A new method is proposed for estimating derivatives of a nonparametric regression function. By applying Taylor expansion technique to a derived symmetric difference sequence, we obtain a sequence of approximate linear regression representation in which the derivative is just the intercept term. Using locally weighted least squares, we estimate the derivative in the linear regression model. The ...

Using the technique of smoothed perturbation analysis, we consider steady-state performance measures for continuous-time Markov chains and derive a derivative estimator that can be estimated from a single sample path of the chain under consideration. The estimator is applicable to multi-class queueing networks, for which previous in nitesimal perturbation analysis estimators failed. A simple mu...

Estimating the frequency of sinusoidal components is the first part of the sinusoidal analysis chain. Among numerous frequency estimators presented in the literature, we propose to study an estimator proposed in [1] known as the derivative algorithm. Thanks to a trigonometric interpretation of this frequency estimator, we are able to propose a new estimator which improves estimation performance...

In volume rendering gradient information is used to classify and color samples along a ray. In this paper we present an analysis of the theoretically ideal gradient estimator and compare some commonly used gradient estimators with the ideal estimator. A new method is presented to calculate the gradient on an arbitrary position, using the derivative of the interpolation lter as the basis for the...

Optical flow estimation can be formulated as two regression stages, derivative estimation and optical flow constraints (OFC) solving. Traditional approaches use LeastSquares at both stages and are sensitive to assumption violations. To improve estimation accuracy especially near motion boundaries, we use a Least Trimmed Squares (LTS) estimator to solve the OFC, obtaining a confidence measure fo...

We study the convergence of Monte Carlo estimators of derivatives when the transition density of the underlying state variables is unknown. Three types of estimators are compared. These are respectively based on Malliavin derivatives, on the covariation with the driving Wiener process, and on finite difference approximations of the derivative. We analyze two different estimators based on Mallia...

We consider parallel global optimization of derivative-free expensive-to-evaluate functions, and proposes an efficient method based on stochastic approximation for implementing a conceptual Bayesian optimization algorithm proposed by [10]. To accomplish this, we use infinitessimal perturbation analysis (IPA) to construct a stochastic gradient estimator and show that this estimator is unbiased.

We construct a density estimator and an estimator of the distribution function in the uniform deconvolution model. The estimators are based on inversion formulas and kernel estimators of the density of the observations and its derivative. Asymptotic normality and the asymptotic biases are derived. AMS classification: primary 62G05; secondary 62E20, 62G07, 62G20

The mean time to failure (MTTF) of a Markovian system can be expressed as a ratio of two expectations. For highly reliable Markovian systems, the resulting ratio formula consists of one expectation that cannot be estimated with bounded relative error when using standard simulation, while the other, which we call a non-rare expectation, can be estimated with bounded relative error. We show that ...