721 research outputs found

    Large-sample study of the kernel density estimators under multiplicative censoring

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    The multiplicative censoring model introduced in Vardi [Biometrika 76 (1989) 751--761] is an incomplete data problem whereby two independent samples from the lifetime distribution GG, Xm=(X1,...,Xm)\mathcal{X}_m=(X_1,...,X_m) and Zn=(Z1,...,Zn)\mathcal{Z}_n=(Z_1,...,Z_n), are observed subject to a form of coarsening. Specifically, sample Xm\mathcal{X}_m is fully observed while Yn=(Y1,...,Yn)\mathcal{Y}_n=(Y_1,...,Y_n) is observed instead of Zn\mathcal{Z}_n, where Yi=UiZiY_i=U_iZ_i and (U1,...,Un)(U_1,...,U_n) is an independent sample from the standard uniform distribution. Vardi [Biometrika 76 (1989) 751--761] showed that this model unifies several important statistical problems, such as the deconvolution of an exponential random variable, estimation under a decreasing density constraint and an estimation problem in renewal processes. In this paper, we establish the large-sample properties of kernel density estimators under the multiplicative censoring model. We first construct a strong approximation for the process k(G^βˆ’G)\sqrt{k}(\hat{G}-G), where G^\hat{G} is a solution of the nonparametric score equation based on (Xm,Yn)(\mathcal{X}_m,\mathcal{Y}_n), and k=m+nk=m+n is the total sample size. Using this strong approximation and a result on the global modulus of continuity, we establish conditions for the strong uniform consistency of kernel density estimators. We also make use of this strong approximation to study the weak convergence and integrated squared error properties of these estimators. We conclude by extending our results to the setting of length-biased sampling.Comment: Published in at http://dx.doi.org/10.1214/11-AOS954 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

    The study of the umbilical system in planktonic foraminifera in relation with depth of the Ziarat-kola section at the Maastrichtian, Central Alborz, IRAN

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    The main aim of this research is study of the planktonic foraminifera morphogroups distinction genus to perform by changing the umbilicus area in Ziarat-kola section to find novel results. Therefore, original objection at this research considers the cause of organizing umbilicus structures (Lip, Portici, Tegilla) at this protests. it seems that phylogeny trend entirely the changes of planktonic foraminifera changing from lip at primary morphogroup to tegilla at development shape which continued this phylogeny trend opening become entirely umbilicus that this trend accompanied to increasing deep. Therefore, the study of planktonic foraminifera morphotype, and recognizing, the obtained results from planktonic foraminifera analysis percent and their comparison with umbilicus structures area diagrams at this section indicats the increasing morphotype three accompany with increase in sea level that here dominated portici and tegilla structure with compressed opening and with decrease of morphotype three which showed decrease sea level, opening structure (lip) dominated. These trends follows the from Pascal law at Ziarat-kola section of the research

    Image up-sampling using the discrete wavelet transform

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    Image up-sampling is an effective technique, useful in today\u27s digital image processing applications and rendering devices. In image up-sampling, an image is enhanced from a lower resolution to a higher resolution with the degree of enhancement depending upon application requirements. It is known that the traditional interpolation based approaches for up-sampling, such as the Bilinear or Bicubic interpolations, blur the resultant images along edges and image features. Furthermore, in color imagery, these interpolation-based up-sampling methods may have color infringing artifacts in the areas where the images contain sharp edges and fine textures. We present an interesting up-sampling algorithm based on the Discrete Wavelet Transform (DWT). The proposed method preserves much of the sharp edge features in the image, and lessens the amount of color artifacts. Effectiveness of the proposed algorithm has been demonstrated based on comparison of PSNR and Ξ” E * ab quality metrics between the original and reconstructed images
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