Related papers: Optimum thresholding using mean and conditional me…
Statistical inference for stochastic processes based on high-frequency observations has been an active research area for more than two decades. One of the most well-known and widely studied problems has been the estimation of the quadratic…
Recently a considerable interest has been paid on the estimation problem of the realized volatility and covolatility by using high-frequency data of financial price processes in financial econometrics. Threshold estimation is one of the…
This paper proposes and analyzes fully data driven methods for inference about the mean function of a stochastic process from a sample of independent trajectories of the process, observed at discrete time points and corrupted by additive…
We propose new nonparametric estimators of the integrated volatility of an It\^{o} semimartingale observed at discrete times on a fixed time interval with mesh of the observation grid shrinking to zero. The proposed estimators achieve the…
Statistical inference for stochastic processes based on high-frequency observations has been an active research area for more than a decade. One of the most well-known and widely studied problems is that of estimation of the quadratic…
Quantum mechanics for many-body systems may be reduced to the evaluation of integrals in 3N dimensions using Monte-Carlo, providing the Quantum Monte Carlo ab initio methods. Here we limit ourselves to expectation values for trial…
The problem of integrated volatility estimation for the solution X of a stochastic differential equation with L{\'e}vy-type jumps is considered under discrete high-frequency observations in both short and long time horizon. We provide an…
Despite the simplicity and intuitive interpretation of Minimum Mean Squared Error (MMSE) estimators, their effectiveness in certain scenarios is questionable. Indeed, minimizing squared errors on average does not provide any form of…
An approximate mean square error (MSE) expression for the performance analysis of implicitly defined estimators of non-random parameters is proposed. An implicitly defined estimator (IDE) declares the minimizer/maximizer of a selected…
We consider a stochastic process driven by a diffusion and jumps. We devise a technique, which is based on a discrete record of observations, for identifying the times when jumps larger than a suitably defined threshold occurred. The…
We find the variance-optimal equivalent martingale measure when multivariate assets are modeled by a regime-switching geometric Brownian motion, and the regimes are represented by a homogeneous continuous time Markov chain. Under this new…
We investigate the problem of representing information measures in terms of the moments of the underlying random variables. First, we derive polynomial approximations of the conditional expectation operator. We then apply these…
For a semi-martingale $X_t$, which forms a stochastic boundary, a rate-optimal estimator for its quadratic variation $\langle X, X \rangle_t$ is constructed based on observations in the vicinity of $X_t$. The problem is embedded in a…
We propose two nonparametric tests for investigating the pathwise properties of a signal modeled as the sum of a L\'{e}vy process and a Brownian semimartingale. Using a nonparametric threshold estimator for the continuous component of the…
We investigate the theoretical foundations of a recently introduced entropy-based formulation of weighted least squares for the approximation of overdetermined linear systems, motivated by robust data fitting in the presence of sparse gross…
We propose a new least-squares Monte Carlo algorithm for the approximation of conditional expectations in the presence of stochastic derivative weights. The algorithm can serve as a building block for solving dynamic programming equations,…
A lower bound on the minimum mean-squared error (MSE) in a Bayesian estimation problem is proposed in this paper. This bound utilizes a well-known connection to the deterministic estimation setting. Using the prior distribution, the bias…
We propose and study an asymptotically optimal Monte Carlo estimator for steady-state expectations of a d-dimensional reflected Brownian motion. Our estimator is asymptotically optimal in the sense that it requires $\tilde{O}(d)$ (up to…
Quantiles and expected shortfalls are usually used to measure risks of stochastic systems, which are often estimated by Monte Carlo methods. This paper focuses on the use of quasi-Monte Carlo (QMC) method, whose convergence rate is…
Threshold and ambiguity phenomena are studied in Part 1 of this work where approximations for the mean-squared-error (MSE) of the maximum likelihood estimator are proposed using the method of interval estimation (MIE), and where approximate…