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Topic: Orthant

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	Abstract for Cowles Foundation Discussion Paper 1021R
		A leading case of such an integral is the negative orthant probability, where B = {v
		The multinomial probit (MNP) model used in econometrics and biometrics has cell probabilities that are negative orthant probabilities, with µ and depending on unknown parameters (and, in general, on covariates).
		Estimation of this model requires, for each trial parameter vector and each observation in a sample, evaluation of P(mu;B) and of its derivatives with respect to mu and Omega.
	cowles.econ.yale.edu /P/ab/a10/a1021-r.htm (168 words)

	Orthant Definition / Orthant Research (Site not responding. Last check: 2007-10-31)
		That is, an orthant is the analogue of a quadrantThe word quadrant can mean: A region of the Cartesian coordinate plane with a specific sign for the x and y coordinates: (+, +), (-, +), (-, -) or (-, +).
		It is the 2-dimensional case of an Orthant Another name for sextant Also see the Wiktionary entry on Quadrant....
		orthant is a subset of R. orthant is a polyhedral cone, whereas the semidefinite cone is not.
	www.elresearch.com /Orthant (299 words)

	what is an orthant?: Philosophy Forums (Site not responding. Last check: 2007-10-31)
		"Orthant" is the generalization of "octant" in three dimensions, "quadrant" in two dimensions, and "half-line" (I guess) in one dimension.
		I don't know what the "positive or negative orthant of a set" means, but maybe you can figure it out from context using this.
		Edit: I'd guess the positive orthant of a vector space is the one where all coordinates are positive, and the negative orthant is the one where all coordinates are negative.
	forums.philosophyforums.com /thread/9716 (180 words)

	Abstract for Cowles Foundation Discussion Paper 1049 (Site not responding. Last check: 2007-10-31)
		A leading case of such an integral is the negative orthant probability, implied by the multinomial probit (MNP) model used in econometrics and biometrics.
		Classical parametric estimation of this model requires, for each trial parameter vector and each observation in a sample, evaluation of a normal orthant probability and its derivatives with respect to the mean vector and the variance-covariance matrix.
		Several Monte Carlo simulators have been developed to approximate the orthant probability integral and its linear and logarithmic derivatives that limit computation while possessing properties that facilitate their use in iterative calculations for statistical inference.
	www.econ.yale.edu /cowles/P/ab/a10/a1049.htm (204 words)

	Improved Inclusion-Exclusion Inequalities for Simplex and Orthant Arrangements
		In particular, associated with an abstract tube is an inclusion-exclusion identity which can be truncated to give an inequality that is guaranteed to be at least as sharp as the inequality obtained by truncating the classical inclusion-exclusion identity.
		We present an abstract tube corresponding to an orthant arrangement where the inclusion-exclusion formula terms are obtained from the incidence structure of the boundary of the union of orthants.
		Thus, the construction of the abstract tube is similar to a construction for Euclidean balls using a Voronoi diagram.
	jipam-old.vu.edu.au /v2n2/031_00.html (407 words)

	Improved Inclusion-Exclusion Inequalities for Simplex and Orthant Arrangements (Site not responding. Last check: 2007-10-31)
		In particular, associated with an abstract tube is an inclusion-exclusion identity which can be truncated to give an inequality that is guaranteed to be at least as sharp as the inequality obtained by truncating the classical inclusion-exclusion identity.
		We present an abstract tube corresponding to an orthant arrangement where the inclusion-exclusion formula terms are obtained from the incidence structure of the boundary of the union of orthants.
		Thus, the construction of the abstract tube is similar to a construction for Euclidean balls using a Voronoi diagram.
	www.maths.tcd.ie /EMIS/journals/JIPAM/accepted_papers/031_00.html (325 words)

