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Journal articles on the topic 'U-processes'

Author: Grafiati

Published: 7 February 2023

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1

Ruymgaart, F. H., and M. C. A. van Zuijlen. "Empirical U-statistics processes." Journal of Statistical Planning and Inference 32, no. 2 (August 1992): 259–69. http://dx.doi.org/10.1016/0378-3758(92)90051-s.

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2

Wendler, Martin. "U-processes, U-quantile processes and generalized linear statistics of dependent data." Stochastic Processes and their Applications 122, no. 3 (March 2012): 787–807. http://dx.doi.org/10.1016/j.spa.2011.11.010.

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3

Arcones, Miguel A., and Evarist Gine. "Limit Theorems for $U$-Processes." Annals of Probability 21, no. 3 (July 1993): 1494–542. http://dx.doi.org/10.1214/aop/1176989128.

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4

Nolan, Deborah, and David Pollard. "$U$-Processes: Rates of Convergence." Annals of Statistics 15, no. 2 (June 1987): 780–99. http://dx.doi.org/10.1214/aos/1176350374.

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5

Li, Hong, Chuanbao Ren, and Luoqing Li. "U-Processes and Preference Learning." Neural Computation 26, no. 12 (December 2014): 2896–924. http://dx.doi.org/10.1162/neco_a_00674.

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Preference learning has caused great attention in machining learning. In this letter we propose a learning framework for pairwise loss based on empirical risk minimization of U-processes via Rademacher complexity. We first establish a uniform version of Bernstein inequality of U-processes of degree 2 via the entropy methods. Then we estimate the bound of the excess risk by using the Bernstein inequality and peeling skills. Finally, we apply the excess risk bound to the pairwise preference and derive the convergence rates of pairwise preference learning algorithms with squared loss and indicator loss by using the empirical risk minimization with respect to U-processes.

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6

Arcones, Miguel A. "A Bernstein-type inequality for U-statistics and U-processes." Statistics & Probability Letters 22, no. 3 (February 1995): 239–47. http://dx.doi.org/10.1016/0167-7152(94)00072-g.

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7

Stute, Winfried. "$U$-Statistic Processes: A Martingale Approach." Annals of Probability 22, no. 4 (October 1994): 1725–44. http://dx.doi.org/10.1214/aop/1176988480.

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8

Nolan, Deborah, and David Pollard. "Functional Limit Theorems for $U$-Processes." Annals of Probability 16, no. 3 (July 1988): 1291–98. http://dx.doi.org/10.1214/aop/1176991691.

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9

Eichelsbacher, P. "Moderate deviations for functional U-processes." Annales de l'Institut Henri Poincare (B) Probability and Statistics 37, no. 2 (March 2001): 245–73. http://dx.doi.org/10.1016/s0246-0203(00)01063-3.

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10

Eichelsbacher, Peter. "Moderate deviations for degenerate U-processes." Stochastic Processes and their Applications 87, no. 2 (June 2000): 255–79. http://dx.doi.org/10.1016/s0304-4149(99)00112-x.

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11

Serfling, Robert, and Wenyang Wang. "A large deviation theorem for U-processes." Statistics & Probability Letters 49, no. 2 (August 2000): 181–93. http://dx.doi.org/10.1016/s0167-7152(00)00047-x.

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12

Eichelsbacher, Peter. "Moderate and large deviations for U-processes." Stochastic Processes and their Applications 74, no. 2 (June 1998): 273–96. http://dx.doi.org/10.1016/s0304-4149(97)00113-0.

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13

Hsing, Tailen, and Wei Biao Wu. "On weighted U-statistics for stationary processes." Annals of Probability 32, no. 2 (April 2004): 1600–1631. http://dx.doi.org/10.1214/009117904000000333.

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14

Kohatsu-Hia, Arturo. "Weak convergence of infinite order U-processes." Statistics & Probability Letters 12, no. 2 (August 1991): 145–50. http://dx.doi.org/10.1016/0167-7152(91)90059-z.

