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Journal articles on the topic "Conditionally independent random variables":
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Foss, Serguei, and Andrew Richards. "On Sums of Conditionally Independent Subexponential Random Variables." Mathematics of Operations Research 35, no. 1 (February 2010): 102–19. http://dx.doi.org/10.1287/moor.1090.0430.
Zhang, Jiaqi, Yanyan Tang, and Jie Xiong. "Conditional Strong Law of Large Numbers under G-Expectations." Symmetry 16, no. 3 (February 25, 2024): 272. http://dx.doi.org/10.3390/sym16030272.
In this paper, we investigate two types of the conditional strong law of large numbers with a new notion of conditionally independent random variables under G-expectation which are related to the symmetry G-function. Our limit theorem demonstrates that the cluster points of empirical averages fall within the bounds of the lower and upper conditional expectations with lower probability one. Moreover, for conditionally independent random variables with identical conditional distributions, we show the existence of two cluster points of empirical averages that correspond to the essential minimum and essential maximum expectations, respectively, with G-capacity one.
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Bayramoglu (Bairamov), Ismihan. "On Conditionally Independent Random Variables, Copula and Order Statistics." Communications in Statistics - Theory and Methods 43, no. 10-12 (April 23, 2014): 2105–17. http://dx.doi.org/10.1080/03610926.2013.818695.
Yuan, De-Mei. "CONVERGENCE RATES FOR SEQUENCES OF CONDITIONALLY INDEPENDENT AND CONDITIONALLY IDENTICALLY DISTRIBUTED RANDOM VARIABLES." Journal of the Korean Mathematical Society 53, no. 6 (November 1, 2016): 1275–92. http://dx.doi.org/10.4134/jkms.j150490.
Gudynas, P. P. "Approximation by distributions of sums of conditionally independent random variables." Lithuanian Mathematical Journal 24, no. 4 (1985): 320–25. http://dx.doi.org/10.1007/bf00969125.
Astashkin, Sergey, Fedor Sukochev, and Chin Pin Wong. "Disjointification of martingale differences and conditionally independent random variables with some applications." Studia Mathematica 205, no. 2 (2011): 171–200. http://dx.doi.org/10.4064/sm205-2-3.
Savinov, Evgeniy Anatolievich. "A Variant of the Necessary Condition for the Absolute Continuity of Symmetric Multivariate Mixture." Mathematics 9, no. 13 (June 27, 2021): 1505. http://dx.doi.org/10.3390/math9131505.
Sufficient conditions are given under which the absolute continuity of the joint distribution of conditionally independent random variables can be violated. It is shown that in the case of a dimension n>1 this occurs for a sufficiently large number of discontinuity points of one-dimensional conditional distributions.
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Fristedt, Bert, and Donald A. Berry. "Optimality of myopic stopping times for geometric discounting." Journal of Applied Probability 25, no. 2 (June 1988): 437–43. http://dx.doi.org/10.2307/3214454.
Consider a sequence of conditionally independent Bernoulli random variables taking on the values 1 and − 1. The objective is to stop the sequence in order to maximize the discounted sum. Suppose the Bernoulli parameter has a beta distribution with integral parameters. It is optimal to stop when the conditional expectation of the next random variable is negative provided the discount factor is less than or equal to . Moreover, is best possible. The case where the parameters of the beta distribution are arbitrary positive numbers is also treated.
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Fristedt, Bert, and Donald A. Berry. "Optimality of myopic stopping times for geometric discounting." Journal of Applied Probability 25, no. 02 (June 1988): 437–43. http://dx.doi.org/10.1017/s0021900200041103.
Consider a sequence of conditionally independent Bernoulli random variables taking on the values 1 and − 1. The objective is to stop the sequence in order to maximize the discounted sum. Suppose the Bernoulli parameter has a beta distribution with integral parameters. It is optimal to stop when the conditional expectation of the next random variable is negative provided the discount factor is less than or equal to . Moreover, is best possible. The case where the parameters of the beta distribution are arbitrary positive numbers is also treated.
