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In this paper, we consider the robust adaptive non parametric estimation problem for the drift coefficient in diffusion processes. An adaptive model selection procedure, based on the improved weighted least square estimates, is proposed.…

Statistics Theory · Mathematics 2019-09-24 Evgeny Pchelintsev , Svyatoslav Perelevskiy , Irina Makarova

The global estimation problem of the drift function is considered for a large class of ergodic diffusion processes. The unknown drift $S(\cdot)$ is supposed to belong to a nonparametric class of smooth functions of order $k\geq1$, but the…

Statistics Theory · Mathematics 2007-06-13 Arnak Dalalyan

In this paper, we consider parameter estimation and quasi-likelihood ratio tests for multidimensional jump-diffusion processes defined by stochastic differential equations. In general, simultaneous estimation faces challenges such as an…

Statistics Theory · Mathematics 2025-02-25 Hiromasa Nishikawa , Tetsuya Kawai , Masayuki Uchida

In this paper, we investigate the adequacy testing problem of high-dimensional factor-augmented regression model. Existing test procedures perform not well under dense alternatives. To address this critical issue, we introduce a novel…

Methodology · Statistics 2025-04-04 Yanmei Shi , Leheng Cai , Xu Guo , Shurong Zheng

We propose a new statistical observation scheme of diffusion processes named convolutional observation, where it is possible to deal with smoother observation than ordinary diffusion processes by considering convolution of diffusion…

Statistics Theory · Mathematics 2020-10-28 Shogo H Nakakita , Masayuki Uchida

We investigate three different methods for systematically approximating the diffusion coefficient of a deterministic random walk on the line which contains dynamical correlations that change irregularly under parameter variation. Capturing…

Mathematical Physics · Physics 2015-05-28 Georgie Knight , Rainer Klages

In this paper, we address a model selection problem for ergodic jump diffusion processes based on high-frequency samples. We evaluate the expected genuine log-likelihood function and derive an Akaike-type information criterion based on the…

Statistics Theory · Mathematics 2025-08-11 Yuma Uehara

A number of discrete time, finite population size models in genetics describing the dynamics of allele frequencies are known to converge (subject to suitable scaling) to a diffusion process in the infinite population limit, termed the…

Probability · Mathematics 2021-09-14 Jaromir Sant , Paul A. Jenkins , Jere Koskela , Dario Spano

Statistical inference for stochastic processes has advanced significantly due to applications in diverse fields, but challenges remain in high-dimensional settings where parameters are allowed to grow with the sample size. This paper…

Statistics Theory · Mathematics 2025-01-29 Dmytro Marushkevych , Francisco Pina , Mark Podolskij

We address the asymptotic and approximate distributions of a large class of test statistics with quadratic forms used in association studies. The statistics of interest do not necessarily follow a chi-square distribution and take the…

Applications · Statistics 2009-09-24 Liping Tong , Jie Yang , Richard S. Cooper

In this article, we consider a jump diffusion process (X_t), with drift function b, diffusion coefficient sigma and jump coefficient xi^{2}. This process is observed at discrete times t=0,Delta,...,nDelta. The sampling interval Delta tends…

Statistics Theory · Mathematics 2013-11-27 Emeline Schmisser

We consider the solution X = (Xt) t$\ge$0 of a multivariate stochastic differential equation with Levy-type jumps and with unique invariant probability measure with density $\mu$. We assume that a continuous record of observations X T =…

Statistics Theory · Mathematics 2020-01-22 Chiara Amorino , Arnaud Gloter

We consider a classic two-state switching diffusion model from a single-particle tracking perspective. The mean and the variance of the time-averaged mean square displacement (TAMSD) are computed exactly. When the measurement time (i.e.,…

Statistical Mechanics · Physics 2019-11-05 Denis S. Grebenkov

We consider the problem of the estimation of the invariant distribution function of an ergodic diffusion process when the drift coefficient is unknown. The empirical distribution function is a natural estimator which is unbiased, uniformly…

Statistics Theory · Mathematics 2007-06-13 Ilia Negri

Likelihood ratio tests are widely used in high-energy physics, where the test statistic is usually assumed to follow a chi-squared distribution with a number of degrees of freedom specified by Wilks' theorem. This assumption breaks down…

High Energy Physics - Experiment · Physics 2025-12-23 Clara Bertinelli Salucci , Hedvig Borgen Reiersrud , A. L. Read , Anders Kvellestad , Riccardo De Bin

We build on recent works on Stein's method for functions of multivariate normal random variables to derive bounds for the rate of convergence of some asymptotically chi-square distributed statistics. We obtain some general bounds and…

Probability · Mathematics 2023-05-15 Robert E. Gaunt , Gesine Reinert

For model-specification purpose, we study asymptotic behavior of the marginal quasi-log likelihood associated with a family of locally asymptotically quadratic (LAQ) statistical experiments. Our result entails a far-reaching extension of…

Statistics Theory · Mathematics 2016-09-26 Shoichi Eguchi , Hiroki Masuda

We consider triangular arrays of Markov chains that converge weakly to a diffusion process. Edgeworth type expansions of third order for transition densities are proved. This is done for time horizons that converge to 0. For this purpose we…

Probability · Mathematics 2007-06-13 Valentin Konakov , Enno Mammen

In testing of hypothesis the robustness of the tests is an important concern. Generally, the maximum likelihood based tests are most efficient under standard regularity conditions, but they are highly non-robust even under small deviations…

Methodology · Statistics 2018-05-01 Ayanendranath Basu , Abhijit Mandal , Nirian Martin , Leandro Pardo

A truncated sequential procedure is constructed for estimating the drift coefficient at a given state point based on discrete data of ergodic diffusion process. A nonasymptotic upper bound is obtained for a pointwise absolute error risk.…

Statistics Theory · Mathematics 2015-09-21 L. I. Galtchouk , S. M. Pergamenshchikov