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15

Bashford, J. D., P. D. Jarvis, J. G. Sumner, and M. A. Steel. "U(1) ×U(1) ×U(1) symmetry of the Kimura 3ST model and phylogenetic branching processes." Journal of Physics A: Mathematical and General 37, no. 8 (February 11, 2004): L81—L89. http://dx.doi.org/10.1088/0305-4470/37/8/l01.

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16

Eichelsbacher, Peter, Peter Eichelsbacher, Matthias Lowe, and Matthias Lowe. "Large deviations principle for partial sums $U$-processes." Teoriya Veroyatnostei i ee Primeneniya 43, no. 1 (1998): 97–115. http://dx.doi.org/10.4213/tvp826.

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17

Eichelsbacher, P., and M. Lowe. "Large Deviations Principle for Partial Sums U-Processes." Theory of Probability & Its Applications 43, no. 1 (January 1999): 26–41. http://dx.doi.org/10.1137/s0040585x97976647.

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18

Zheng, Jing, Chang-qing Tong, and Gui-jun Zhang. "Modeling stochastic mortality with O-U type processes." Applied Mathematics-A Journal of Chinese Universities 33, no. 1 (March 2018): 48–58. http://dx.doi.org/10.1007/s11766-018-3349-7.

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19

Basu, A. K., and Arindam Kundu. "Limit Distribution for Conditional U-Statistics for Dependent Processes." Calcutta Statistical Association Bulletin 52, no. 1-4 (March 2002): 381–408. http://dx.doi.org/10.1177/0008068320020522.

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20

Smirnov, E., and G. Elmanov. "Radiation enhanced diffusion processes in UO2and (U,Pu)O2." IOP Conference Series: Materials Science and Engineering 130 (April 2016): 012063. http://dx.doi.org/10.1088/1757-899x/130/1/012063.

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21

Grusho, A. A. "On Convergence of Counting Processes Associated with U-Statistics." Theory of Probability & Its Applications 30, no. 3 (September 1986): 626–30. http://dx.doi.org/10.1137/1130082.

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22

Neumeyer, Natalie. "A central limit theorem for two-sample U-processes." Statistics & Probability Letters 67, no. 1 (March 2004): 73–85. http://dx.doi.org/10.1016/j.spl.2002.12.001.

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23

Arcones, Miguel A., and Yishi Wang. "Some new tests for normality based on U-processes." Statistics & Probability Letters 76, no. 1 (January 2006): 69–82. http://dx.doi.org/10.1016/j.spl.2005.07.003.

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24

Lévy-Leduc, C., H. Boistard, E. Moulines, M. S. Taqqu, and V. A. Reisen. "Asymptotic properties of U-processes under long-range dependence." Annals of Statistics 39, no. 3 (June 2011): 1399–426. http://dx.doi.org/10.1214/10-aos867.

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25

Arcones, M. A. "The Law of the Iterated Logarithm for U-Processes." Journal of Multivariate Analysis 47, no. 1 (October 1993): 139–51. http://dx.doi.org/10.1006/jmva.1993.1075.

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26

Csörgõ, M., B. Szyszkowicz, and Q. Wang. "Asymptotics of Studentized U-type processes for changepoint problems." Acta Mathematica Hungarica 121, no. 4 (September 18, 2008): 333–57. http://dx.doi.org/10.1007/s10474-008-7217-4.

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27

Bertoin, Jean. "How linear reinforcement affects Donsker’s theorem for empirical processes." Probability Theory and Related Fields 178, no. 3-4 (September 18, 2020): 1173–92. http://dx.doi.org/10.1007/s00440-020-01001-9.

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Abstract A reinforcement algorithm introduced by Simon (Biometrika 42(3/4):425–440, 1955) produces a sequence of uniform random variables with long range memory as follows. At each step, with a fixed probability $$p\in (0,1)$$ p ∈ ( 0 , 1 ) , $${\hat{U}}_{n+1}$$ U ^ n + 1 is sampled uniformly from $${\hat{U}}_1, \ldots , {\hat{U}}_n$$ U ^ 1 , … , U ^ n , and with complementary probability $$1-p$$ 1 - p , $${\hat{U}}_{n+1}$$ U ^ n + 1 is a new independent uniform variable. The Glivenko–Cantelli theorem remains valid for the reinforced empirical measure, but not the Donsker theorem. Specifically, we show that the sequence of empirical processes converges in law to a Brownian bridge only up to a constant factor when $$p<1/2$$ p < 1 / 2 , and that a further rescaling is needed when $$p>1/2$$ p > 1 / 2 and the limit is then a bridge with exchangeable increments and discontinuous paths. This is related to earlier limit theorems for correlated Bernoulli processes, the so-called elephant random walk, and more generally step reinforced random walks.