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Shervashidze, T. "Local Limit Theorems for Conditionally Independent Random Variables Controlled by a Finite Markov Chain." Theory of Probability & Its Applications 44, no. 1 (January 2000): 131–35. http://dx.doi.org/10.1137/s0040585x97977446.
Dissertations / Theses on the topic "Conditionally independent random variables":
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Vuong, Christophe. "Contributions to stochastic analysis for non-diffusive structures." Electronic Thesis or Diss., Institut polytechnique de Paris, 2023. http://www.theses.fr/2023IPPAT054.
Cette thèse a pour sujet l'étude de structures sans propriété de diffusion. Nous nous intéressons à deux classes de telles structures.Le premier sujet traite du calcul de Malliavin pour les variables aléatoires conditionnellement indépendantes qui est un cas de calcul de Malliavin discret. Il généralise aussi celui théorisé sur des produits dénombrables d'espaces de probabilité, pour les variables aléatoires indépendantes. Dans notre cas, l'intérêt d'un tel calcul est de venir compléter des résultats d'analyse stochastique avec des preuves d'inégalités fonctionnelles (inégalité de Poincaré, inégalité de McDiarmid) et de théorèmes limites. Une des applications phares est la détermination de la vitesse de convergence de théorèmes centraux limites via la méthode de Stein. En combinant le calcul de Malliavin avec la structure de Dirichlet sous-jacente aux variables aléatoires, nous obtenons une formule d'intégration par parties cruciale pour déterminer des bornes supérieures sur les vitesses de convergence. Nous montrons des théorèmes limites quantitatifs, dont un théorème de quatrième moment avec reste. En particulier, nous discutons d'une application à la normalité asymptotique du comptage de motifs dans des hypergraphes aléatoires échangeables.Le deuxième sujet étudie les fonctionnelles d'une mesure de Poisson en utilisant la notion d'inversibilité de transformations de cette mesure sur l'espace échantillon des mesures aléatoires. Nous utilisons l'identification de ces mesures et des processus ponctuels marqués associés. Les transformations inversibles sont obtenues via le théorème de Girsanov, en respectant l'absolue continuité par rapport à la mesure de référence. Il en résulte un critère entropique pour l'inversibilité des transformations. Enfin, nous faisons le lien avec les équations différentielles stochastiques dirigées par des mesures de Poisson This thesis is concerned with the study of non-diffusive structures. We focus on two classes of such structures.The first subject deals with Malliavin calculus for conditionally independent random variables, which is a special case of discrete Malliavin calculus. It also generalizes the calculus that has been developed for countable products of probability spaces, for independent random variables.In our case, the interest of such a calculus is to complement results in stochastic analysis with proofs of functional inequalities (Poincaré inequality, McDiarmid's inequality) and limit theorems. One of the main applications is the determination of the convergence rate of central limit theorems via the Stein method.By combining Malliavin calculus with the underlying Dirichlet structure of the random variables, we obtain an integration by parts formula which is key to the derivations of so-called Stein bounds of the rates of convergence. We show quantitative limit theorems, including a fourth moment theorem with remainder. In particular, we discuss an application to the asymptotic normality of motif counting in exchangeable random hypergraphs.The second subject studies functionals of a Poisson measure using the notion of invertibility of transformations of that measure on the sample space of random measures. We use the identification of these measures and the associated marked point processes. Invertible transformations are obtained via the Girsanov's theorem, respecting absolute continuity with respect to the reference measure. This results in an entropy criterion for the invertibility of transformations. Finally, we make the connection with stochastic differential equations driven by Poisson measures
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Kasparavičiūtė, Aurelija. "Theorems of large deviations for the sums of a random number of independent random variables." Doctoral thesis, Lithuanian Academic Libraries Network (LABT), 2014. http://vddb.library.lt/obj/LT-eLABa-0001:E.02~2014~D_20140121_101308-41106.
