In mathematical modeling, determining most influential parameters on outputs is of major importance. Thus, sensitivity analysis of parameters plays an important role in model validation. We give detailed procedure of constructing a new derivative estimator for general performance measure in Gaussian systems. We will take advantage of using score function and measure-value derivative estimators ...

In various statistical model, such as density estimation and estimation of regression curves or hazard rates, monotonicity constraints can arise naturally. A frequently encountered problem in nonparametric statistics is to estimate a monotone density function f on a compact interval. A known estimator for density function of f under the restriction that f is decreasing, is Grenander estimator, ...

Suppose we have a system of independent Gaussian random variables Xi ∼ N (μ, σ2 i ), i ∈ 1, . . . , N in (Ω,F ,P). We can determine the derivative estimator of D(X; ·) w.r.t a parameter, σ, of a system L(X, ·) if on (Ω,F), D(X; ·), L(X; ·) is given by the expression ∂ ∂σEP[L(X;σ)] = EQ[D(X;σ)]. This thesis provides an analysis to Gaussian random variables w.r.t three types of unbiased derivativ...

We consider a block thresholding and vaguelet–wavelet approach to certain statistical linear inverse problems. Based on an oracle inequality, an adaptive block thresholding estimator for linear inverse problems is proposed and the asymptotic properties of the estimator are investigated. It is shown that the estimator enjoys a higher degree of adaptivity than the standard term-by-term thresholdi...

Estimation of density derivatives is a versatile tool in statistical data analysis. A naive approach is to first estimate the density and then compute its derivative. However, such a two-step approach does not work well because a good density estimator does not necessarily mean a good densityderivative estimator. In this paper, we give a direct method to approximate the density derivative witho...

State estimation is a classical problem in quantum information. In optimization of estimation scheme, to find a lower bound to the error of the estimator is a very important step. So far, all the proposed tractable lower bounds use derivative of density matrix. However, sometimes, we are interested in quantities with singularity, e.g. concurrence etc. In the paper, lower bounds to a Mean Square...

Abs t rac t . To estimate the quantile density function (the derivative of the quantile function) by kernel means, there are two alternative approaches. One is the derivative of the kernel quantile estimator, the other is essentially the reciprocal of the kernel density estimator. We give ways in which the former method has certain advantages over the latter. Various closely related smoothing i...

In this paper, we study the estimation of derivative a regression function in standard univariate model. The estimators are defined either by derivating nonparametric least-squares or estimating projection derivative. We prove two simple risk bounds allowing to compare our estimators. More elaborate under stability assumption then provided. Bases and spaces on which can illustrate assumptions f...

In this paper we introduce the Extended Method of Moments (XMM) estimator. This estimator accommodates a more general set of moment restrictions than the standard Generalized Method of Moments (GMM) estimator. More specifically, the XMM differs from the GMM in that it can handle not only uniform conditional moment restrictions (i.e. valid for any value of the conditioning variable), but also lo...

We propose an estimator for the α fractional derivative of a distribution function. Our estimator, based on finite differences of the empirical df generalizes the estimator proposed by Maltz (1974) for the nonnegative real case. The asymptotic bias, variance and the consistency of the estimator are studied. Finally, the optimal choice for the ”smoothing parameter” proves that even in the fracti...