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28

Helmers, R., Victor H. de la Pena, and Evarist Gine. "Decoupling, from Dependence to Independence, Randomly Stopped Processes, U-Statistics and Processes, Martingales and beyond." Journal of the American Statistical Association 95, no. 451 (September 2000): 1017. http://dx.doi.org/10.2307/2669501.

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29

Eichelsbacher, Peter, and Peter Eichelsbacher. "Large deviations for partial sums $U$-processes in dependent cases." Teoriya Veroyatnostei i ee Primeneniya 45, no. 4 (2000): 670–93. http://dx.doi.org/10.4213/tvp498.

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30

Eichelsbacher, P. "Large Deviations for Partial Sums U-Processes in Dependent Cases." Theory of Probability & Its Applications 45, no. 4 (January 2001): 569–88. http://dx.doi.org/10.1137/s0040585x97978531.

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31

Dehling, H., A. Rooch, and M. Wendler. "Two-sample U-statistic processes for long-range dependent data." Statistics 51, no. 1 (January 2, 2017): 84–104. http://dx.doi.org/10.1080/02331888.2016.1270542.

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32

Večeřa, Jakub, and Viktor Beneš. "Approaches to asymptotics for U-statistics of Gibbs facet processes." Statistics & Probability Letters 122 (March 2017): 51–57. http://dx.doi.org/10.1016/j.spl.2016.10.024.

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33

Iltis, X., J. Allenou, B. Verhaeghe, H. Palancher, O. Tougait, A. Bonnin, and R. Tucoulou. "About molybdenum behaviour during U(Mo)/Al(Si) interaction processes." Journal of Nuclear Materials 433, no. 1-3 (February 2013): 255–64. http://dx.doi.org/10.1016/j.jnucmat.2012.09.028.

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34

Rejchel, Wojciech. "Oracle inequalities for ranking and U -processes with Lasso penalty." Neurocomputing 239 (May 2017): 214–22. http://dx.doi.org/10.1016/j.neucom.2017.02.018.

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35

Večeřa, Jakub. "Central limit theorem for Gibbsian U-statistics of facet processes." Applications of Mathematics 61, no. 4 (August 2016): 423–41. http://dx.doi.org/10.1007/s10492-016-0140-z.

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36

Wang, Yanling, and Limin Liu. "Portfolio selection problem with stopping time under O-U processes." International Mathematical Forum 9 (2014): 131–36. http://dx.doi.org/10.12988/imf.2014.312247.

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37

Rudisill, Frank, Lewis A. Litteral, and Don Walter. "Modified U Charts for Monitoring and Controlling Poisson Attribute Processes." Quality Engineering 16, no. 4 (January 7, 2004): 637–42. http://dx.doi.org/10.1081/qen-120038024.

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38

Reitzner, Matthias, and Matthias Schulte. "Central limit theorems for $U$-statistics of Poisson point processes." Annals of Probability 41, no. 6 (November 2013): 3879–909. http://dx.doi.org/10.1214/12-aop817.

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39

M�ller, A., B. Schuch, W. Groh, and E. Salzborn. "Multiple-electron processes in 1.4 MeV/u ion-atom collisions." Zeitschrift f�r Physik D Atoms, Molecules and Clusters 7, no. 3 (September 1987): 251–60. http://dx.doi.org/10.1007/bf01384992.

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40

Clifford, Peter, and David Stirzaker. "History-dependent random processes." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 464, no. 2093 (February 5, 2008): 1105–24. http://dx.doi.org/10.1098/rspa.2007.0291.