The research object of this thesis is the sum of a random number of summands of independent identically distributed random variables with positive weights. Such sums appear as models, for example, in insurance, finance mathematics. Throughout the thesis, it is assumed that the random number of summands is independent of the summands, the summands satisfy S. N. Bernstein's condition, and the random number of summands together with weights satisfy some compatibility conditions. The aim of this dissertation is a normal approximation to a distribution of the sum of a random number of summands of independent identically distributed random variables with positive weights that takes into consideration large deviations in both the Cramer and the power Linnik zones. Disertacinio darbo tyrimo objektas yra atsitiktinio dėmenų skaičiaus nepriklausomų vienodai pasiskirsčiusių atsitiktinių dydžių su teigiamais svoriniais koeficientais sumos, kurios kaip modelis sutinkamos, pavyzdžiui, finansų, draudos matematikose. Daromos prielaidos, kad atsitiktinis dėmenų skaičius yra nepriklausomas nuo sumos dėmenų, atsitiktiniai dėmenys tenkina apibendrintą S. N. Bernšteino sąlygą, o atsitiktinis dėmenų skaičius kartu su svoriais tenkina tam tikras suderinamumo sąlygas. Disertacijos tikslas yra standartizuotos (centruotos ir normuotos) minėtos atsitiktinės sumos skirstinio aproksimacija standartiniu normaliuoju dėsniu didžiųjų nuokrypių tiek Kramero, tiek ir laipsninėse Liniko zonose.
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Sambale, Holger [Verfasser]. "Second order concentration for functions of independent random variables / Holger Sambale." Bielefeld : Universitätsbibliothek Bielefeld, 2016. http://d-nb.info/1084888173/34.
Wu, Hao-cun. "Independent component analysis and its applications in finance." Click to view the E-thesis via HKUTO, 2007. http://sunzi.lib.hku.hk/HKUTO/record/B39559099.
吳浩存 and Hao-cun Wu. "Independent component analysis and its applications in finance." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2007. http://hub.hku.hk/bib/B39559099.
Baumgarten, Christoph [Verfasser], and Frank [Akademischer Betreuer] Aurzada. "Persistence of sums of independent random variables, iterated processes and fractional Brownian motion / Christoph Baumgarten. Betreuer: Frank Aurzada." Berlin : Universitätsbibliothek der Technischen Universität Berlin, 2013. http://d-nb.info/1035276445/34.
Paditz, Ludwig. "Über die Annäherung von Summenverteilungsfunktionen gegen unbegrenzt teilbare Verteilungsfunktionen in der Terminologie der Pseudomomente." Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2013. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-112967.
Die Pseudomomente dienen als Charakteristikum der Annäherung der Komponenten einer Summenverteilungsfunktion gegen die Komponenten der Grenzverteilungsfunktion. In der Terminologie der Pseudomomente werden Abschätzungen der Annäherung der Summenverteilungsfunktion gegen eine unbegrenz teilbare Verteilungsfunktion angegeben. Dabei werden die Aussagen ohne die Voraussetzung der sogenannten Infinitesimalitätsbedingung hergeleitet. Es werden Abschätzungen angegeben sowohl unter der Voraussetzung endlicher Streuungen als auch ohne diese Voraussetzung. Abschließend werden einige Literaturhinweise angegeben The pseudo-moments serve as a characteristic of the approach of the components of a cumulative distribution function to the components of the limit distribution function. In the terminology of pseudo-moments estimates of the approximation of the cumulative distribution function by an indefinite divisible distribution function can be specified. The results are derived without the assumption of the so-called condition of infinitesimality. There are given some estimations with or without the assumption of finite variances. Finally some references are given
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Bacro, Jean-Noël. "Sur les accroissements des processus de sommes partielles de variables aléatoires indépendantes." Paris 6, 1986. http://www.theses.fr/1986PA066372.
Considérant une suite de variables aléatoires non-dégénérées, indépendantes et de même loi, on s'intéresse au maximum des suites de sommes partielles pour des incréments dont la longueur est la partie entière de l'expression c log(n) + d log(log(n)), ou log désigne la fonction logarithme, c une constante strictement positive, d’une constante réelle et n la taille de l'échantillon. Ce genre de problème est directement lié aux lois de type Erdoes-Renyi-Shepp. A l'aide d'un théorème de grande déviation, nous montrons comment se comportent la limite en probabilité et les limites inferieures et supérieures presque sûres de la différence entre le maximum concerne et sa limite presque sure, en fonction de d. Les résultats obtenus sont alors appliqués à un processus de renouvellement et permettent de mettre en évidence la vitesse de convergence optimale du maximum et du minimum du processus pour des accroissements de type Erdoes-Renyi; le cas particulier du processus de poisson standard est explicite. Pour finir, considérant le cas particulier ou les variables aléatoires sont indépendantes, de loi normale centrée réduite, on donne des bornes inferieures et supérieures de la distribution limite de la statistique de Shepp. Conformément aux résultats précédents, il apparait que le maximum de Shepp a un comportement limite en loi de nature oscillante, proche d'une loi de Gumel.
