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作者：BOSE, A; BOUKAI, B
作者单位：Purdue University System; Purdue University; Purdue University in Indianapolis
摘要：We consider the problem of sequentially estimating one parameter in a class of two-parameter exponential family of distributions. We assume a weighted squared error loss with a fixed cost of estimation error. The stopping rule, based on the maximum likelihood estimate of the nuisance parameter, is shown to be independent of the terminal estimate. The asymptotic normality of the stopping variable is established and approximations to its mean and to the regret associated with it are also provide...
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作者：BARRY, D
摘要：Observations y(ij) are made at points (x1i, x2j) according to the model y(ij) = F(x1i, x2j) + e(ij), where the e(ij) are independent normals with constant variance. In order to test that F(x1, x2) is an additive function of x1 and x2, a likelihood ratio test is constructed comparing F(x1, X2) = mu + Z1(x1) + Z2(x2) with F(x1, x2) = mu + Z1(x1) + Z2(x2) + Z(x1, x2), where Z1, Z2 are Brownian motions and Z is a Brownian sheet. The ratio of Brownian sheet variance to error variance alpha is chose...
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作者：LELE, C
摘要：In this paper we consider the problem of estimating the loss of point estimators and study admissibility of such estimators of loss. We adapt and extend the ''unified admissibility proof'' idea of Brown and Hwang to this problem. We first present the result in the Gaussian setup. We then generaIize the procedure to general exponential family distributions and apply it to the Poisson distribution. The result for the gamma distribution is also stated. The role played by the ''polydisc transform'...
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作者：MAMMEN, E
摘要：In this paper two bootstrap procedures are considered for the estimation of the distribution of linear contrasts and of F-test statistics in high dimensional linear models. An asymptotic approach will be chosen where the dimension p of the model may increase for sample size n --> infinity. The range of validity will be compared for the normal approximation and for the bootstrap procedures. Furthermore, it will be argued that the rates of convergence are different for the bootstrap procedures i...
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作者：MESSER, K; GOLDSTEIN, L
作者单位：University of Southern California
摘要：We introduce a new class of variable kernels which depend on the smoothing parameter b through a simple scaling operation, and which have good integrated mean square error (IMSE) convergence properties. These kernels deform ''automatically'' near the boundary, eliminating boundary bias. Computational formulas are given for all orders of kernel in terms of exponentially damped sines and cosines. The kernel is a computationally convenient approximation to a certain Green's function, with the res...
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作者：YING, ZL
摘要：Large sample approximations are developed to establish asymptotic linearity of the commonly used linear rank estimating functions, defined as stochastic integrals of counting processes over the whole line, for censored regression data. These approximations lead to asymptotic normality of the resulting rank estimators defined as solutions of the linear rank estimating equations. A second kind of approximations is also developed to show that the estimating functions can be uniformly approximated...
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作者：KOUL, HL; SALEH, AKME
作者单位：Carleton University
摘要：In an AR(p) model, R-estimation of a subset of parameters is considered when the complementary subset is possibly redundant. Along with the rank test of the full hypothesis and the subhypothesis of the parameters, both preliminary test and shrinkage R-estimators are considered. In the light of asymptotic distributional risks, the relative asymptotic risk-efficiency results are given. Though, the shrinkage R-estimator may dominate their classical versions, they do not in general dominate the pr...
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作者：OSULLIVAN, F
摘要：Nonparametric estimation of the relative risk in a generalized Cox model with multivariate time dependent covariates is considered. Estimation is based on a penalized partial likelihood. Using techniques from Andersen and Gill, and Cox and O'Sullivan, upper bounds on rate of convergence in a variety of norms are obtained. These upper bounds match the optimal rates available for linear nonparametric regression and density estimation. The results are uniform in the smoothing parameter, which is ...
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作者：TANG, DI
摘要：Model robustness in optimal regression design is studied by introducing a family of nonparametric models, which are defined as neighborhoods of classical parametric models in terms of the uniform norm. Optimal designs are sought under a minimax criterion for estimating linear functionals on such models that may be put as integrals using measures of finite support. A set of conditions equivalent to design optimality is derived using a Lagrangian principle applicable when the dimension is infini...
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作者：SHAO, J
摘要：In statistical applications the unknown parameter of interest can frequently be defined as a functional theta = T(F), where F is an unknown population. Statistical inferences about 0 are usually made based on the statistic T(F(n)), where F(n) is the empirical distribution. Assessing T(F(n)) (as an estimator of theta) or making large sample inferences usually requires a consistent estimator of the asymptotic variance of T(F(n)). Asymptotic behaviour of the jackknife variance estimator is closel...
