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A variance reduction technique in nonparametric smoothing is proposed: at each point of estimation, form a linear combination of a preliminary estimator evaluated at nearby points with the coefficients specified so that the asymptotic bias remains unchanged. The nearby points are chosen to maximize the variance reduction. We study in detail the case of univariate local linear regression. While the new estimator retains many advantages of the local linear estimator, it has appealing asymptotic relative efficiencies. Bandwidth selection rules are available by a simple constant factor adjustment of those for local linear estimation. A simulation study indicates that the finite sample relative efficiency often matches the asymptotic relative efficiency for moderate sample sizes. This technique is very general and has a wide range of applications.
In the Gaussian linear regression model (with unknown mean and variance), we show that the standard confidence set for one or two regression coefficients is admissible in the sense of Joshi (1969). This solves a long-standing open problem in mathemat
For a nonlinear regression model the information matrices of designs depend on the parameter of the model. The adaptive Wynn-algorithm for D-optimal design estimates the parameter at each step on the basis of the employed design points and observed r
Markov chain Monte Carlo (MCMC) algorithms are used to estimate features of interest of a distribution. The Monte Carlo error in estimation has an asymptotic normal distribution whose multivariate nature has so far been ignored in the MCMC community.
Calculating a Monte Carlo standard error (MCSE) is an important step in the statistical analysis of the simulation output obtained from a Markov chain Monte Carlo experiment. An MCSE is usually based on an estimate of the variance of the asymptotic n
We study the least squares estimator in the residual variance estimation context. We show that the mean squared differences of paired observations are asymptotically normally distributed. We further establish that, by regressing the mean squared diff