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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...
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作者：KEMPERMAN, JHB
摘要：We derive necessary and sufficient conditions in order that each mixture of a given family of probability densities have no more than s modal intervals, with special attention to ordinary unimodality and strong unimodality of such mixtures.
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作者：FAN, JQ
摘要：Deconvolution problems arise in a variety of situations in statistics. An interesting problem is to estimate the density f of a random variable X based on n i.i.d. observations from Y = X + epsilon, where epsilon is a measurement error with a known distribution. In this paper, the effect of errors in variables of nonparametric deconvolution is examined. Insights are gained by showing that the difficulty of deconvolution depends on the smoothness of error distributions: the smoother, the harder...
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作者：GOUTIS, C; CASELLA, G
作者单位：Cornell University
摘要：Confidence intervals for the variance of a normal distribution with unknown mean are constructed which improve upon the usual shortest interval based on the sample variance alone. These intervals have guaranteed coverage probability uniformly greater than a predetermined value 1 - alpha and have uniformly shorter length. Using information relating the size of the sample mean to that of the sample variance, we smoothly shift the usual minimum length interval closer to zero, simultaneously bring...
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作者：COX, DD
摘要：An asymptotic analysis is presented for estimation in the three-parameter first-order autoregressive model, where the parameters are the mean, autoregressive coefficient and variance of the shocks. The nearly nonstationary asymptotic model is considered wherein the autoregressive coefficient tends to 1 as sample size tends to infinity. Three different estimators are considered: the exact Gaussian maximum likelihood estimator, the conditional maximum likelihood or least squares estimator and so...