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Ulam has defined a history-dependent random sequence by the recursion X n +1 = X n + X U ( n ) , where ( U ( n ); n ≥1) is a sequence of independent random variables with U ( n ) uniformly distributed on {1, …, n } and X 1 =1. We introduce a new class of continuous-time history-dependent random processes regulated by Poisson processes. The simplest of these, a univariate process regulated by a homogeneous Poisson process, replicates in continuous time the essential properties of Ulam's sequence, and greatly facilitates its analysis. We consider several generalizations and extensions of this, including bivariate and multivariate coupled history-dependent processes, and cases when the dependence on the past is not uniform. The analysis of the discrete-time formulations of these models would be at the very least an extremely formidable project, but we determine the asymptotic growth rates of their means and higher moments with relative ease.

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41

Lokk, Katrin, and Kalev Pärna. "On risk processes with double barriers." Acta et Commentationes Universitatis Tartuensis de Mathematica 8 (December 31, 2004): 187–94. http://dx.doi.org/10.12697/acutm.2004.08.14.

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We consider risk processes with two barriers. The risk process starts with an initial capital u>0 and the two barriers are set at 0 and v(>u). We are interested in finding the probability φ(u,v) that the risk process hits the upper barrier v before 0. Both cases of positive and negative relative safety loading are considered. Explicit formulae for φ(u,v) are obtained in the case of positive safety loading and in a special case of negative safety loading when the claims are exponentially distributed. For the general case of negative safety loading an integral equation is derived for φ(u,v), similar to the classical result for the case of a single barrier at 0.

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42

Gautheron, Cécile, Mathias Hueck, Sébastien Ternois, Beatrix Heller, Stéphane Schwartz, Philippe Sarda, and Laurent Tassan-Got. "Investigating the Shallow to Mid-Depth (>100–300 °C) Continental Crust Evolution with (U-Th)/He Thermochronology: A Review." Minerals 12, no. 5 (April 29, 2022): 563. http://dx.doi.org/10.3390/min12050563.

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Quantifying geological processes has greatly benefited from the development and use of thermochronometric methods over the last fifty years. Among them is the (U-Th)/He dating method, which is based on the production and retention, within a crystal structure, of radiogenic 4He atoms associated with the alpha decay of U, Th and Sm nuclei. While apatite has been the main target of (U-Th)/He studies focusing on exhumation and burial processes in the upper levels of the continental crust (~50–120 °C), the development of (U-Th)/He methods for typical phases of igneous and metamorphic rocks (e.g., zircon and titanite) or mafic and ultramafic rocks (e.g., magnetite) over the last two decades has opened up a myriad of geological applications at higher temperatures (>100–300 °C). Thanks to the understanding of the role of radiation damage in He diffusion and retention for U-Th-poor and rich mineral phases, the application of (U-Th)/He thermochronometry to exhumation processes and continental evolution through deep time is now mainstream. This contribution reviews the (U-Th)/He thermochronometer principle and the influence of radiation damage in modifying the diffusion behavior. It presents applications of (U-Th)/He dating to problems in tectonic and surface processes at shallow to middle crustal depths (>100–300 °C). New and promising applications using a combination of methods will stimulate a research avenue in the future.

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43

Matsak, I. "ON EXTREME VALUES OF BIRTH AND DEATH PROCESSES." Bukovinian Mathematical Journal 9, no. 1 (2021): 237–49. http://dx.doi.org/10.31861/bmj2021.01.20.

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We establish the convergence rate to exponential distribution in a limit theorem for extreme values of birth and death processes. Some applications of this result are given to processes specifying queue length.). We establish uniform estimates for the convergence rate in the exponential distribution in a limit theorem for extreme values of birth and death processes. This topic is closely related to the problem on the time of ﬁrst intersection of some level u by a regenerating process. Of course, we assume that both time t and level u grow inﬁnitely. The proof of our main result is based on an important estimate for general regenerating processes. Investigations of the kind are needed in diﬀerent ﬁelds: mathematical theory of reliability, queueing theory, some statistical problems in physics. We also provide with examples of applications of our results to extremal queueing problems M/M/s. In particular case of queueing M/M/1, we show that the obtained estimates have the right order with respect to the probability q(u) of the exceeding of a level u at one regeneration cycle, that is, only improvement of the corresponding constants is possible.

