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作者：TANG, SM; MACNEILL, IB
作者单位：Western University (University of Western Ontario)
摘要：It is shown that serial correlation can produce striking effects in distributions of change-point statistics. Failure to account for these effects is shown to invalidate change-point tests, either through increases in the type 1 error rates if low frequency spectral mass predominates in the spectrum of the noise process, or through diminution of the power of the tests when high frequency mass predominates. These effects are characterized by the expression (2pif(0)/integral-pi/-pi f(lambda)dlam...
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作者：NEUHAUS, G
摘要：For the two-sample problem with randomly censored data, there exists a general asymptotic theory of rank statistics which are functionals of stochastic integrals with respect to certain empirical martingales. In the present paper a conditional counterpart of this theory is developed. The conditional martingales are versions of the original ones reduced to the unit interval having their jumps at fixed lattice points. The resulting conditional tests are strictly distribution free under the null ...
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作者：GRUBEL, R; PITTS, SM
作者单位：University of London; University College London
摘要：We introduce a nonparametric estimator for the renewal function and discuss its properties, including consistency, asymptotic normality and asymptotic validity of bootstrap confidence regions. The underlying theme is that stochastic models can be regarded as functionals or nonlinear operators. This view leads to nonparametric estimators in a natural way and statistical properties of the estimators can be related to the local behaviour of the functionals.
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作者：STEIN, ML
摘要：Smoothing splines of a fixed order are commonly used as nonparametric regression estimates. The only parameter, then, that needs to be estimated is the smoothing parameter, which is often estimated using some form of cross validation. This work allows the order of the smoothing spline to be estimated using a model in which the order parameter is continuous. Within this setting, generalized cross validation and modified maximum likelihood estimates of the order and smoothing parameters are comp...
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作者：JAMES, AT; VENABLES, WN
摘要：For small sample random effects models, results are derived which show in certain cases, and indicate in general, that an estimated random effects variance matrix may be used in the weight matrices without causing undue error in the empirically weighted mean. Exact error variances are derived mathematically for the empirically weighted mean for the two sample case in one and two dimensions. Simulation is used to determine errors for a practical example of six five-variate samples. For estimati...
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作者：FOSTER, DP; GEORGE, EI
作者单位：University of Texas System; University of Texas Austin
摘要：Consider the problem of estimating mu, based on the observation of Y0, Y1,...,Y(n), where it is assumed only that Y0, Y1,...,Y(kappa) iid N(mu, sigma2) for some unknown kappa. Unlike the traditional change-point problem, the focus here is not on estimating kappa, which is now a nuisance parameter. When it is known that kappa = k, the sample mean Y(k)BAR = SIGMA0(k)Y(i)/(k + 1), provides, in addition to wonderful efficiency properties, safety in the sense that it is minimax under squared error ...
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作者：YING, ZL
摘要：We study in detail asymptotic properties of maximum likelihood estimators of parameters when observations are taken from a two-dimensional Gaussian random field with a multiplicative Ornstein-Uhlenbeck covariance function. Under the complete lattice sampling plan, it is shown that the maximum likelihood estimators are strongly consistent and asymptotically normal. The asymptotic normality here is normalized by the fourth root of the sample size and is obtained through higher order expansions o...
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作者：HALL, P; LI, KC
作者单位：Commonwealth Scientific & Industrial Research Organisation (CSIRO); University of California System; University of California Los Angeles
摘要：This paper studies the shapes of low dimensional projections from high dimensional data. After standardization, let x be a p-dimensional random variable with mean zero and identity covariance. For a projection beta'x, \\beta\\ = 1, find another direction b so that the regression curve of b'x against beta'x is as nonlinear as possible. We show that when the dimension of x is large, for most directions beta even the most nonlinear regression is still nearly linear. Our method depends on the cons...
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作者：LI, G; DOSS, H
作者单位：Purdue University System; Purdue University; State University System of Florida; Florida State University
摘要：Suppose that X1,...,X(n) are i.i.d. approximately F, and we wish to test the null hypothesis that F is a member of the parametric family F = {F(theta)(x); theta is-an-element-of THETA} where THETA is-an-element-of R(q). The classical Pearson-Fisher chi-square test involves partitioning the real axis into k cells I1,...,I(k) and forming the chi-square statistic X2 = SIGMA(i=1)k(O(i)-nF(theta)(I(i)))2/nF(theta)(I(i)), where O(i) is the number of observations falling into cell i and theta is the ...
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作者：TRAN, LT
摘要：Let (X(t), Y(t)) be a stationary time series with X(t) being R(d)-valued and Y(t) real valued, and where Y(t) is not necessarily bounded. Let E(Y0\X0) be the conditional mean function. Under appropriate regularity conditions, local average estimators of this function can be chosen to achieve the optimal rate of convergence (n-1 log n)1/(d+2) in L(infinity) norm restricted to a compact. The result answers a question raised by Truong and Stone.