	Orthant - Wikipedia, the free encyclopedia
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		In geometry of n dimensions, an orthant is one of the 2
		That is, an orthant is the analogue of a quadrant in the plane, and is defined by a system of inequalities
	en.wikipedia.org /wiki/Orthant (94 words)

	focs,37th Annual Symposium on Foundations of Computer Science (FOCS '96) (Site not responding. Last check: 2007-10-31)
		This is a function of the form: ce(-x/sup T/Ax) where A is an n/spl times/n positive definite matrix, a: is the n-vector of the random variables and c is a suitable constant.
		The first problem we consider is the (approximate) evaluation of the integral of this function over the positive orthant /spl int/(x/sub 1/=0)/sup /spl infin///spl int/(x/sub 2/=0)/sup /spl infin///spl middot//spl middot//spl middot//spl int/(x/sub n/=0)/sup /spl infin//ce(-x/sup T/Ax).
		Related to it is the problem of drawing a sample from the positive orthant with probability density (approximately) equal to ce(-x/sup T/Ax).
	doi.ieeecomputersociety.org /10.1109/SFCS.1996.548479 (377 words)

	Orthant Probabilities (Site not responding. Last check: 2007-10-31)
		Calculation of orthant normal probabilities for a tridiagonal corelation matrix
		The following SAS/IML-program calculates orthant probabilities of the multivariate normal distribution possessing a tridiagonal correlation matrix.
		The algorithm used here is based on the representations given by Sun (1988) and Sun and Asano (1989).
	www.bioinf.uni-hannover.de /~bretz/software/orthant.html (158 words)

	Orthant Probabilities
		Calculation of orthant normal probabilities for a tridiagonal corelation matrix
		The following SAS/IML-program calculates orthant probabilities of the multivariate normal distribution possessing a tridiagonal correlation matrix.
		The algorithm used here is based on the representations given by Sun (1988) and Sun and Asano (1989).
	www.biostat.uni-hannover.de /staff/bretz/software/orthant.html (158 words)

	Interior-Point Abstracts
		Furthermore, it can be shown that the solution to the subproblem using a Newton's method converges to the subproblem optimal point in one iteration, if the current point and the subproblem optimal point are in the same orthant of $\Re^n$.
		This is of particular note, since the algorithm can therefore be viewed in three parts: Move from an exterior point in ${\cal C}_\alpha$ to some point in ${\cal C}_\alpha \cap {\cal O}$ where ${\cal O}$ is the orthant containing the subproblem optimal point.
		Move back towards the positive orthant the step length prescribed by the algorithm.
	www-unix.mcs.anl.gov /otc/InteriorPoint/abstracts/Kelly-Ecker-2.html (232 words)

	[No title] (Site not responding. Last check: 2007-10-31)
		A leading case of such an integral is the negative orthant probability.
		The multinomial probit (MNP) model used in econometrics and biometrics has cell probabilities that are negative orthant probabilities, with means and covariances depending on unknown parameters (and, in general, on covariates).
		Estimation of this model requires, for each trial parameter vector and each observation in a sample, evaluation of the probability and its derivatives with respect to mean and covariance parameters.
	emlab.berkeley.edu /wp/mcfadden_abs/4.26 (236 words)

	Checking for orthant orderings between discrete multivariate distributions (Site not responding. Last check: 2007-10-31)
		Checking for orthant orderings between discrete multivariate distributions
		The orders are called lower orthant order, upper orthant order, lower orthant concave order and upper orthant convex order, respectively.
		We provide an algorithm to check whether one of these four stochastic orderings holds, when X and Y have finitely discrete probability distributions.
	www.uni-koeln.de /wiso-fak/wisostatsem/abstracts/chorordi/chorordi.html (127 words)

	Limit, logic, and computation -- Freedman 95 (1): 95 -- Proceedings of the National Academy of Sciences
		There is a toy model of computation, the search of a database, in which this paradigm applies.
		Consider the databases consisting of the positive orthant of Z
		is the limiting solution to the infinitary version of the search problem in which all points in the positive orthant of R
	www.pnas.org /cgi/content/full/95/1/95 (2030 words)

	Markov Processes and Related Filelds
		The Laplace Operator in an Orthant (Algebraic Geometry Approach) pp.
		79-90 Explicit integral formulas for the resolvent of the discrete Laplace operator in an orthant are obtained, thus providing an analytic continuation of the resolvent.
		We use another approach and describe the dynamics in terms of the so-called second vector field in an orthant $R^N_+$, where $N$ is the number of nodes in the network [V.A. Malyshev, Networks and dynamical systems, Adv.
	mech.math.msu.su /~malyshev/abs95.htm (2139 words)

