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作者：BROWN, LD; LOW, MG
作者单位：University of California System; University of California Berkeley
摘要：This paper compares three methods for producing lower bounds on the minimax risk under quadratic loss. The first uses the bounds from Brown and Gajek. The second method also uses the information inequality and results in bounds which are always at least as good as those form the first method. The third method is the hardest-linear-family method described by Donoho and Liu. These methods are applied in four examples, the last of which relates to a frequently considered problem in nonparametric ...
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作者：EATON, ML; TYLER, DE
作者单位：Rutgers University System; Rutgers University New Brunswick
摘要：A relatively obscure eigenvalue inequality due to Wielandt is used to give a simple derivation of the asymptotic distribution of the eigenvalues of a random symmetric matrix. The asymptotic distributions are obtained under a fairly general setting. An application of the general theory to the bootstrap distribution of the eigenvalues of the sample covariance matrix is given.
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作者：GOLUBEV, GK; HASMINSKII, RZ
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作者：BHANSALI, RJ; PAPANGELOU, F
作者单位：University of Manchester
摘要：Given a realization of T consecutive observations of a stationary autoregressive process of unknown, possibly infinite, order m, it is assumed that a process of arbitrary finite order p is fitted by least squares. Under appropriate conditions it is known that the estimators of the autoregressive coefficients are asymptotically normal. The question considered here is whether the moments of the (scaled) estimators converge, as T --> infinity, to the moments of their asymptotic distribution. We e...
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作者：BICKEL, PJ; RITOV, Y; WELLNER, JA
作者单位：Hebrew University of Jerusalem; University of Washington; University of Washington Seattle
摘要：Suppose that P is the distribution of a pair of random variables (X, Y) on a product space X x Y with known marginal distributions P(X) and P(Y). We study efficient estimation of functions theta(h) = integral h dP for fixed h: X x Y --> R under iid sampling of (X, Y) pairs from P and a regularity condition on P. Our proposed estimator is based on partitions of both X and Y and the modified minimum chi-square estimates of Deming and Stephan (1940). The asymptotic behavior of our estimator is go...
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作者：DUAN, N; LI, KC
作者单位：University of California System; University of California Los Angeles
摘要：Consider a general regression model of the form y = g(alpha + x'beta, epsilon), with an arbitrary and unknown link function g. We study a link-free method, the slicing regression, for estimating the direction of beta. The method is easy to implement and does not require interative computation. First, we estimate the inverse regression function E(x\y) using a step function. We then estimate GAMMA = Cov[E(x\y)], using the estimated inverse regression function. Finally, we take the spectral decom...
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作者：FOSTER, DP
摘要：A predictor is a method of estimating the probability of future events over an infinite data sequence. One predictor is as strong as another if for all data sequences the former has at most the mean square error (MSE) of the latter. Given any countable set D of predictors, we explicitly construct a predictor S that is at least as strong as every element of D. Finite sample bounds are also given which hold uniformly on the space of all possible data.
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作者：FALK, M; KAUFMANN, E
摘要：An asymptotic expansion of length 2 is established for the coverage probabilities of confidence intervals for the underlying q-quantile which are derived by bootstrapping the sample q-quantile. The corresponding level error turns out to be of order O(n-1/2) which is unexpectedly low. A confidence interval of even more practical use is derived by using backward critical points. The resulting confidence interval is of the same length as the one derived by ordinary bootstrap but it is distributio...
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作者：HELMERS, R
摘要：The asymptotic accuracy of the estimated one-term Edgeworth expansion and the bootstrap approximation for a Studentized U-statistic is investigated. It is shown that both the Edgeworth expansion estimate and the bootstrap approximation are asymptotically closer to the exact distribution of a Studentized U-statistic than the normal approximation. The conditions needed to obtain these results are weak moment assumptions on the kernel h of the U-statistic and a nonlattice condition for the distri...
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作者：STEFANSKI, LA; CARROLL, RJ
作者单位：Texas A&M University System; Texas A&M University College Station
摘要：Consider a generalized linear model with response Y and scalar predictor X. Instead of observing X, a surrogate W = X + Z is observed, where Z represents measurement error and is independent of X and Y. The efficient score test for the absence of association depends on m(w) = E(X\W = w) which is generally unknown. Assuming that the distribution of Z is known, asymptotically efficient tests are constructed using nonparametric estimators of m(w). Rates of convergence for the estimator of m(w) ar...