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Halconruy, Hélène. "Calcul de Malliavin et structures de Dirichlet pour des variables aléatoires indépendantes." Electronic Thesis or Diss., Institut polytechnique de Paris, 2020. http://www.theses.fr/2020IPPAT016.
Cette thèse porte sur le calcul de Malliavin dont on munit deux cadres discrets. On équipe tout produit dénombrable d'espaces de probabilités d'une structure de Dirichlet-Malliavin au moyen d'opérateurs (gradient, divergence, opérateur nombre), d'une formule d'intégration par parties, et des formes de Dirichlet induites. On obtient les analogues discrets aux identités fonctionnelles classiques des processus Brownien et Poisson dont les structures de Dirichlet s'écrivent comme limites des structures induites par notre formalisme. Des critères de Stein-Malliavin discrets sont établis pour les approximations Normale et Gamma. Le second cadre est celui d'un modèle financier ternaire sous-tendu par un processus géométrique composé à trois points, et équivalent en loi au modèle trinomial. Toute fonctionnelle de ce processus géométrique composé de carré intégrable possède un développement en chaos "modifié" sur lequel agissent des opérateurs d'annihilation/gradient et de création/divergence vérifiant en outre une formule de commutation généralisée. S'ensuit de la formulede Clark "géométrique" qu'il est alors possible d'établir, une formule de hedging pour l'initié dont l'utilité additionnelle espérée s'exprime en termes d'entropie relative, comme dans le cas continu Malliavin calculus was initially developed to provide an infinite-dimensional variational calculus on the Wiener space and further extended to other spaces. In this work, we develop such one in two discrete frameworks. First, we equip any countable product of probability spaces with a discrete Dirichlet-Malliavin structure, consisting of a family of Malliavin operators (gradient, divergence, number operator), an integration by parts formula, and the induced Dirichlet forms. We get the analogues of the classical functional identities and retrieve the usual Poisson and Brownian Dirichlet structures as limits of our induced structures. We provide discrete Stein-Malliavin criterions for the Normal and the Gamma approximations. Second we study insider's trading in a ternary model, Iying on a three-points compound geometric process. We state a modified chaotic decomposition and define the geometric gradient and divergence operators as the annihilation and creation operators acting on it. We state a geometric Ocone-Karatzas formula. We express the insider's additional expected logarithmic utility in terms of relative entropy as in the continuous case
In diesem Artikel werden notwendige und hinreichende Bedingungen für die Gültigkeit von Grenzwertsätzen für mittlere Abweichungen untersucht. In der Terminilogie von J.V.LINNIK (1971) werden die x-Bereiche für mittlere Abweichungen gewöhnlich als "sehr enge" Zonen der integralen normalen Anziehung bezeichnet. Darüber hinaus werden die Restglieder untersucht, die in den asymptotischen Beziehungen auftreten. Die Ordnung der Konvergenzgeschwindigkeit wird angegeben. Frühere Ergebnisse einiger Autoren werden verallgemeinert. Abschließend werden einige Literaturhinweise angegeben In this paper we study necessary and sufficient conditions for the validity of limit theorems on moderate deviations. Usually x-zones for moderate deviations are called in the terminilogy by YU.V.LINNIK (1971) "very narrow" zones of integral normal attraction. Moreover we analyse the remainder term appearing in the asymptotic relations. Informations on the order of the rate of convergence are given. Earlier results by several authors are generalized. Finally some references are given
M, Lee Lawrence, Nicol David, and United States. National Aeronautics and Space Administration., eds. On the minimum of independent geometrically distributed random variables. Hampton, VA: Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 1994.