	Dependence Structures of Multivariate Phase-Type Distributions (Site not responding. Last check: 2007-10-31)
		Note that the orthant orders, coupled with identical marginals, emphasize the comparisons of dependence strengths of the two vectors by separating the marginals from consideration.
		We will apply the discrete algorithm to multivariate discrete Freund distributions with the goal of identifying the relationship between parameters which leads to negative dependence.
		Study the comparison results on dependence structures of multivariate discrete Marshall-Olkin distributions using orthant comparison techniques.
	www.nawwal.org /~mrgoff/research/proposal/node4.html (499 words)

	RUTH J. WILLIAMS
		L. Taylor and R. Williams, Existence and uniqueness of semimartingale reflecting Brownian motions in an orthant, Probability Theory and Related Fields, 96 (1993), 283-317.
		R. Williams, Semimartingale reflecting Brownian motions in the orthant, Stochastic Networks, IMA Volumes in Mathematics and Its Applications, Volume 71, eds.
		R. Williams, An invariance principle for semimartingale reflecting Brownian motions in an orthant, Queueing Systems: Theory and Applications, 30 (1998), 5-25.
	math.ucsd.edu /~williams/pubs/pubs.html (1595 words)

	Level Probabilities (Site not responding. Last check: 2007-10-31)
		The calculation of level probabilities is based on a recursive relationship of orthant normal probabilities with a tridiagonal correlation matrix (see Robertson et al., 1988, p.
		A SAS/IML module for calculating the orthant probabilities up to dimension 11 can be found here.
		A required SAS/IML module for calculating the maximum likelihood estimates under total order restriction can be found here.
	www.bioinf.uni-hannover.de /~bretz/software/levprob.html (121 words)

	A Subsidy-Surplus Model and the Skorokhod Problem in an Orthant (Site not responding. Last check: 2007-10-31)
		We consider the deterministic Skorokhod problem in an orthant of the form Zw(t) = w(t) + ∫ b(u, Yw(u), Zw(u)) du + ∫ R(u, Yw(u–); Zw(u–))dYw(u) with (Yw)
		Comparison result for (SP) vis-a-vis the usual partial order on the orthant is studied; we show that the more “inward looking” the reflection vectors and the drift, the larger the values of Yw will be but the values of Zw will be smaller.
		In addition to showing that the Leontief-type output is a feasible subsidy, connection between (SP) and “minimality” of feasible subsidies is discussed (consequently it is suggested that (SP) may be taken as a continuous time feedback-form analogue of open Leontief model).
	dx.doi.org /10.1287/moor.25.3.509.12215 (237 words)

	Preservation of positive and negative orthant dependence concepts under mixtures and applications, Félix Belzunce, ...
		Preservation of positive and negative orthant dependence concepts under mixtures and applications, Félix Belzunce, Patrizia Semeraro
		Preservation of positive and negative orthant dependence concepts under mixtures and applications
		In this paper we consider some dependence properties and orders among multivariate distributions, and we study their preservation under mixtures.
	projecteuclid.org /Dienst/UI/1.0/Summarize/euclid.jap/1101840543 (464 words)

	General equilibrium model with a convex cone as the set of commodity bundles
		The commodities are treated separately, and so a commodity bundle is an element of the positive orthant of the Euclidean space IR l, wherelis the number of com- modities.
		If we take the positive orthant of the Euclidean space IR l as the pointed convex cone then the partial ordering coincides with the Euclidean order relation on IR l taken in the classical approach.
		In this setting, given a nite number of consumers each with an ini- tial endowment and a preference relation on the commodity cone, we prove existence of a Walrasian equilibrium under assumptions which are essentially the same as the ones in Arrow and Debreu's model.
	ideas.repec.org /p/dgr/kubrem/1996740.html (557 words)

	Maple Lab 4 (Site not responding. Last check: 2007-10-31)
		What is the area under the curve for the part of the curve that is in the positive orthant?
		What is the length of the part of the curve in the positive orthant?
		With b=12, what is the effect of using values of a larger than 2?
	www.lib.rpi.edu /~mitchj/math1020/lab4/lab4.html (175 words)

	A Lyapunov Function for Tridiagonal Competitive-cooperative Systems
		The same function is a Lyapunov function for Kolmogorov tridiagonal systems, which are defined on a closed positive orthant in R
		We show that all bounded orbits converge to the set of equilibria.
		Moreover, we show that there can be no heteroclinic cycles on the boundary of the first orthant, extending the results of H. Freedman and H. Smith [ Differential Equations Dynam.
	epubs.siam.org /sam-bin/dbq/article/31614 (119 words)

