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作者：Donoho, DL
作者单位：Stanford University; University of California System; University of California Berkeley
摘要：We study what we call dyadic CART'-a method of nonparametric regression which constructs a recursive partition by optimizing a complexity penalized sum of squares, where the optimization is over all recursive partitions arising from midpoint splits. We show that the method is adaptive to unknown degrees of anisotropic smoothness. Specifically, consider the anisotropic smoothness classes of Nikol'skii, consisting of bivariate functions f(x(1), x(2)) whose finite difference of distance h in dire...
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作者：Routledge, R; Tsao, M
作者单位：Simon Fraser University; University of Victoria
摘要：Although the cumulative distribution function may be differentiated to obtain the corresponding density function, whether or not a similar relationship exists between their asymptotic expansions remains a question. We provide a rigorous argument to prove that Lugannani and Rice's asymptotic expansion for the cumulative distribution function of the mean of a sample of i.i.d. observations may be differentiated to obtain Daniels's asymptotic expansion for the corresponding density function. We th...
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作者：Resnick, SI
作者单位：Cornell University
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作者：Wu, HQ
作者单位：University of Michigan System; University of Michigan
摘要：Fitting a circle to a set of data points on a plane is very common in engineering and science. An important practical problem is how to choose the locations of measurement on a circular feature. So far little attention has been paid to this design issue and only some simulation results are available. Ill this paper, for Berman's bivariate four-parameter model, Phi-optimality is defined and shown to be equivalent to all phi(p)-criteria with p epsilon [-infinity, 1]. Then Phi-optimal exact desig...
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作者：Konev, V; Pergamenshchikov, S
作者单位：Tomsk State University
摘要：This paper considers the problem of sequential point estimation of the mean of a stable autoregressive process with unknown scale and autoregressive parameters. The construction of a sequential procedure makes use of special stopping rules and some modifications of least-squares estimates. The procedure enables estimating the mean with prescribed mean-square accuracy uniformly in nuisance parameters. The uniform asymptotic normality and the asymptotic minimaxity of the sequential estimate are ...
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作者：Berry, DA; Chen, RW; Zame, A; Heath, DC; Shepp, LA
作者单位：Duke University; University of Miami; Cornell University; AT&T
摘要：We consider a bandit problem consisting of a sequence of n choices from an infinite number of Bernoulli arms, with n --> infinity. The objective is to minimize the long-run failure rate. The Bernoulli parameters are independent observations from a distribution F. We first assume F to be the uniform distribution on (0, 1) and consider various extensions. In the uniform case we show that the best lower bound for the expected failure proportion is between root 2/root n and 2/root n and we exhibit...