Meerschaert, Mark M. Limit Distributions for Sums of Independent Random Vectors: Heavy Tails in Theory and Practice. New York, USA: John Wiley & Sons, 2001.
Lemeshko, Boris, and Irina Veretel'nikova. Criteria for testing hypotheses about randomness and the absence of a trend. Application Guide. ru: INFRA-M Academic Publishing LLC., 2021. http://dx.doi.org/10.12737/1587437.
The monograph discusses the application of statistical criteria aimed at testing hypotheses about the absence of a trend in the analyzed samples. The rejection of such a hypothesis gives grounds to consider the analyzed data as samples of independent equally distributed random variables. We consider a set of special criteria aimed at testing such hypotheses, as well as a set of criteria for the uniformity of laws, the uniformity of averages and the uniformity of variances, which can also be used for these purposes. The disadvantages and advantages of various criteria are emphasized, the application of criteria in conditions of violation of standard assumptions is considered. Estimates of the power of the criteria are given, which allows you to navigate when choosing the most preferred criteria. Following the recommendations will ensure the correctness and increase the validity of statistical conclusions when analyzing data.
It is intended for specialists who are interested in the application of statistical methods for the analysis of various aspects and trends of the surrounding reality and who are in contact with the processing of experimental results, the need for data analysis in their activities. It will be useful for engineers, researchers, specialists of various profiles (doctors, biologists, sociologists, economists, etc.) who face the need for statistical analysis of experimental results in their activities. It will also be useful for university teachers, graduate students and students.
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Schurz, Henri, Philip J. Feinsilver, Gregory Budzban, and Harry Randolph Hughes. Probability on algebraic and geometric structures: International research conference in honor of Philip Feinsilver, Salah-Eldin A. Mohammed, and Arunava Mukherjea, June 5-7, 2014, Southern Illinois University, Carbondale, Illinois. Edited by Mohammed Salah-Eldin 1946- and Mukherjea Arunava 1941-. Providence, Rhode Island: American Mathematical Society, 2016.
Book chapters on the topic "Conditionally independent random variables":
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Kvatadze, Z. A., and T. L. Shervashidze. "On limit theorems for conditionally independent random variables controlled by a finite Markov chain." In Lecture Notes in Mathematics, 250–58. Berlin, Heidelberg: Springer Berlin Heidelberg, 1988. http://dx.doi.org/10.1007/bfb0078480.
Jacod, Jean, and Philip Protter. "Independent Random Variables." In Universitext, 65–75. Berlin, Heidelberg: Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-642-55682-1_10.
Gooch, Jan W. "Independent Random Variables." In Encyclopedic Dictionary of Polymers, 983. New York, NY: Springer New York, 2011. http://dx.doi.org/10.1007/978-1-4419-6247-8_15255.
Jacod, Jean, and Philip Protter. "Independent Random Variables." In Universitext, 61–72. Berlin, Heidelberg: Springer Berlin Heidelberg, 2000. http://dx.doi.org/10.1007/978-3-642-51431-9_10.
Catalano, Costanza, and Alberto Gandolfi. "Partially Independent Random Variables." In Springer Proceedings in Mathematics & Statistics, 33–56. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-46310-0_3.
Jacod, Jean, and Philip Protter. "Sums of Independent Random Variables." In Universitext, 117–23. Berlin, Heidelberg: Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-642-55682-1_15.
de la Peña, Víctor H., and Evarist Giné. "Sums of Independent Random Variables." In Probability and its Applications, 1–50. New York, NY: Springer New York, 1999. http://dx.doi.org/10.1007/978-1-4612-0537-1_1.
Fristedt, Bert, and Lawrence Gray. "Sums of Independent Random Variables." In A Modern Approach to Probability Theory, 147–62. Boston, MA: Birkhäuser Boston, 1997. http://dx.doi.org/10.1007/978-1-4899-2837-5_10.
Chow, Yuan Shih, and Henry Teicher. "Sums of Independent Random Variables." In Springer Texts in Statistics, 113–64. New York, NY: Springer New York, 1997. http://dx.doi.org/10.1007/978-1-4612-1950-7_5.
