Related papers: Sharp adaptive nonparametric testing for constant …
Consider discrete time observations (X_{\ell\delta})_{1\leq \ell \leq n+1}$ of the process $X$ satisfying $dX_t= \sqrt{V_t} dB_t$, with $V_t$ a one-dimensional positive diffusion process independent of the Brownian motion $B$. For both the…
We propose a novel non-parametric adaptive anomaly detection algorithm for high dimensional data based on score functions derived from nearest neighbor graphs on $n$-point nominal data. Anomalies are declared whenever the score of a test…
In a wide range of applications, the stochastic properties of the observed time series change over time. The changes often occur gradually rather than abruptly: the properties are (approximately) constant for some time and then slowly start…
We consider the problem of the construction of the Goodness-of-Fit test in the case of continuous time observations of a diffusion process with small noise. The null hypothesis is parametric and we use a minimum distance estimator of the…
The local volatility model is a widely used for pricing and hedging financial derivatives. While its main appeal is its capability of reproducing any given surface of observed option prices---it provides a perfect fit---the essential…
In the present paper we consider Laplace deconvolution for discrete noisy data observed on the interval whose length may increase with a sample size. Although this problem arises in a variety of applications, to the best of our knowledge,…
We consider covariance parameter estimation for Gaussian processes with functional inputs. From an increasing-domain asymptotics perspective, we prove the asymptotic consistency and normality of the maximum likelihood estimator. We extend…
We consider the problem of testing a particular type of composite null hypothesis under a nonparametric multivariate regression model. For a given quadratic functional $Q$, the null hypothesis states that the regression function $f$…
We consider testing for presence of a signal in Gaussian white noise with intensity 1/sqrt(n), when the alternatives are given by smoothness ellipsoids with an L2-ball of (squared) radius rho removed. It is known that, for a fixed Sobolev…
We study nonparametric density estimation in non-stationary drift settings. Given a sequence of independent samples taken from a distribution that gradually changes in time, the goal is to compute the best estimate for the current…
We consider a stochastic differential equation of the form \[dX_t=\theta a(t,X_t)\,dt+\sigma_1(t,X_t)\sigma_2(t,Y_t)\,dW_t\] with multiplicative stochastic volatility, where $Y$ is some adapted stochastic process. We prove…
We consider an unknown response function $f$ defined on $\Delta=[0,1]^d$, $1\le d\le\infty$, taken at $n$ random uniform design points and observed with Gaussian noise of known variance. Given a positive sequence $r_n\to 0$ as $n\to\infty$…
Motivated by models for multiway comparison data, we consider the problem of estimating a coordinate-wise isotonic function on the domain $[0, 1]^d$ from noisy observations collected on a uniform lattice, but where the design points have…
We consider the detection problem of a two-dimensional function from noisy observations of its integrals over lines. We study both rate and sharp asymptotics for the error probabilities in the minimax setup. By construction, the derived…
We study goodness-of-fit testing for non-causal autoregressive time series with non-Gaussian stable noise. To model time series exhibiting sharp spikes or occasional bursts of outlying observations, the exponent of the non-Gaussian stable…
Computational level explanations based on optimal feedback control with signal-dependent noise have been able to account for a vast array of phenomena in human sensorimotor behavior. However, commonly a cost function needs to be assumed for…
In this paper we propose a new test for the hypothesis of a constant coefficient of variation in the common nonparametric regression model. The test is based on an estimate of the $L^2$-distance between the square of the regression function…
In this paper, we consider adaptive estimation of an unknown planar compact, convex set from noisy measurements of its support function on a uniform grid. Both the problem of estimating the support function at a point and that of estimating…
We consider a nonparametric goodness of fit test problem for the drift coefficient of one-dimensional small diffusions. Our test is based on discrete observation of the processes, and the diffusion coefficient is a nuisance function which…
Robust uncertainty quantification is increasingly important in modern data analysis and is often formalized under Huber's model, which allows an $\varepsilon$-fraction of arbitrary corruptions. In many experimental sciences, however, the…