	[No title] (Site not responding. Last check: 2007-10-31)
		From: horst.kraemer@snafu.de (Horst Kraemer) Subject: Re: half spaces and first orthant in R^n Date: Wed, 01 Sep 1999 21:12:10 GMT Newsgroups: sci.math Keywords: linear optimization On Wed, 01 Sep 1999 12:24:42 +0100, Geert Stremersch
		So a_1 and a_2 are row matrices with n columns and x is column matrix > with n rows.
		There is a very simple necessary and sufficient condition.
	www.math.niu.edu /~rusin/known-math/99/lin_opt (174 words)

	EULER Record Details (Site not responding. Last check: 2007-10-31)
		Dai, J.G.; Harrison, J.M. Reflected Brownian motion in an orthant: Numerical methods for steady- state analysis.
		The paper is concerned with the reflected Brownian motion (RBM).
		More precisely, there are two developed techniques for numerical analysis, of a semimartingale RBM (SRBM) having as state space the nonnegative orthant of an $n$-dimensional Euclidean space.
	www.emis.de /projects/EULER/detail?ide=1992dai-reflbrowmoti&matchno=67&matchtotal=277&q=cr%3AJ%2A+Harrison+ (144 words)

	research article : Equilibrium in a reinsurance market with short sale constraints
		This paper deals with the existence of equilibrium in a dynamic reinsurance market with short sale constraints, driven by a marked point process, as studied in Bernis and Jouini (2001).
		We use the set of reinsurance treaties as consumption set, which is the positive orthant of some Banach lattice that can be identified to a space $H^q$ of martingales, $q\in [1, +\infty[$.
		The properness of preferences is a key assumption for us to prove the existence of an equilibrium.
	www.ideas.uqam.ca /ideas/data/Articles/sprjoecthv:20:y:2002:i:2:p:295-320.html (301 words)

	Citations: Interior point methods: current status and future directions - Freund, Mizuno (ResearchIndex)
		, and many smoothing methods developed recently [1] 12] 18, 20, 22, 30, 34, 40, 41] The well known interior point path following algorithm can be considered as a continuation method, where all iterates are confined within the positive orthant.
		Many interior point algorithms have been shown to solve a subclass of NCPs, including linear programs and quadratic programs, in polynomial time.
		On the other hand, the so called non interior continuation methods require neither the smoothing path nor the initial and intermediate iterates to be in the positive orthant.
	citeseer.ist.psu.edu /context/608339/10652 (741 words)

	On the Local Times and Boundary Properties of Reflected Diusions with Jumps in the Positive Orthant Francisco J. Piera ... (Site not responding. Last check: 2007-10-31)
		Abstract: In this paper we study the boundary characteristics of reflected di#usions with jumps in the positive orthant.
		We consider a model with oblique reflections and study the reflection map in terms of the local time at the boundary (or reflection) faces of +.
		Piera, F., Mazumdar, R. and Guillemin, F. On the local times and boundary properties of reflected di#usions with jumps in the positive orthant.
	citeseer.lcs.mit.edu /piera03local.html (298 words)

	Weymark, John A.: Social Choice with Analytic Preferences (Site not responding. Last check: 2007-10-31)
		We provide examples of economic and political preference domains for which the Arrow social welfare function axioms are inconsistent, but whose choice-theoretic counterparts (with nondictatorship strengthened to anonymity) yield a social choice correspondence possibility theorem when combined with a natural agenda domain.
		In both examples, agendas are compact subsets of the nonnegative orthant of a multidimensional Euclidean space.
		In our first possibility theorem, we consider the standard Euclidean spatial model used in many political models.
	www.nuff.ox.ac.uk /users/doornik/eswc2000/a/1050.html (305 words)

	SICON Volume 34 Issue 1
		By using LOCUS you agree to abide by the
		Multiplicative Interior Gradient Methods for Minimization over the Nonnegative Orthant
		We prove that the algorithm combined with an appropriate line search is weakly convergent to a saddle point of the minimization problem, when the minimand is a differentiable function with bounded level sets.
	locus.siam.org /SICON/volume-34/art_0334017.html (202 words)

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