is applicable to cloud amount at any level and to total cloud cover. One year's global cloud data can be stored on 2.5 computer magnetic tapes in contrast to the 13 tapes suggested by GARP/JOC (1980) and ISCCP (1982). The resultant new cloud archive will have the advantage of being equally useful for all scientific users (e.g. remote sensing and climate modelling groups) and each group's post-processing time will be greatly reduced.     

Allocating the fixed cost: an approach based on data envelopment analysis and cooperative game

Annals of Operations Research - Allocating the fixed cost among a set of users in a fair way is an important issue both in management and economic research. Recently, Du et al. (Eur J Oper Res...     

Regularization of a two-dimensional strongly damped wave equation with statistical discrete data

In this paper, we consider an inverse problem for a strongly damped wave equation in two dimensional with statistical discrete data. Firstly, we give a representation for the solution and then present a discretization form of the Fourier coefficients. Secondly, we show that the solution does not depend continuously on the data by stating a concrete example, which makes the solution be not stable and thus the present problem is ill-posed in the sense of Hadamard. Next, we use the trigonometric least squares method associated with the Fourier truncation method to regularize the instable solution of the problem. Finally, the convergence rate of the error between the regularized solution and the sought solution is estimated and also investigated numerically.     

Bifurcation analysis of a non-cooperative differential game with one weak player

We study a bifurcation problem for a system of two differential equations in implicit form. For each value of the parameter θ, the solution yields a pair of Nash equilibrium strategies in feedback form, for a non-cooperative differential game. When θ=0, the second player has no power to influence the dynamics of the system, and his optimal strategy is myopic. The game thus reduces to an optimal control problem for the first player. By studying the bifurcation in the solutions to the corresponding system of Hamilton-Jacobi equations, one can establish existence and multiplicity of solutions to the differential game, as θ becomes strictly positive.     

Instability of statistical factor analysis

Factor analysis, a popular method for interpreting multivariate data, models the covariance among variables as being due to a small number (, ) of hidden variables. A factor analysis of can be thought of as an ordered or unordered collection, , of linearly independent lines in . Let be the collection of data sets for which is defined. The ``singularities' of are those data sets, , in the closure, , at which the limit, , does not exist. is unstable near its singularities.

Let be the direct sum of the lines in . determines a -plane bundle, , over a subset, , of . If 1$"> and is rich enough, ordered or, at least if or 3, unordered, must have a singularity at some data set in . The proofs are applications of algebraic topology. Examples are provided.