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44

Çömez, Doğan. "An Ergodic Theorem for Multidimensional Superadditive Processes." Canadian Journal of Mathematics 37, no. 4 (August 1, 1985): 612–34. http://dx.doi.org/10.4153/cjm-1985-032-5.

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The ergodic theorem for multidimensional strongly subadditive processes relative to a semigroup induced by a measure preserving point transformation on X was proved by R. T. Smythe [18]. His results have been generalized by M. A. Akçoğlu and U. Krengel [4] to the continuous parameter case. The definition of superadditivity they used is stronger than Smythe's but weaker than strong superadditivity. R. Emilion and B. Hachem [10] extended this result to strongly superadditive processes relative to a semigroup generated by a pair of commuting Markovian operators which are also L∞-contractions. The basic tool in the proof is a technique which may be referred to as “reduction of dimension“ and they used a version of it due to A. Brunei [6].The purpose of this paper is to show that if F = {F(uv)}u>0 is a bounded strongly superadditive process with respect to a two-dimensional strongly continuous Markovian semigroup of operators on L1, then u-2F(uu) converges a.e. as u → ∞.

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45

Ji, Lanpeng, and Xiaofan Peng. "Extrema of multi-dimensional Gaussian processes over random intervals." Journal of Applied Probability 59, no. 1 (February 28, 2022): 81–104. http://dx.doi.org/10.1017/jpr.2021.37.

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AbstractThis paper studies the joint tail asymptotics of extrema of the multi-dimensional Gaussian process over random intervals defined as $P(u)\;:\!=\; \mathbb{P}\{\cap_{i=1}^n (\sup_{t\in[0,\mathcal{T}_i]} ( X_{i}(t) +c_i t )>a_i u )\}$ , $u\rightarrow\infty$ , where $X_i(t)$ , $t\ge0$ , $i=1,2,\ldots,n$ , are independent centered Gaussian processes with stationary increments, $\boldsymbol{\mathcal{T}}=(\mathcal{T}_1, \ldots, \mathcal{T}_n)$ is a regularly varying random vector with positive components, which is independent of the Gaussian processes, and $c_i\in \mathbb{R}$ , $a_i>0$ , $i=1,2,\ldots,n$ . Our result shows that the structure of the asymptotics of P(u) is determined by the signs of the drifts $c_i$ . We also discuss a relevant multi-dimensional regenerative model and derive the corresponding ruin probability.

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46

Sherman, Robert P. "U-Processes in the Analysis of a Generalized Semiparametric Regression Estimator." Econometric Theory 10, no. 2 (June 1994): 372–95. http://dx.doi.org/10.1017/s0266466600008458.

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We prove -consistency and asymptotic normality of a generalized semiparametric regression estimator that includes as special cases Ichimura's semiparametric least-squares estimator for single index models, and the estimator of Klein and Spady for the binary choice regression model. Two function expansions reveal a type of U-process structure in the criterion function; then new U-process maximal inequalities are applied to establish the requisite stochastic equicontinuity condition. This method of proof avoids much of the technical detail required by more traditional methods of analysis. The general framework suggests other -consistent and asymptotically normal estimators.

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47

Schneemeier, Wilhelm. "Weak Convergence and Glivenko-Cantelli Results for Weighted Empirical $U$-Processes." Annals of Probability 21, no. 2 (April 1993): 1170–84. http://dx.doi.org/10.1214/aop/1176989287.

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48

Khashimov, Sh A. "Limiting Behavior of Generalized U-Statistics of Weakly Dependent Stationary Processes." Theory of Probability & Its Applications 37, no. 1 (January 1993): 148–50. http://dx.doi.org/10.1137/1137034.

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49

Goldman, I. B., and A. Krajewski. "An Ultra‐violet (U‐V) Conformal Coating System: Materials and Processes." Circuit World 12, no. 1 (April 1985): 4–7. http://dx.doi.org/10.1108/eb043774.

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50

Gombay, Edit, and Lajos Horváth. "Rates of convergence for U-statistic processes and their bootstrapped versions." Journal of Statistical Planning and Inference 102, no. 2 (April 2002): 247–72. http://dx.doi.org/10.1016/s0378-3758(01)00085-4.

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