-*- mode: org -*-
Seemingly unrelated noise from the query or database (duplicate entries)
*   1(<-479): [Improving hyperspectral matching method through feature-selection/weighting based on SVM].

(duplicated entry)

In the present article, feature selection/weighting based on SVM was
employed to improve the algorithm of choosing reference spectrum
through a multi-objective optimization approach proposed in
reference. Based on the sensitive analysis, half of features having
low weights in SVM classification model were eliminated
iteratively. Two criteria, matching accuracy and classification
confidence, were used to select the best-performing feature
subset. Three scenarios were designed: (1) only feature subset
selected by SVM was used; (2) both feature subset and global weights
were used, in which global weights were the coefficients of selected
features in the SVM classification model; (3) both feature subset and
local weights, which changed with the distance of a sample point to
the SVM separation plan, were used. Experiment executed on the popular
Indiana AVIRIS data set indicate that under all the three scenarios,
spectral matching accuracies were increased by 13%-17% compared to the
situation without feature selection. The result obtained under
scenario 3 is the most accurate and the most stable, which can be
primarily attributed to the ability of local weights to accurately
describe local distribution of spectra from the same class in feature
space. Moreover, scenario 3 can be regarded as the extension of
scenario 2 because when spectra far away from the separation plane are
selected as reference spectrums for matching, the features' weights
will not be considered. The results obtained under scenario 1 and 2
are very similar, indicating that considering global weights is not
necessary. The research presented in this paper advanced the spectrum
analysis using SVM to a higher level.

2009


* 184(<-562): On proto-differentiability of generalized perturbation maps

This paper is devoted to the sensitivity analysis in optimization
problems and variational inequalities. The concept of
proto-differentiability of set-valued maps (see [R.T. Rockafellar,
Proto-differentiability of set-valued mappings and its applications in
optimization, Ann. Inst. H. Poincare Anal. Non Lineaire 6 (1989)
449-482]) plays the key role in our investigation. It is proved that,
under some suitable qualification conditions, the generalized
perturbation maps (that is, the solution set map to a parameterized
constraint system, to a parameterized variational inequality, or to a
parameterized optimization problem) are proto-differentiable. (c) 2006
Elsevier Inc. All rights reserved.

2006



* 185(<-111): Concepts of efficiency for uncertain multi-objective optimization problems based on set order relations

In this paper we present new concepts of efficiency for uncertain
multi-objective optimization problems. We analyze the connection
between the concept of minmax robust efficiency presented by Ehrgott
et al. (Eur J Oper Res, 2014, doi:10.1016/j.ejor.2014.03.013) and the
upper set less order relation <=(u)(s) introduced by Kuroiwa (1998,
1999). From this connection we derive new concepts of efficiency for
uncertain multi-objective optimization problems by replacing the set
ordering with other set orderings. Those are namely the lower set less
ordering (see Kuroiwa 1998, 1999), the set less ordering (see
Nishnianidze in Soobshch Akad Nauk Gruzin SSR 114(3):489-491, 1984;
Young in Math Ann 104(1):260-290, 1931, doi:10.1007/BF01457934;
Eichfelder and Jahn in Vector Optimization. Springer, Berlin, 2012),
the certainly less ordering (see Eichfelder and Jahn in Vector
Optimization. Springer, Berlin, 2012), and the alternative set less
ordering (see Ide et al. in Fixed Point Theory Appl, 2014,
doi:10.1186/1687-1812-2014-83; Kobis 2014). We analyze the resulting
concepts of efficiency and present numerical results on the occurrence
of the various concepts. We conclude the paper with a short comparison
between the concepts, and an outlook to further work.

2014




* 186(<-570): A fiscal regime solving the incentive inconsistency problem

This paper proposes a fiscal taxation/subsidy regime, which can
mitigate the incentive inconsistency problem in the selection of a
price policy (Yao and Lai, Ann Reg Sci, 2006). Through this regime, a
Pareto improvement may be achieved. The results show that the efficacy
of governmental intervention is more direct in the case of rectangular
demand than that in linear demand. The distortion due to the incentive
inconsistency cannot be easily regulated.

