Bernoulli最新文献_第10页

Martingale Wasserstein inequality for probability measures in the convex order 凸阶概率测度的Martingale-Wasserstein不等式

IF 1.5 2区数学

Bernoulli Pub Date : 2020-11-23 DOI: 10.3150/21-bej1368

B. Jourdain, W. Margheriti

引用次数: 5

Concentration inequality for U-statistics of order two for uniformly ergodic Markov chains 一致遍历马尔可夫链二阶u统计量的浓度不等式

IF 1.5 2区数学

Bernoulli Pub Date : 2020-11-20 DOI: 10.3150/22-bej1485

Quentin Duchemin, Y. D. Castro, C. Lacour

{"title":"Concentration inequality for U-statistics of order two for uniformly ergodic Markov chains","authors":"Quentin Duchemin, Y. D. Castro, C. Lacour","doi":"10.3150/22-bej1485","DOIUrl":"https://doi.org/10.3150/22-bej1485","url":null,"abstract":"We prove a new concentration inequality for U-statistics of order two for uniformly ergodic Markov chains. Working with bounded π-canonical kernels, we show that we can recover the convergence rate of Arcones and Gine (1993) who proved a concentration result for U-statistics of independent random variables and canonical kernels. Our proof relies on an inductive analysis where we use martingale techniques, uniform ergodicity, Nummelin splitting and Bernstein's type inequality where the spectral gap of the chain emerges. Our result allows us to conduct three applications. First, we establish a new exponential inequality for the estimation of spectra of trace class integral operators with MCMC methods. The novelty is that this result holds for kernels with positive and negative eigenvalues, which is new as far as we know. In addition, we investigate generalization performance of online algorithms working with pairwise loss functions and Markov chain samples. We provide an online-to-batch conversion result by showing how we can extract a low risk hypothesis from the sequence of hypotheses generated by any online learner. We finally give a non-asymptotic analysis of a goodness-of-fit test on the density of the invariant measure of a Markov chain. We identify the classes of alternatives over which our test based on the L2 distance has a prescribed power.","PeriodicalId":55387,"journal":{"name":"Bernoulli","volume":" ","pages":""},"PeriodicalIF":1.5,"publicationDate":"2020-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46570568","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 4

Defective Galton-Watson processes in a varying environment 不同环境下高尔顿-沃森过程的缺陷

IF 1.5 2区数学

Bernoulli Pub Date : 2020-11-17 DOI: 10.3150/21-bej1393

G. Kersting, C. Minuesa

引用次数: 1

Nonparametric Bayesian volatility estimation for gamma-driven stochastic differential equations 伽玛驱动随机微分方程的非参数贝叶斯波动性估计

IF 1.5 2区数学

Bernoulli Pub Date : 2020-11-16 DOI: 10.3150/21-bej1413

D. Belomestny, S. Gugushvili, Moritz Schauer, P. Spreij

引用次数: 3

Mixing properties of non-stationary INGARCH(1,1) processes 非平稳INGARCH（1,1）过程的混合性质

IF 1.5 2区数学

Bernoulli Pub Date : 2020-11-11 DOI: 10.3150/21-bej1362

P. Doukhan, Anne Leucht, Michael H. Neumann

引用次数: 10

Rank-based testing for semiparametric VAR models: A measure transportation approach 半参数VAR模型的秩检验：一种度量运输方法

IF 1.5 2区数学

Bernoulli Pub Date : 2020-11-11 DOI: 10.3150/21-bej1456

M. Hallin, D. L. Vecchia, Han Liu

{"title":"Rank-based testing for semiparametric VAR models: A measure transportation approach","authors":"M. Hallin, D. L. Vecchia, Han Liu","doi":"10.3150/21-bej1456","DOIUrl":"https://doi.org/10.3150/21-bej1456","url":null,"abstract":"We develop a class of tests for semiparametric vector autoregressive (VAR) models with unspecified innovation densities, based on the recent measure-transportation-based concepts of multivariate center-outward ranks and signs. We show that these concepts, combined with Le Cam's asymptotic theory of statistical experiments, yield novel testing procedures, which (a) are valid under a broad class of innovation densities (possibly non-elliptical, skewed, and/or with infinite moments), (b) are optimal (locally asymptotically maximin or most stringent) at selected ones, and (c) are robust against additive outliers. In order to do so, we establish a Hajek asymptotic representation result, of independent interest, for a general class of center-outward rank-based serial statistics. As an illustration, we consider the problems of testing the absence of serial correlation in multiple-output and possibly non-linear regression (an extension of the classical Durbin-Watson problem) and the sequential identification of the order p of a vector autoregressive (VAR(p)) model. A Monte Carlo comparative study of our tests and their routinely-applied Gaussian competitors demonstrates the benefits (in terms of size, power, and robustness) of our methodology; these benefits are particularly significant in the presence of asymmetric and leptokurtic innovation densities. A real data application concludes the paper.","PeriodicalId":55387,"journal":{"name":"Bernoulli","volume":" ","pages":""},"PeriodicalIF":1.5,"publicationDate":"2020-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49488933","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 16

Testing and inference for fixed times of discontinuity in semimartingales 半鞅不连续固定时间的检验与推理

IF 1.5 2区数学

Bernoulli Pub Date : 2020-11-02 DOI: 10.3150/20-bej1211

V. Todorov

{"title":"Testing and inference for fixed times of discontinuity in semimartingales","authors":"V. Todorov","doi":"10.3150/20-bej1211","DOIUrl":"https://doi.org/10.3150/20-bej1211","url":null,"abstract":"We develop a nonparametric test for deciding whether a semimartingale process, modeling an asset price, contains a fixed time of discontinuity, i.e., a positive probability of a jump, at a given point in time, and we further propose a rate-optimal estimator of the jump distribution when this is the case. Itô semimartingales used commonly in applied work have absolutely continuous in time, with respect to Lebesgue measure, jump compensators, and this rules out fixed times of discontinuity in their paths. However, certain phenomena, such as scheduled economic announcements in finance, make the existence of such discontinuities a possibility. The inference in the paper is based on noisy observations of options written on the asset with different strikes and two different expiration dates. The asymptotics is joint in which the times to maturity of the options shrink to zero and the number of observed options increases to infinity. The test is based on estimates of the characteristic function of the increments of the semimartingale, constructed from the option data, and the fact that the asymptotic limit of the increments and their characteristic functions is different with and without fixed time of discontinuity. The limit distribution of the test statistic is derived and feasible inference is developed on the basis of wild bootstrap type techniques. A Monte Carlo and an empirical illustration show the applicability of the developed inference procedures.","PeriodicalId":55387,"journal":{"name":"Bernoulli","volume":"26 1","pages":"2907-2948"},"PeriodicalIF":1.5,"publicationDate":"2020-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45406255","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 2

Deviation inequalities for random polytopes in arbitrary convex bodies 任意凸体中随机多面体的偏差不等式

IF 1.5 2区数学

Bernoulli Pub Date : 2020-11-01 DOI: 10.3150/19-bej1164

Victor-Emmanuel Brunel

引用次数: 2

Asymptotic properties of penalized splines for functional data 函数数据惩罚样条的渐近性质

IF 1.5 2区数学

Bernoulli Pub Date : 2020-11-01 DOI: 10.3150/20-bej1209

Luo Xiao

引用次数: 11

Design of c-optimal experiments for high-dimensional linear models 高维线性模型的c-最优实验设计