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Given a sample from a discretely observed compound Poisson process, we consider estimation of the density of the jump sizes. We propose a kernel type nonparametric density estimator and study its asymptotic properties. An order bound for…

Statistics Theory · Mathematics 2007-09-14 Bert van Es , Shota Gugushvili , Peter Spreij

The basic model for high-frequency data in finance is considered, where an efficient price process is observed under microstructure noise. It is shown that this nonparametric model is in Le Cam's sense asymptotically equivalent to a…

Statistics Theory · Mathematics 2010-01-25 Markus Reiß

We consider a nonparametric model $\mathcal{E}^{n},$ generated by independent observations $X_{i},$ $i=1,...,n,$ with densities $p(x,\theta_{i}),$ $i=1,...,n,$ the parameters of which $\theta _{i}=f(i/n)\in \Theta $ are driven by the values…

Statistics Theory · Mathematics 2024-12-20 Ion Grama , Michael Nussbaum

Asymptotic local equivalence in the sense of Le Cam is established for inference on the drift in multidimensional ergodic diffusions and an accompanying sequence of Gaussian shift experiments. The nonparametric local neighbourhoods can be…

Statistics Theory · Mathematics 2012-08-20 Arnak Dalalyan , Markus Reiss

A compound Poisson process whose parameters are all unknown is observed at finitely many equispaced times. Nonparametric estimators of the jump and L\'evy distributions are proposed and functional central limit theorems using the uniform…

Statistics Theory · Mathematics 2017-02-06 Alberto J. Coca

Consider estimation of the regression function based on a model with equidistant design and measurement errors generated from a fractional Gaussian noise process. In previous literature, this model has been heuristically linked to an…

Statistics Theory · Mathematics 2014-12-02 Johannes Schmidt-Hieber

In this paper we study the asymptotics of linear regression in settings with non-Gaussian covariates where the covariates exhibit a linear dependency structure, departing from the standard assumption of independence. We model the covariates…

Machine Learning · Statistics 2024-12-10 Behrad Moniri , Hamed Hassani

This paper establishes the global asymptotic equivalence, in the sense of the Le Cam $\Delta$-distance, between scalar diffusion models with unknown drift function and small variance on the one side, and nonparametric autoregressive models…

Probability · Mathematics 2015-03-05 Ester Mariucci

We consider high-dimensional estimation problems where the number of parameters diverges with the sample size. General conditions are established for consistency, uniqueness, and asymptotic normality in both unpenalized and penalized…

Statistics Theory · Mathematics 2025-04-08 Jana Gauss , Thomas Nagler

In this paper we compare and contrast the behavior of the posterior predictive distribution to the risk of the maximum a posteriori estimator for the random features regression model in the overparameterized regime. We will focus on the…

Machine Learning · Statistics 2023-10-30 Youngsoo Baek , Samuel I. Berchuck , Sayan Mukherjee

We consider nonparametric statistical inference for L\'evy processes sampled irregularly, at low frequency. The estimation of the jump dynamics as well as the estimation of the distributional density are investigated. Non-asymptotic risk…

Statistics Theory · Mathematics 2015-11-23 Johanna Kappus

We study parametric inference for diffusion processes when observations occur nonsynchronously and are contaminated by market microstructure noise. We construct a quasi-likelihood function and study asymptotic mixed normality of…

Statistics Theory · Mathematics 2015-12-29 Teppei Ogihara

We investigate the significance of change-points within fully nonparametric regression contexts, with a particular focus on panel data where data generation processes vary across units, and error terms may display complex dependency…

Econometrics · Economics 2025-01-07 Likai Chen , Georg Keilbar , Liangjun Su , Weining Wang

We provide new asymptotic theory for kernel density estimators, when these are applied to autoregressive processes exhibiting moderate deviations from a unit root. This fills a gap in the existing literature, which has to date considered…

Statistics Theory · Mathematics 2019-08-19 James A. Duffy

This paper discusses infill asymptotics for logistic regression estimators for spatio-temporal point processes whose intensity functions are of log-linear form. We establish strong consistency and asymptotic normality for the parameters of…

Statistics Theory · Mathematics 2022-08-26 M. N. M. van Lieshout , C. Lu

We study nonasymptotic (finite-sample) confidence intervals for treatment effects in randomized experiments. In the existing literature, the effective sample sizes of nonasymptotic confidence intervals tend to be looser than the…

The estimation of the covariance structure from a discretely observed multivariate Gaussian process under asynchronicity and noise is analysed under high-frequency asymptotics. Asymptotic lower and upper bounds are established for a general…

Statistics Theory · Mathematics 2020-04-21 Sebastian Holtz

Given a sample from a discretely observed multidimensional compound Poisson process, we study the problem of nonparametric estimation of its jump size density $r_0$ and intensity $\lambda_0$. We take a nonparametric Bayesian approach to the…

Statistics Theory · Mathematics 2015-06-08 Shota Gugushvili , Frank van der Meulen , Peter Spreij

A model of Poissonian observation having a jump (change-point) in the intensity function is considered. Two cases are studied. The first one corresponds to the situation when the jump size converges to a non-zero limit, while in the second…

Statistics Theory · Mathematics 2015-02-25 Serguei Dachian , Lin Yang

Nonparametric density and regression estimators commonly depend on a bandwidth. The asymptotic properties of these estimators have been widely studied when bandwidths are nonstochastic. In practice, however, in order to improve finite…

Statistics Theory · Mathematics 2014-09-02 Carlos Martins-Filho , Paulo Saraiva