-
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...
-
作者：BERAN, R
摘要：Consider the problem of constructing a prediction region D(n) for a potentially observable variable X on the basis of a learning sample of size n. Usually, the requirement that D(n) contain X with probability alpha, conditionally on the learning sample, does not uniquely determine D(n). This paper develops a general probability-centering concept for prediction regions that extends to vector-valued or function-valued X the classical notion of an equal-tailed prediction interval. The dual requir...
-
作者：GEIGER, D; PEARL, J
作者单位：University of California System; University of California Los Angeles
摘要：This article develops an axiomatic basis for the relationship between conditional independence and graphical models in statistical analysis. In particular, the following relationships are established: (1) every axiom for conditional independence is an axiom for graph separation, (2) every graph represents a consistent set of independence and dependence constraints, (3) all binary factorizations of strictly positive probability models can be encoded and determined in polynomial time using their...
-
作者：GREENSHTEIN, E
作者单位：Hebrew University of Jerusalem
摘要：Let X1, X2,... be a sequence of random variables, (X1,...,X(n)) approximately F(theta)n theta is-an-element-of THETA. In a work by Bahadur it was shown that, for some sequential problems, an inference may be based on a sequence of sufficient and transitive statistics S(n) = S(n)(X1,..., X(n)) without any loss in statistical performance. A simple criterion for transitivity is given in Theorem 1.
-
作者：QIN, J
摘要：It is well known that we can use the likelihood ratio statistic to test hypotheses and to construct confidence intervals in full parametric models. Recently, Owen introduced the empirical likelihood method in nonparametric models. In this paper, we generalize his results to biased sample problems. A Wilks theorem leading to a likelihood ratio confidence interval for the mean is given. Some extensions, discussion and simulations are presented.
-
作者：FAN, JQ
摘要：In this paper, a method for finding global minimax lower bounds is introduced. The idea is to adjust automatically the direction of a local one-dimensional subproblem at each location to the nearly hardest one, and to use locally the difficulty of the one-dimensional subproblem. This method has the advantages of being easily implemented and understood. The lower bound is then applied to nonparametric deconvolution to obtain the optimal rates of convergence for estimating a whole function. Othe...
-
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...
-
作者：CHEN, JH; SHAO, J
作者单位：University of Ottawa
摘要：In a heteroscedastic linear model, we establish the asymptotic normality of the iterative weighted least squares estimators with weights constructed by using the within-group residuals obtained from the previous model fitting. An adaptive procedure is proposed which ensures that the iterative process stops after a finite number of iterations and produces an estimator asymptotically equivalent to the best estimator that can be obtained by using the iterative procedure. Theoretical and empirical...
-
作者：HOSOYA, Y; TANIGUCHI, M
作者单位：University of Osaka
-
作者：KIM, JH
摘要：We consider general chi-square goodness-of-fit test statistics for randomly censored data-call these generalized Pearson statistics-which are nonnegative definite quadratic forms in the cell frequencies obtained from the product-limit estimator, allowing random cells and general estimators of nuisance parameters. This class of statistics generalizes the class studied by Moore and Spruill in the no censoring case. The large sample behavior of these statistics under the null hypothesis and local...
