Limit theorems for the site frequency spectrum of neutral mutations in an exponentially growing population [0.03%]
中性突变在指数增长种群中的位点频率谱的极限定理
Einar Bjarki Gunnarsson,Kevin Leder,Xuanming Zhang
Einar Bjarki Gunnarsson
The site frequency spectrum (SFS) is a widely used summary statistic of genomic data. Motivated by recent evidence for the role of neutral evolution in cancer, we investigate the SFS of neutral mutations in an exponentially growing populati...
Jianqing Fan,Yongyi Guo,Bai Jiang
Jianqing Fan
High-dimensional linear regression has been intensively studied in the community of statistics in the last two decades. For the convenience of theoretical analyses, classical methods usually assume independent observations and sub-Gaussian-...
Perturbation bounds for Monte Carlo within Metropolis via restricted approximations [0.03%]
限制逼近下的蒙特卡洛伴随 Métropicsis 方法的摄动界值分析
Felipe Medina-Aguayo,Daniel Rudolf,Nikolaus Schweizer
Felipe Medina-Aguayo
The Monte Carlo within Metropolis (MCwM) algorithm, interpreted as a perturbed Metropolis-Hastings (MH) algorithm, provides an approach for approximate sampling when the target distribution is intractable. Assuming the unperturbed Markov ch...
MARKOV PROCESSES CONDITIONED ON THEIR LOCATION AT LARGE EXPONENTIAL TIMES [0.03%]
在大型指数时间下对马尔可夫过程进行条件设置以确定其位置
Steven N Evans,Alexandru Hening
Steven N Evans
Suppose that (Xt ) t ≥0 is a one-dimensional Brownian motion with negative drift -μ. It is possible to make sense of conditioning this process to be in the state 0 at an independent exponential random time and if we kill the conditioned p...
Mathias Beiglböck,Walter Schachermayer,Bezirgen Veliyev
Mathias Beiglböck
Every submartingale S of class D has a unique Doob-Meyer decomposition S = M + A , where M is a martingale and A is a predictable increasing process starting at 0. We provide a short proof of the Doob-Meyer decomposition theorem. Several pr...
N N Leonenko,I Papić,A Sikorskii et al.
N N Leonenko et al.
We define heavy-tailed fractional reciprocal gamma and Fisher-Snedecor diffusions by a non-Markovian time change in the corresponding Pearson diffusions. Pearson diffusions are governed by the backward Kolmogorov equations with space-varyin...
DOOB-MARTIN COMPACTIFICATION OF A MARKOV CHAIN FOR GROWING RANDOM WORDS SEQUENTIALLY [0.03%]
逐个增长的随机单词的马尔可夫链的DOOB-MATRIN紧化
Hye Soo Choi,Steven N Evans
Hye Soo Choi
We consider a Markov chain that iteratively generates a sequence of random finite words in such a way that the nth word is uniformly distributed over the set of words of length 2n in which n letters are a and n letters are b: at each step a...
James Robins,Lingling Li,Eric Tchetgen et al.
James Robins et al.
We prove conditional asymptotic normality of a class of quadratic U-statistics that are dominated by their degenerate second order part and have kernels that change with the number of observations. These statistics arise in the construction...
Finite sampling inequalities: an application to two-sample Kolmogorov-Smirnov statistics [0.03%]
有限采样不等式及其在两样本Kolmogorov-Smirnov统计中的应用
Evan Greene,Jon A Wellner
Evan Greene
We review a finite-sampling exponential bound due to Serfling and discuss related exponential bounds for the hypergeometric distribution. We then discuss how such bounds motivate some new results for two-sample empirical processes. Our deve...
Lutz Dümbgen,Jon A Wellner,Malcolm Wolff
Lutz Dümbgen
In this note we prove the following law of the iterated logarithm for the Grenander estimator of a monotone decreasing density: If f(t0) > 0, f'(t0)