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It is shown how various exact nonparametric inferences based on an ordinary right or progressively Type-II right censored sample can be generalized to situations where two independent samples are combined. We derive the relevant formulas for the combined ordered samples to construct confidence intervals for a given quantile, prediction intervals, and tolerance intervals. The results are valid for...
Under a suitable choice of bandwidth, Nadaraya’s estimator of the pth quantile yields smaller mean squared error than the unsmoothed pth sample quantile. We investigate the problem of bootstrap estimation of the variance of the Nadaraya quantile estimator and show that the error of the variance estimator can be reduced by smoothing the bootstrap. A novel approach, which calibrates the order p of the...
Consistent procedures are constructed for testing the goodness-of-fit of the error distribution in nonparametric regression models. The test starts with a kernel-type regression fit and proceeds with the construction of a test statistic in the form of an L2 distance between a parametric and a nonparametric estimates of the residual characteristic function. The asymptotic null distribution and the...
In the context of capture–recapture experiments heterogeneous capture probabilities are often perceived as one of the most challenging features to be incorporated in statistical models. In this paper we propose within a Bayesian framework a new modeling strategy for inference on the unknown population size in the presence of heterogeneity of subject characteristics. Our approach is attractive in that...
Conditions are given for linear functions of skew-normal random vectors to maximize skewness and kurtosis. As a direct implication, several measures of their multivariate skewness and kurtosis are shown to be equivalent. An estimator of the shape parameter with good statistical properties is also considered. These results are strictly related to canonical forms of skew-normal distributions and linear...
In longitudinal studies, it is common to observe repeated measurements data from a sample of subjects where noisy measurements are made at irregular times, with a random number of measurements per subject. Often a reasonable assumption is that the data are generated by the trajectories of a smooth underlying stochastic process. In some cases, one observes multivariate time courses generated by a multivariate...
The problem of testing multinormality against some alternatives invariant with respect to a subgroup of affine transformations is studied. Using the Laplace expansion for integrals, some approximations to the most powerful invariant (MPI) tests are derived. The cases of bivariate exponential and bivariate uniform alternatives are studied in detail, whereas higher-dimensional extensions are only outlined...
We investigate the properties of a kernel-type multivariate regression estimator first proposed by Mack and Müller (Sankhya 51:59–72, 1989) in the context of univariate derivative estimation. Our proposed procedure, unlike theirs, assumes that bandwidths of the same order are used throughout; this gives more realistic asymptotics for the estimation of the function itself but makes the asymptotic distribution...
Extending the model of progressive Type-II censoring, we introduce an adaption process. It allows us to choose the next censoring number taking into account both the previous censoring numbers and previous failure times. After deriving some distributional results, we show that maximum likelihood estimators coincide with those in deterministic progressive Type-II censoring. Finally, we establish inferential...
This comment refers to the invited paper available at: doi: 10.1007/s11749-010-0197-z . Fan’s research was partially supported by NSF Grants DMS-0704337 and DMS-0714554 and NIH Grant R01-GM072611. Lv’s research was partially supported by NSF Grant DMS-0806030. We sincerely thank the Co-Editor, Professor Ricardo Cao, for his kind invitation to comment on this discussion paper.
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