Kotulski, Zbigniew, and Wojciech Szczepiński. "Functions of Independent Random Variables." In Error Analysis with Applications in Engineering, 91–105. Dordrecht: Springer Netherlands, 2009. http://dx.doi.org/10.1007/978-90-481-3570-7_4.
Conference papers on the topic "Conditionally independent random variables":
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Zhang, Yanbao, Akshay Seshadri, and Emanuel Knill. "Confidence-Interval Construction with Non-I.I.D. Spot-Checking Trials & its Application in Quantum Information." In Quantum 2.0. Washington, D.C.: Optica Publishing Group, 2023. http://dx.doi.org/10.1364/quantum.2023.qtu3a.20.
We develop a method to estimate the sum of conditional means of a sequence of random variables given our access to only a subsequence by spot-checking. The method works with non-independent-and-identically-distributed (non-i.i.d.) random variables and can be applied for certifying ongoing quantum information tasks.
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Hu, Zhen, Sankaran Mahadevan, and Xiaoping Du. "Uncertainty Quantification in Time-Dependent Reliability Analysis." In ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/detc2015-47925.
One of the essential steps in time-dependent reliability analysis is the characterization of stochastic load processes and system random variables based on experimental or historical data. Limited data results in uncertainty in the modeling of random variables and stochastic loadings. The uncertainty in random variable and stochastic load models later causes uncertainty in the results of reliability analysis. An uncertainty quantification framework is developed in this paper for time-dependent reliability analysis. The effects of two kinds of uncertainty sources, namely data uncertainty and model uncertainty on the results of time-dependent reliability analysis are investigated. The Bayesian approach is employed to model the epistemic uncertainty sources in random variables and stochastic processes. A straightforward formulation of uncertainty quantification in time-dependent reliability analysis results in a double-loop implementation, which is computationally expensive. Therefore, this paper builds a surrogate model for the conditional reliability index in terms of variables with imprecise parameters. Since the conditional reliability index is independent of the epistemic uncertainty, the surrogate model is applicable for any realizations of the epistemic uncertainty. Based on the surrogate model, the uncertainty in time-dependent reliability analysis is quantified without evaluating the original limit-state function, which increases the efficiency of uncertainty quantification. The effectiveness of the proposed method is demonstrated using a mathematical example and an engineering application example.
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Chen, Qi, Fan Cheng, Tie Liu, and Raymond W. Yeung. "A marginal characterization of entropy functions for conditional mutually independent random variables (with application to Wyner's common information)." In 2015 IEEE International Symposium on Information Theory (ISIT). IEEE, 2015. http://dx.doi.org/10.1109/isit.2015.7282600.
Daskalakis, Constantinos, Ilias Diakonikolas, Ryan ODonnell, Rocco A. Servedio, and Li-Yang Tan. "Learning Sums of Independent Integer Random Variables." In 2013 IEEE 54th Annual Symposium on Foundations of Computer Science (FOCS). IEEE, 2013. http://dx.doi.org/10.1109/focs.2013.31.
Karloff, Howard, and Yishay Mansour. "On construction of k-wise independent random variables." In the twenty-sixth annual ACM symposium. New York, New York, USA: ACM Press, 1994. http://dx.doi.org/10.1145/195058.195409.
Sun, Liye, Teresa Vidal-Calleja, and Jaime Valls Miro. "Coupling conditionally independent submaps for large-scale 2.5D mapping with Gaussian Markov Random Fields." In 2017 IEEE International Conference on Robotics and Automation (ICRA). IEEE, 2017. http://dx.doi.org/10.1109/icra.2017.7989358.
Charalambous, Charalambos D., and Jan H. van Schuppen. "Characterization of Conditional Independence and Weak Realizations of Multivariate Gaussian Random Variables: Applications to Networks." In 2020 IEEE International Symposium on Information Theory (ISIT). IEEE, 2020. http://dx.doi.org/10.1109/isit44484.2020.9174403.