2006



* 187(<-636): Geometrical properties of Pareto distribution

The differential-geometrical framework for analyzing statistical
problems related to Pareto distribution, is given. A classical and
intuitive way of description the relationship between the differential
geometry and the statistics, is introduced [Publicationes Mathematicae
Debrecen, Hungary, vol. 61 (2002) 1-14; RAAG Mem. 4 (1968) 373;
Ann. Statist. 10 (2) (1982) 357; Springer Lecture Notes in Statistics,
1985; Tensor, N.S. 57 (1996) 282; Commun. Statist. Theor. Meth. 29 (4)
(2000) 859; Tensor, N.S. 33 (1979) 347; Int. J. Eng. Sci. 19 (1981)
1609; Tensor, N.S. 57 (1996) 300; Differential Geometry and
Statistics, 1993], but in a slightly modified manner. This is in order
to provide an easier introduction for readers not familiar with
differential geometry. The parameter space of the Pareto distribution
using its Fisher's matrix is defined. The Riemannian and scalar
curvatures to parameter space are calculated. The differential
equations of the geodesics are obtained and solved. The J-divergence,
the geodesic distance and the relations between of them in that space
are found. A development of the relation between the J-divergence and
the geodesic distance is illustrated. The scalar curvature of the
J-space is represented. (C) 2002 Elsevier Inc. All rights reserved.

2003



* 188(<-491): Positive- versus zero-sum majoritarian ultimatum games: An experimental study

Politics can involve a Movement from a position off the Pareto
frontier to a point on it (a positive-sum game as exemplified in the
classic [Buchanan, J.M., Tullock, G., 1962. The Calculus of
Consent. University of Michigan Press, Ann Arbor] work), OF a movement
along the Pareto frontier (a zero-SLIM game as exemplified in the
classic [Riker, W., 1962. The theory of political coalitions. Yale
University Press, New Haven] work). In this paper we shed light on
their differentiation experimentally by making a comparison between a
positive-sum and a zero-sum majoritarian ultimatum game. Our main
findings include (I) the fraction Of Subjects who adopted minimum
winning rather than oversized coalitions increases significantly as
the game form varies from positive-sum to zero-sum, (ii) oversized
coalitions are attributable to non-strategic considerations, and (iii)
subjects who choose to adopt the minimum winning coalition have a
tendency to seek cheaper responders as their partners in the zero-sum
game, but there is no evidence Of Such a tendency in the positive-sum
game. Overall, the weight of the evidence revealed by our experimental
data indicates that relative scarcity (embodied in the zero-sum game)
promotes behavior more in line with the predictions of economics. (C)
2008 Elsevier B.V. All rights reserved.

2008



* 189(<-650): Extremist vs. centrist decision behavior: quasi-convex utility functions for interactive multi-objective linear programming problems

This paper presents the fundamental theory and algorithms for
identifying the most preferred alternative for a decision maker (DM)
having a non-centrist (or extremist) preferential behavior. The DM is
requested to respond to a set of questions in the form of paired
comparison of alternatives. The approach is different than other
methods that consider the centrist preferential behavior. In this
paper, an interactive approach is presented to solve the multiple
objective linear programming (MOLP) problem. The DM's underlying
preferential function is represented by a quasi-convex value (utility)
function, which is to be maximized. The method presented in this paper
solves MOLP problems with quasi-convex value (utility) functions by
using paired comparison of alternatives in the objective space. From
the mathematical point of view, maximizing a quasi-convex (or a
convex) function over a convex set is considered a difficult problem
to solve, while solutions for quasi-concave (or concave) functions are
currently available. We prove that our proposed approach converges to
the most preferred alternative. We demonstrate that the most preferred
alternative is an extreme point of the MOLP problem, and we develop an
interactive method that guarantees obtaining the global most preferred
alternative for the MOLP problem. This method requires only a finite
number of pivoting operations using a simplex-based method, and it
asks only a limited number of paired comparison questions of
alternatives in the objective space. We develop a branch and bound
algorithm that extends a tree of solutions at each iteration until the
MOLP problem is solved. At each iteration, the decision maker has to
identify the most preferred alternatives from a given subset of
efficient alternatives that are adjacent extreme points to the current
basis. Through the branch and bound algorithm, without asking many
questions from the decision maker, all branches of the tree Eire
implicitly enumerated until the most preferred alternative is
obtained. An example is provided to show the details of the
algorithm. Some computational experiments are also presented.

