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作者：Dette, H; Wong, WK
作者单位：University of California System; University of California Los Angeles
摘要：We study properties of the variance function of the least squares estimator for the response surface. For polynomial models, we identify a class of approximate designs for which their Variance functions are maximized at the extreme points of the design space. As an application, we examine robustness properties of D-optimal designs and D-n-r-optimal designs under various polynomial model assumptions. Analytic formulas for the G-efficiencies of these designs are derived, along with their D-effic...
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作者：Chan, NH; Terrin, N
作者单位：Carnegie Mellon University
摘要：An autoregressive time series is said to be unstable if all of its characteristic roots lie on or outside the unit circle, with at least one on the unit circle. This paper aims at developing asymptotic inferential schemes for an unstable autoregressive model generated by long-memory innovations. This setting allows both nonstationarity and long-memory behavior in the modeling of low-frequency phenomena. In developing these procedures, a novel weak convergence result for a sequence of long-memo...
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作者：ROSENTHAL, JS
作者单位：University of Minnesota System; University of Minnesota Twin Cities
摘要：This paper analyzes the Gibbs sampler applied to a standard variance component model, and considers the question of how many iterations are required for convergence. It is proved that for K location parameters, with J observations each, the number of iterations required for convergence (for large K and J) is a constant times (1 + log K/log J). This is one of the first rigorous, a priori results about time to convergence for the Gibbs sampler. A quantitative version of the theory of Harris recu...
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作者：Cheng, C
摘要：Various smoothing methods for quantile density estimation are unified into a generalized kernel smoothing. Based on a stochastic upper bound of the derivatives sequence for a sequence of smoothed Brownian bridges, uniform in-probability consistency of generalized kernel quantile density estimators on any closed subinterval of the open unit interval is derived.
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作者：Prentice, MJ; Mardia, KV
作者单位：University of Leeds
摘要：This paper deals with the statistical analysis of matched pairs of shapes of configurations of landmarks in the plane. We provide inference procedures on the complex projective plane for a basic measure of shape change in the plane, on observing that shapes of configurations of (k + 1) landmarks in the plane may be represented as points on CPk-1 and that complex rotations are the only maps on CSk-1 which preserve the usual Hermitian inner product. Specifically, if u(1), ..., u(n) are fixed poi...
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作者：ELLIS, SP
作者单位：University of Rochester; Rutgers University System; Rutgers University New Brunswick; Rutgers University Biomedical & Health Sciences
摘要：Let n > p > k > O be integers. Let delta be any technique for fitting k-planes to p-variate data sets of size n, for example, linear regression, principal components-or projection pursuit. Let J be the set of data sets which are (1) singularities of delta, that is, near them delta is unstable (for example, collinear data sets are singularities of least squares regression) and (2) nondegenerate, that is, their rank, after centering, is at least k. It is shown that the Hausdorff dimension, dim(H...
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作者：MYKLAND, PA
摘要：This paper introduces the concept of dual likelihood as a method of improving accuracy in inference situations depending on martingale estimating equations. Asymptotic results are given for the dual likelihood ratio statistic, and the structure of the family of alternatives is explored. Applications to survival analysis and also to time series, likelihood inference and independent observations are given. Connections to nonparametric likelihood (including empirical likelihood) are established.
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作者：GREENWOOD, PE; WEFELMEYER, W
作者单位：Universitat Siegen
摘要：Suppose we observe a uniformly ergodic Markov chain with unknown transition distribution. The empirical estimator for a linear functional of the (invariant) joint distribution of two successive observations is defined using the pairs of successive observations. Its efficiency is proved using a martingale approximation. As a corollary we show efficiency of the empirical joint distribution function in the sense of a functional convolution theorem.
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作者：Stein, ML
摘要：For predicting integral(G)v(x)Z(x) dx, where v is a fixed known function and Z is a stationary random field, a good sampling design should have a greater density of observations where v is relatively large in absolute value. Designs using this idea when G = [0, 1] have been studied for some time. For G a region in two dimensions, very little is known about the statistical properties of cubature rules based on designs with varying density. This work proposes a class of designs that are locally ...
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作者：Chang, T; Ko, DJ
作者单位：Virginia Commonwealth University
摘要：This paper calculates the influence functions and asymptotic distributions of M-estimators of the rotation A in a spherical regression model on the unit sphere in p dimensions with isotropic errors. The problem arises in the reconstruction of the motion of a rigid body on the surface of the sphere. The comparable model for p-dimensional Euclidean space data is that (upsilon(1),...,upsilon(n)) are independent with upsilon(i) symmetrically distributed around gamma A . u(i) + b, u(i) known, where...
