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作者：DONOHO, DL; LIU, RC
摘要：Consider estimating a functional T(F) of an unknown distribution F member-of F from data X1,...,X(n) i.i.d. F. Let omega(epsilon) denote the modulus of continuity of the functional T over F, computed with respect to Hellinger distance. For well-behaved loss functions l(t), we show that inf(T)n sup(F) E(F)l(T(n) - T(F)) is equivalent to l(omega(n-1/2)) to within constants, whenever T is linear and F is convex. The same conclusion holds in three nonlinear cases: estimating the rate of decay of a...
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作者：KANO, Y
摘要：This paper presents the asymptotic distribution of Ihara and Kano's noniterative estimator of the uniqueness in exploratory factor analysis. When the number of factors is overestimated, the estimator is not a continuous function of the sample covariance matrix and its asymptotic distribution is not normal, but the consistency holds. It is also shown that the first-order moment of the asymptotic distribution does not exist.
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作者：CHIU, ST
摘要：The problem of automatic bandwidth selection for a kernel density estimator is considered. It is well recognized that the bandwidth estimate selected by the least squares cross-validation is subject to large sample variation. This difficulty limits the application of the cross-validation estimate. Based on characteristic functions, an important expression for the cross-validation bandwidth estimate is obtained. The expression clearly points out the source of variation. To stabilize the variati...
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作者：PORTNOY, S
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作者：ZAMAN, A
摘要：Suppose X(i) are i.i.d. random variables taking values in X, THETA is a parameter space and y: X x THETA --> R is a map. Define the averages S(n)(y, theta) = (1/n)SIGMA(i = 1)(n)y(X(i), theta) and the truncated expectations T(m)(y, theta) = E max(y(X1, theta), - m). Under the hypothesis of global dominance [i.e., E sup(THETA) y(X1, theta) < infinity] and some regularity conditions, the main result of the paper characterizes the asymptotic suprema of S(n) as follows. For any subset G of THETA, ...
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作者：BRANDWEIN, AC; STRAWDERMAN, WE
作者单位：Rutgers University System; Rutgers University New Brunswick
摘要：This paper is primarily concerned with extending the results of Stein to spherically symmetric distributions. Specifically, when X approximately f(parallel-to X - theta parallel-to2), we investigate conditions under which estimators of the form X + ag(X) dominate X for loss functions parallel-to-delta - theta-parallel-to 2 and loss functions which are concave in parallel-to-delta - parallel-to-delta2. Additionally, if the scale is unknown we investigate estimators of the location parameter of ...
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作者：CHIU, ST
作者单位：Chinese Academy of Sciences
摘要：The problem of bandwidth selection for nonparametric kernel regression is considered. It is well recognized that the classical bandwidth selectors are subject to large sample variation. Due to the large variation, these selectors might not be very useful in practice. Based on the frequency-domain representation of the residual sum of squares (RSS), the source of the variation is pointed out. The observation leads to consideration of a procedure which stabilizes the RSS by modifying the periodo...
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作者：HSING, TL
摘要：Let X1, X2, ... be possibly dependent random variables having the same marginal distribution. Consider the situation where FBAR(x): = P[X1 > x] is regularly varying at infinity with an unknown index -alpha < 0 which is to be estimated. In the i.i.d. setting, it is well known that Hill's estimator is consistent for alpha-1, and is asymptotically normally distributed. It is the purpose of this paper to demonstrate that such properties of Hill's estimator extend considerably beyond the independen...
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作者：BARINGHAUS, L
摘要：Rotationally invariant tests based on test statistics of the von Mises type are proposed under the hypothesis of spherical symmetry of a multivariate distribution. The tests are distribution-free when the hypothesis of spherical symmetry is true. The asymptotic distributions of the test statistics are derived under the null hypothesis and under any fixed alternative. A simple criterion for consistency is given. The results are illustrated by numerous examples of test statistics which give rise...
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作者：DYKSTRA, R; KOCHAR, S; ROBERTSON, T
摘要：Stochastic ordering between probability distributions is a widely studied concept. It arises in numerous settings and has useful applications. Since it is often easy to make value judgments when such orderings exist, it is desirable to recognize their occurrence and to model distributional structure under such orderings. Unfortunately, the necessary theory for statistical inference procedures has not been developed for many problems involving stochastic ordering and this development seems to b...