2002



* 190(<-622): Estimating catastrophic quantile levels for heavy-tailed distributions

Estimation of the occurrence of extreme events is of prime interest
for actuaries. Heavy-tailed distributions are used to model large
claims and losses. Within this setting we present a new extreme
quantile estimator based on an exponential regression model that was
introduced by Feuerverger and Hall [Ann. Stat. 27 (1999) 760] and
Beirlant et al. [Extremes 2 (1999) 177]. We also discuss how this
approach is to be adjusted in the presence of right censoring. This
adaptation can also be linked to robust quantile estimation as this
solution is based on a Winsorized mean of extreme order statistics
which replaces the classical Hill estimator. We also propose adaptive
threshold selection procedures for Weissman's [J. Am. Stat. Assoc. 73
(1978) 812] quantile estimator which can be used both with and without
censoring. Finally some asymptotic results are presented, while small
sample properties are compared in a simulation study. (C) 2004
Elsevier B.V. All rights reserved.

2004



* 191(<-634): On a bivariate lack of memory property under binary associative operation

A binary operation over real numbers is said to be associative if (x *
y) * z = x * (y * z) and it is said to be reducible if x * y = x * z
or y * w = z * w if and only if z = y. The operation * is said to have
an identity element (e) over tilde if x * (e) over tilde = x. Roy
[Roy, D. (2002). On bivariate lack of memory property and a new
definition. Ann. Inst. Statist. Math. 54:404-410] introduced a new
definition for bivariate lack of memory property and characterized the
bivariate exponential distribution introduced by Gumbel [Gumbel,
E. (1960). Bivariate exponential distributions. J
Am. Statist. Assoc. 55:698-707] under the condition that each of the
conditional distributions should have the univariate lack of memory
property. We generalize this definition and characterize different
classes of bivariate probability distributions under binary
associative operations between random variables.

2004



* 192(<-395): Modulated Branching Processes, Origins of Power Laws, and Queueing Duality

Power law distributions have been repeatedly observed in a wide
variety of socioeconomic, biological, and technological areas. In many
of the observations, e. g., city populations and sizes of living
organisms, the objects of interest evolve because of the replication
of their many independent components, e. g., births and deaths of
individuals and replications of cells. Furthermore, the rates of
replications are often controlled by exogenous parameters causing
periods of expansion and contraction, e. g., baby booms and busts,
economic booms and recessions, etc. In addition, the sizes of these
objects often have reflective lower boundaries, e. g., cities do not
fall below a certain size, low-income individuals are subsidized by
the government, companies are protected by bankruptcy laws,
etc. Hence, it is natural to propose reflected modulated branching
processes as generic models for many of the preceding
observations. Indeed, our main results show that the proposed
mathematical models result in power law distributions under quite
general polynomial Gartner-Ellis conditions, the generality of which
could explain the ubiquitous nature of power law distributions. In
addition, on a logarithmic scale, we establish an asymptotic
equivalence between the reflected branching processes and the
corresponding multiplicative ones. The latter, as recognized by Goldie
[Goldie, C. M. 1991. Implicit renewal theory and tails of solutions of
random equations. Ann. Appl. Probab. 1(1) 126-166], is known to be
dual to queueing/additive processes. We emphasize this duality further
in the generality of stationary and ergodic processes.

2010



* 193(<-406): LAMPERTI-TYPE LAWS

This paper explores various distributional aspects of random variables
defined as the ratio of two independent positive random variables
where one variable has an alpha-stable law, for 0 < alpha < 1, and the
other variable has the law defined by polynomially tilting the density
of an alpha-stable random variable by a factor theta > -alpha. When
theta = 0, these variables equate with the ratio investigated by
Lamperti [Trans. Amer. Math. Soc. 88 (1958) 380-387] which,
remarkably, was shown to have a simple density. This variable arises
in a variety of areas and gains importance from a close connection to
the stable laws. This rationale, and connection to the PD(alpha,
theta) distribution, motivates the investigations of its
generalizations which we refer to as Lamperti-type laws. We identify
and exploit links to random variables that commonly appear in a
variety of applications. Namely Linnik, generalized Pareto and
z-distributions. In each case we obtain new results that are of
potential interest. As some highlights, we then use these results to
(i) obtain integral representations and other identities for a class
of generalized Mittag-Leffler functions, (ii) identify explicitly the
Levy density of the semigroup of stable continuous state branching
processes (CSBP) and hence corresponding limiting distributions
derived in Slack and in Zolotarev [Z. Wahrsch. Verw. Gebiete 9 (1968)
139-145, Teor. Veroyatn. Primen. 2 (1957) 256-266], which are related
to the recent work by Berestycki, Berestycki and Schweinsberg, and
Bertoin and LeGall [Ann. Inst. H. Poincare Probab. Statist. 44 (2008)
214-238, Illinois J. Math. 50 (2006) 147-181] on beta
coalescents. (iii) We obtain explicit results for the occupation time
of generalized Bessel bridges and some interesting stochastic
equations for PD(alpha, theta)-bridges. In particular we obtain the
best known results for the density of the time spent positive of a
Bessel bridge of dimension 2 - 2 alpha.

