Related papers: Some limits to nonparametric estimation for ergodi…
We derive consistency and asymptotic normality results for quasi-maximum likelihood methods for drift parameters of ergodic stochastic processes observed in discrete time in an underlying continuous-time setting. The special feature of our…
Completely nonparametric transformation models with heteroscedastic errors are considered. Despite their flexibility, such models have rarely been used so far, since estimators of the model components have been missing and even…
Weighted estimators are commonly used for estimating exposure effects in observational settings to establish causal relations. These estimators have a long history of development when the exposure of interest is binary and where the weights…
We define a notion of entropy for an infinite family $\mathcal{C}$ of measurable sets in a probability space. We show that the mean ergodic theorem holds uniformly for $\mathcal{C}$ under every ergodic transformation if and only if…
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…
In this paper we consider the estimation of unknown parameters in Bayesian inverse problems. In most cases of practical interest, there are several barriers to performing such estimation, This includes a numerical approximation of a…
A residual-based empirical distribution function is proposed to estimate the distribution function of the errors of a heteroskedastic nonparametric regression with responses missing at random based on completely observed data, and this…
In a recent paper Birke and Bissantz (2008) considered the problem of nonparametric estimation in inverse regression models with convolution-type operators. For multivariate predictors nonparametric methods suffer from the curse of…
We consider the extreme value statistics of centrally-biased random walks with asymptotically-zero drift in the ergodic regime. We fully characterize the asymptotic distribution of the maximum for this class of Markov chains lacking…
A set of probabilistic predictions is well calibrated if the events that are predicted to occur with probability p do in fact occur about p fraction of the time. Well calibrated predictions are particularly important when machine learning…
A problem of goodness-of-fit test for ergodic diffusion processes is presented. In the null hypothesis the drift of the diffusion is supposed to be in a parametric form with unknown shift parameter. Two Cramer-Von Mises type test statistics…
We construct an efficient estimator for the error distribution function of the nonparametric regression model Y = r(Z) + e. Our estimator is a kernel smoothed empirical distribution function based on residuals from an under-smoothed local…
Parametric estimation for diffusion processes is considered for high frequency observations over a fixed time interval. The processes solve stochastic differential equations with an unknown parameter in the diffusion coefficient. We find…
We derive an asymptotic theory of nonparametric estimation for a time series regression model $Z_t=f(X_t)+W_t$, where \ensuremath\{X_t\} and \ensuremath\{Z_t\} are observed nonstationary processes and $\{W_t\}$ is an unobserved stationary…
We study the problem of finding an universal estimation scheme $h_n:\mathbb{R}^n\to \mathbb{R}$, $n=1,2,...$ which will satisfy \lim_{t\rightarrow\infty}{\frac{1}{t}}\sum_{i=1}^t|h_ i(X_0,X_1,...,X_{i-1})-E(X_i|X_0,X_1,...,X_{i-1})|^p=0…
We research adaptive maximum likelihood-type estimation for an ergodic diffusion process where the observation is contaminated by noise. This methodology leads to the asymptotic independence of the estimators for the variance of observation…
We propose a novel Bayesian approach to solve stochastic optimization problems that involve finding extrema of noisy, nonlinear functions. Previous work has focused on representing possible functions explicitly, which leads to a two-step…
We construct ergodic probability measures with infinite metric entropy for typical continuous maps and homeomorphisms on compact manifolds. We also construct sequences of such measures that converge to a zero-entropy measure.
The negative binomial distribution has been widely used as a more flexible model than the Poisson distribution for count data. However, when the true data-generating process is Poisson, it is often challenging to distinguish it from a…
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…