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作者：Inglot, T; Kallenberg, WCM; Ledwina, T
作者单位：Wroclaw University of Science & Technology; University of Twente
摘要：The classical problem of testing goodness-of-fit of a parametric family is reconsidered. A new test for this problem is proposed and investigated. The new test statistic is a combination of the smooth test statistic and Schwarz's selection rule. More precisely, as the sample size increases, an increasing family of exponential models describing departures from the null model is introduced and Schwarz's selection rule is presented to select among them. Schwarz's rule provides the right dimension...
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作者：Lepski, OV; Mammen, E; Spokoiny, VG
作者单位：Federal Research Center Computer Science & Control of RAS; Institute Systems Analysis of Russian Academy of Sciences; Ruprecht Karls University Heidelberg; Russian Academy of Sciences; Kharkevich Institute for Information Transmission Problems of the RAS; Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics
摘要：A new variable bandwidth selector for kernel estimation is proposed. The application of this bandwidth selector leads to kernel estimates that achieve optimal rates of convergence over Besov classes. This implies that the procedure adapts to spatially inhomogeneous smoothness. In particular, the estimates share optimality properties with wavelet estimates based on thresholding of empirical wavelet coefficients.
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作者：Schmid, W; Schöne, A
作者单位：European University Viadrina Frankfurt Oder; Ulm University
摘要：Schmid extended the classical EWMA control chart to autocorrelated processes. Here, we consider the tail probability of the run length in the in-control state. The in-control process is assumed to be a stationary Gaussian process. It is proved that the tails for the autocorrelated process are larger than in the case of independent variables if all autocovariances are greater than or equal to zero. The inequality is strict. Moreover, this result is still valid for stationary processes having el...
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作者：Doss, H; Huffer, FW; Lawson, KL
作者单位：University System of Ohio; Ohio State University; Abbott Laboratories; State University System of Florida; Florida State University
摘要：We consider a coherent system S consisting of m independent components for which we do not know the distributions of the components' lifelengths. If we know the structure function of the system, then we can estimate the distribution of the system lifelength by estimating the distributions of the lifelengths of the individual components. Suppose that we can collect data under the autopsy model, wherein a system is run until a failure occurs and then the status (functioning or dead) of each comp...
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作者：Huang, J
作者单位：University of Iowa
摘要：We show that the nonparametric maximum likelihood estimator (NPMLE) of a distribution function based on balanced ranked set samples is consistent, converges weakly to a Gaussian process and is asymptotically efficient. The covariance function of the limiting process is described in terms of the solution to a Fredholm integral equation of the second kind.
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作者：Wang, KM; Gasser, T
作者单位：University of Zurich
摘要：When studying some process or development in different subjects or units-be it biological, chemical or physical-we usually see a typical pattern, common to all curves. Yet there is variation both in amplitude and dynamics between curves. Following some ideas of structural analysis introduced by Kneip and Gasser, we study a method-dynamic time warping with a proper cost function-for estimating the shift or warping function from one curve to another to align the two functions. For some models th...
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作者：Bosq, D
作者单位：Sorbonne Universite
摘要：We show that local irregularity of observed sample paths provides additional information which allows nonparametric estimators and predictors for continuous time processes to reach parametric rates in mean square as well as in a.s. uniform convergence. For example, we prove that under suitable conditions the kernel density estimator f(T) associated with the observed sample path (X-t, 0 less than or equal to t less than or equal to T) satisfies [GRAPHICS] where f denotes the unknown marginal de...
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作者：Birgé, L
作者单位：Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS)
摘要：The Grenander estimator of a decreasing density, which is defined as the derivative of the concave envelope of the empirical c.d.f, is known to be a very good estimator of an unknown decreasing density on the half-line R+ when this density is not assumed to be smooth. It is indeed the maximum likelihood estimator and one can get precise upper bounds for its risk when the loss is measured by the L-1-distance between densities. Moreover, if one restricts oneself to the compact subsets of decreas...
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作者：Mammen, E; Van de Geer, S
作者单位：Ruprecht Karls University Heidelberg; Leiden University - Excl LUMC; Leiden University
摘要：Consider a partial linear model, where the expectation of a random variable Y depends on covariates (x, z) through F(theta(o)x + m(o)(z)), with theta(o) an unknown parameter, and m(o) an unknown function. We apply the theory of empirical processes to derive the asymptotic properties of the penalized quasi-likelihood estimator.
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作者：Tsybakov, AB
作者单位：Sorbonne Universite; Russian Academy of Sciences
摘要：Let X-1,...,X-n be independent identically distributed observations from an unknown probability density f((.)). Consider the problem of estimating the level set G = G(f)(lambda)= (x epsilon R-2: f(x) greater than or equal to lambda) from the sample X-1,...,X-n, under the assumption that the boundary of G has a certain smoothness. We propose piecewise-polynomial estimators of G based on the maximization of local empirical excess masses. We show that the estimators have optimal rates of converge...