2010



* 194(<-455): Maximum likelihood estimation of extreme value index for irregular cases

A method in analyzing extremes is to fit a generalized Pareto
distribution to the exceedances over a high threshold. By varying the
threshold according to the sample size [Smith, R.L., 1987. Estimating
tails of probability distributions. Ann. Statist. 15, 1174-1207] and
[Drees, H., Ferreira, A., de Haan, L., 2004. On maximum likelihood
estimation of the extreme value
index. Ann. Appl. Probab. 14,1179-1201] derived the asymptotic
properties of the maximum likelihood estimates (MLE) when the extreme
value index is larger than -1/2. Recently Zhou [2009. Existence and
consistency of the maximum likelihood estimator for the extreme value
index. J. Multivariate Anal. 100, 794-815] showed that the MLE is
consistent when the extreme value index is larger than -1. In this
paper, we study the asymptotic distributions of MLE when the extreme
value index is in between -1 and -1/2 (including -1/2). Particularly,
we consider the MLE for the endpoint of the generalized Pareto
distribution and the extreme value index and show that the asymptotic
limit for the endpoint estimate is non-normal, which connects with the
results in Woodroofe [1974. Maximum likelihood estimation of
translation parameter of truncated distribution II. Ann. Statist. 2,
474-488]. Moreover, we show that same results hold for estimating the
endpoint of the underlying distribution, which generalize the results
in Hall [1982. On estimating the endpoint of a
distribution. Ann. Statist. 10, 556-568] to irregular case. and
results in Woodroofe [1974. Maximum likelihood estimation of
translation parameter of truncated distribution
II. Ann. Statist. 2,474-488] to the case of unknown extreme value
index. (C) 2009 Elsevier B.V. All rights reserved.

2009



* 195(<-516): Peaks-over-threshold stability of multivariate generalized Pareto distributions

It is well-known that the univariate generalized Pareto distributions
(GPD) are characterized by their peaks-over-threshold (POT)
stability. We extend this result to multivariate GPDs. It is also
shown that this POT stability is asymptotically shared by
distributions which are in a certain neighborhood of a multivariate
GPD. A multivariate extreme value distribution is a typical
example. The usefulness of the results is demonstrated by various
applications. We immediately obtain, for example, that the excess
distribution of a linear portfolio Sigma(i <= d) a(i)U(i) with
positive weights a(i), i <= d, is independent of the weights, if
(U(1),...,U(d)) follows a multivariate GPD with identical univariate
polynomial or Pareto margins, which was established by Macke [On the
distribution of linear combinations of multivariate EVD and GPD
distributed random vectors with an application to the expected
shortfall of portfolios, Diploma Thesis, University of Wurzburg, 2004,
(in German)] and Falk and Michel [Testing for tail independence in
extreme value models. Ann. Inst. Statist. Math. 58 (2006)
261-290]. This implies, for instance, that the expected shortfall as a
measure of risk fails in this case. (c) 2007 Elsevier Inc. All rights
reserved.

2008



* 196(<-517): Extreme value theory for space-time processes with heavy-tailed distributions

