The Annals of Statistics

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• The jackknife estimate of variance of a Kaplan-Meier integral AI翻译
  作者：Stute, W
  摘要：Let (F) over cap(n) be the Kaplan-Meier estimator of a distribution function F computed from randomly censored data. It is known that, under certain integrability assumptions on a function phi, the Kaplan-Meier integral integral phi d (F) over cap(n), when properly standardized, is asymptotically normal. In this paper it is shown that, with probability 1, the jackknife estimate of variance consistently estimates the (limit) variance.
• A frequency domain bootstrap for ratio statistics in time series analysis AI翻译
  作者：Dahlhaus, R; Janas, D
  摘要：The asymptotic properties of the bootstrap in the frequency domain based on Studentized periodogram ordinates are studied, It is proved that this bootstrap approximation is valid for ratio statistics such as autocorrelations. By using Edgeworth expansions it is shown that the bootstrap approximation even outperforms the normal approximation. The results carry over to Whittle estimates. In a simulation study the behavior of the bootstrap is studied for empirical correlations and Whittle estimat...
• Limit theorem for maximum of standardized U-statistics with an application AI翻译
  作者：Horvath, L; Shao, QM
  作者单位：University of Oregon
  摘要：We show that the maximally selected standardized U-statistic goes in distribution to an infinite sum of weighted chi-square random variables in the degenerate case. The result is applied to the detection of possible changes in the distribution of a sequence observation.
• Uniform rates of estimation in the semiparametric Weibull mixture model AI翻译
  作者：Ishwaran, HZ
  摘要：This paper presents a uniform estimator for a finite-dimensional parameter in the semiparametric Weibull mixture model. The rates achieved hv the estimator hold uniformly over shrinking sequences of models much more general than traditional sequences that are required to satisfy a Hellinger differentiable property. We show that these rates are optimal in a class of identified models constrained by a moment condition on the nonparametric mixing distribution.
• Asymptotically optimal estimation in misspecified time series models AI翻译
  作者：Dahlhaus, R; Wefelmeyer, W
  作者单位：Universitat Siegen
  摘要：A concept of asymptotically efficient estimation is presented when a misspecified parametric time series model is fitted to a stationary process. Efficiency of several minimum distance estimates is proved and the behavior of the Gaussian maximum likelihood estimate is studied. Furthermore, the behavior of estimates that minimize the h-step prediction enter is discussed briefly. The paper answers to some extent the question what happens when a misspecified model is fitted to time series data an...
• A minimaxity criterion in nonparametric regression based on large-deviations probabilities AI翻译
  作者：Korostelev, A
  摘要：A large-deviations criterion is proposed for optimality of nonparametric regression estimators. The criterion is one of minimaxity of the large-deviations probabilities. We study the case where the underlying class of regression functions is either Lipschitz or Holder, and when the loss function involves estimation at a point or in supremum norm. Exact minimax asymptotics are found in the Gaussian case.
• Shrinkage estimators, Skorokhod's problem and stochastic integration by parts AI翻译
  作者：Evans, SN; Stark, PB
  摘要：For a broad class of error distributions that includes the spherically symmetric ones, we give a short proof that the usual estimator of the mean in a cl-dimensional shift model is inadmissible under quadratic loss when d greater than or equal to 3. Our proof involves representing the error distribution as that of a stopped Brownian motion and using elementary stochastic analysis to obtain a generalization of an integration by parts lemma due to Stein in the Gaussian case.
• Efficient estimation for the proportional hazards model with interval censoring AI翻译
  作者：Huang, J
  摘要：The maximum likelihood estimator (MLE) for the proportional hazards model with case 1 interval censored data is studied. It is shown that the MLE for the regression parameter is asymptotically normal with root n convergence rate and achieves the information bound, even though the MLE for the baseline cumulative hazard function only converges at n(1/3) rate. Estimation of the asymptotic variance matrix for the MLE of the regression parameter is also considered. To prove our main results, we als...
• Mobius transformation and Cauchy parameter estimation AI翻译
  作者：McCullagh, P
  摘要：Some properties of the ordinary two-parameter Cauchy family, the circular or wrapped Cauchy family, and their connection via Mobius transformation are discussed. A key simplification is achieved by taking the parameter theta = mu + i sigma to be a point in the complex plane rather than the real plane. Maximum likelihood estimation is studied in some detail. It is shown that the density of any equivariant estimator is harmonic on the upper half-plane. In consequence, the maximum likelihood esti...
• Asymptotic optimality of regular sequence designs AI翻译
  作者：Ritter, K
  摘要：We study linear estimators for the weighted integral of a stochastic process. The process may only be observed on a finite sampling design. The error is defined in a mean square sense, and the process is assumed to satisfy Sacks-Ylvisaker regularity conditions of order r is an element of N-0. We show that sampling at the quantiles of a particular density already yields asymptotically optimal estimators. Hereby we extend the results of Sacks and Ylvisaker for regularity r = 0 or 1, and we confi...