Kuo, C. J., and Y. F. Hsu. "On the quantization efficiency of independent and uncorrelated random variables." In [Proceedings] ICASSP-92: 1992 IEEE International Conference on Acoustics, Speech, and Signal Processing. IEEE, 1992. http://dx.doi.org/10.1109/icassp.1992.226349.
Schudy, Warren, and Maxim Sviridenko. "Concentration and Moment Inequalities for Polynomials of Independent Random Variables." In Proceedings of the Twenty-Third Annual ACM-SIAM Symposium on Discrete Algorithms. Philadelphia, PA: Society for Industrial and Applied Mathematics, 2012. http://dx.doi.org/10.1137/1.9781611973099.37.
De, Anindya, Philip M. Long, and Rocco A. Servedio. "Learning Sums of Independent Random Variables with Sparse Collective Support." In 2018 IEEE 59th Annual Symposium on Foundations of Computer Science (FOCS). IEEE, 2018. http://dx.doi.org/10.1109/focs.2018.00036.
This paper is part of series on self-contained papers in which a large part, if not the full extent, of the asymptotic limit theory of summands of independent random variables is exposed. Each paper of the series may be taken as review exposition but specially as a complete exposition expect a few exterior resources. For graduate students and for researchers (beginners or advanced), any paper of the series should be considered as a basis for constructing new results. The contents are taken from advanced books but the organization and the proofs use more recent tools, are given in more details and do not systematically follow previous one. Sometimes, theorems are completed and innovated
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Schlenker, George J. Methods for Calculating the Probability Distribution of Sums of Independent Random Variables. Fort Belvoir, VA: Defense Technical Information Center, July 1986. http://dx.doi.org/10.21236/ada170465.
Nuttall, Albert H. Joint Probability Density Function of Selected Order Statistics and the Sum of the Remainder as Applied to Arbitrary Independent Random Variables. Fort Belvoir, VA: Defense Technical Information Center, November 2003. http://dx.doi.org/10.21236/ada419339.
Edwards, Susan L., Marcus E. Berzofsky, and Paul P. Biemer. Addressing Nonresponse for Categorical Data Items Using Full Information Maximum Likelihood with Latent GOLD 5.0. RTI Press, September 2018. http://dx.doi.org/10.3768/rtipress.2018.mr.0038.1809.
Full information maximum likelihood (FIML) is an important approach to compensating for nonresponse in data analysis. Unfortunately, only a few software packages implement FIML and even fewer have the capability to compensate for missing not at random (MNAR) nonresponse. One of these packages is Statistical Innovations’ Latent GOLD; however, the user documentation for Latent GOLD provides no mention of this capability. The purpose of this paper is to provide guidance for fitting MNAR FIML models for categorical data items using the Latent GOLD 5.0 software. By way of comparison, we also provide guidance on fitting FIML models for nonresponse missing at random (MAR) using the methods of Fuchs (1982) and Fay (1986), who incorporated item nonresponse indicators within a structural modeling framework. We compare both FIML for MAR and FIML for MNAR nonresponse models for independent and dependent variables. Also, we provide recommendations for future applications of FIML using Latent GOLD.
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Schulz, Jan, Daniel Mayerhoffer, and Anna Gebhard. A Network-Based Explanation of Perceived Inequality. Otto-Friedrich-Universität, 2021. http://dx.doi.org/10.20378/irb-49393.
Across income groups and countries, the public perception of economic inequality and many other macroeconomic variables such as inflation or unemployment rates is spectacularly wrong. These misperceptions have far-reaching consequences, as it is perceived inequality, not actual inequality informing redistributive preferences. The prevalence of this phenomenon is independent of social class and welfare regime, which suggests the existence of a common mechanism behind public perceptions. We propose a network-based explanation of perceived inequality building on recent advances in random geometric graph theory. The literature has identified several stylised facts on how individual perceptions respond to actual inequality and how these biases vary systematically along the income distribution. Our generating mechanism can replicate all of them simultaneously. It also produces social networks that exhibit salient features of real-world networks; namely, they cannot be statistically distinguished from small-world networks, testifying to the robustness of our approach. Our results, therefore, suggest that homophilic segregation is a promising candidate to explain inequality perceptions with strong implications for theories of consumption behaviour.