Many real-life time series exhibit clusters of outlying observations
that cannot be adequately modeled by a Gaussian
distribution. Heavy-tailed distributions such as the Pareto
distribution have proved useful in modeling a wide range of bursty
phenomena that occur in areas as diverse as finance, insurance,
telecommunications, meteorology, and hydrology. Regular variation
provides a convenient and unified background for studying multivariate
extremes when heavy tails are present. In this paper, we study the
extreme value behavior of the space-time process given by
X(t)(s)=(infinity)Sigma(i=0)psi(i)(s)Z(t-i)(s), s epsilon [0,1](d),
where (Zt)(t epsilon Z) is an iid sequence of random fields on [0,
1](d) with values in the Skorokhod space D([0, 1](d)) of cadlag
functions on [0, 1](d) equipped with the J(1)-topology. The
coefficients Psi(i) are deterministic real-valued fields on D([0,
1](d)). The indices s and t refer to the observation of the process at
location s and time t. For example, X(t) (s), t = 1, 2,,.., could
represent the time series of annual maxima of ozone levels at location
s. The problem of interest is determining the probability that the
maximum ozone level over the entire region [0, 1](2) does not exceed a
given standard level f epsilon D([0, 1](2)) in n years. By
establishing a limit theory for point processes based on (Xt (s)), t =
1,..., n, we are able to provide approximations for probabilities of
extremal events. This theory builds on earlier results of de Haan and
Lin [L. de Haan, T. Lin, On convergence toward an extreme value
distribution in C[0, 1], Ann. Probab. 29 (2001) 467-483] and Hult and
Lindskog [H. Hult, F. Lindskog, Extremal behavior of regularly varying
stochastic processes, Stochastic Process. Appl. 115 (2) (2005)
249-274] for regular variation on D([0, 1](d)) and Davis and Resnick
[R.A. Davis, S.I. Resnick, Limit theory for moving averages of random
variables with regularly varying tail probabilities, Ann. Probab. 13
(1985) 179-195] for extremes of linear processes with heavy-tailed
noise. (C) 2007 Elsevier B.V. All rights reserved.

2008



* 197(<- 40): Max-stable processes and the functional D-norm revisited

Aulbach et al. (Extremes 16, 255283, 2013) introduced a max-domain of
attraction approach for extreme value theory in C[0,1] based on
functional distribution functions, which is more general than the
approach based on weak convergence in de Haan and Lin
(Ann. Probab. 29, 467483, 2001). We characterize this new approach by
decomposing a process into its univariate margins and its copula
process. In particular, those processes with a polynomial rate of
convergence towards a max-stable process are considered. Furthermore
we investigate the concept of differentiability in distribution of a
max-stable processes.

2015



* 198(<-643): The generalized extreme value distribution

This paper determines the type of asymptotic distribution for the
extreme changes in stock prices, foreign exchange rates and interest
rates. To find the correct limiting distribution for the maximal and
minimal changes in market variables, a more general extreme value
distribution is introduced using the Box-Cox transformation. Both the
generalized Pareto distribution of Pickands [Ann. Stat. 3 (1975) 119]
and the generalized extreme value distribution of Jenkinson
[Q. J. R. Meteorol. Soc. 87 (1955) 145] are strongly rejected in favor
of the newly proposed Box-Cox-GEV distribution. (C) 2003 Elsevier
Science B.V. All rights reserved.

2003



* 207(<-629): A new extreme quantile estimator for heavy-tailed distributions

The classical estimation method for extreme quantiles of heavy-tailed
distributions was presented by Weissman (J. Amer. Statist. Assoc. 73
(1978) 812-815) and makes use of the Hill estimator (Ann. Statist. 3
(1975) 1163-1174) for the positive extreme value index. This index
estimator can be interpreted as all estimator of the slope in the
Pareto quantile plot in case one considers regression lines passing
through a fixed anchor point. In this Note we propose a new extreme
quantile estimator based on an unconstrained least squares estimator
of the index, introduced by Kratz and Resnick
(Comm. Statist. Stochastic Models 12 (1996) 699-724) and Schultze and
Steinebach (Statist. Decisions 14 (1996) 353-372) and we Study its
asymptotic behavior. (C) 2004 Academie des sciences. Published by
Elsevier SAS. All rights reserved.

2004




* 239(<-145): [Genetic algorithm based multi-objective least square support vector machine for simultaneous determination of multiple components by near infrared spectroscopy].

(duplicated entry)

The near infrared (NIR) spectrum contains a global signature of
composition, and enables to predict different proper ties of the
material. In the present paper, a genetic algorithm and an adaptive
modeling technique were applied to build a multiobjective least square
support vector machine (MLS-SVM), which was intended to simultaneously
determine the concentrations of multiple components by NIR
spectroscopy. Both the benchmark corn dataset and self-made Forsythia
suspense dataset were used to test the proposed approach. Results show
that a genetic algorithm combined with adaptive modeling allows to
efficiently search the LS-SVM hyperparameter space. For the corn data,
the performance of multi-objective LS-SVM was significantly better
than models built with PLS1 and PLS2 algorithms. As for the Forsythia
suspense data, the performance of multi-objective LS-SVM was
equivalent to PLS1 and PLS2 models. In both datasets, the over-fitting
phenomena were observed on RBFNN models. The single objective LS-SVM
and MLS-SVM didn't show much difference, but the one-time modeling
convenience al lows the potential application of MLS-SVM to
multicomponent NIR analysis.

2014