In order to reduce the …nite sample bias and improve the rate of convergence, local polynomial estimators have been introduced into the econometric literature to estimate the regression discontinuity model. In this paper, we show that, when the degree of smoothness is known, the local polynomial estimator achieves the optimal rate of convergence within the Hölder smoothness class. However, when...

We analyze the problem of estimating 3-D motion in an optimal manner using correspondences of features in two views. The importance of having an optimal estimator is twofold: first, for the estimation itself and, second, for the bound it offers on how much sensitivity one can expect from a two-frame, point-based motion algorithm. The optimal estimator turns out to be nonlinear, and for that rea...

The Kalman filter is the optimal minimum-variance state estimator for linear dynamic systems with Gaussian noise. In addition, the Kalman filter is the optimal linear state estimator for linear dynamic systems with non-Gaussian noise. For nonlinear systems various modifications of the Kalman filter (e.g., the extended Kalman filter, the unscented Kalman filter, and the particle filter) have bee...

The Kitanidis filter is a natural extension of the Kalman to systems subject arbitrary unknown inputs or disturbances. Though optimality was founded for general time varying more than 30 years ago, its boundedness and stability analysis still limited time-invariant systems, up authors’ knowledge. In framework this article establishes upper lower bounds error covariance filter, as well all auxil...

The empirical Bayes estimators of treatment effects in a factorial experiment were derived and their asymptotic properties were explored. It was shown that they were asymptotically optimal and the estimator of the scale parameter had a limiting gamma distribution while the estimators of the factor effects had a limiting multivariate normal distribution. A Bootstrap analysis was performed to ill...

The close relationship between heart and kidney diseases was studied with respect to the 'Shrunken pore syndrome' that is characterized by a difference in renal filtration between cystatin C and creatinine. Patients were retrieved from the HeARt and brain failure inVESTigation trail (HARVEST) which is an ongoing study undertaken in individuals hospitalized for the diagnosis of heart failure. Ni...

This paper introduces a family of blind feedforward nonlinear least-squares (NLS) estimators for joint estimation of the carrier phase and frequency offset of general quadrature amplitude modulated (QAM) transmissions. As an extension of the Viterbi and Viterbi (V&V) estimator, a constellation-dependent optimal matched nonlinear estimator is derived such that its asymptotic (large sample) varia...

Optimal bandwidths for local polynomial regression usually involve functionals of the derivatives of the unknown regression function. In the multivariate case, estimates of these functionals are not readily available, primarily because estimating multivariate derivatives is complicated. In this paper, an estimator of multivariate second derivative is obtained via local quadratic regression with...

Meta learning of optimal classifier error rates allows an experimenter to empirically estimate the intrinsic ability of any estimator to discriminate between two populations, circumventing the difficult problem of estimating the optimal Bayes classifier. To this end we propose a weighted nearest neighbor (WNN) graph estimator for a tight bound on the Bayes classification error; the Henze-Penros...