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231.
In this article, small sample properties of the maximum-likelihood estimator (m.l.e.) for the offspring distribution (pk) and its mean m are considered in the context of the simple branching process. A representation theorem is given for the m.l.e. of (Pk) from which the m.l.e. of m is obtained. The case where p0 + p1 + p2 = 1 is studied in detail: numerical results are given for the exact bias of these estimators as a function of the age of the process; a curve fitting analysis expresses the bias of m? as a function of the mean and the variance of the offspring distribution and finally an “approximate m.l.e.” for (pk) is given. 相似文献
232.
Alain Boulanger 《Revue canadienne de statistique》1983,11(4):271-284
This paper is concerned with the estimation of a shift parameter δo, based on some nonnegative functional Hg1 of the pair (DδN(x), f?δN(x)), where DδN(x) = KN/b {F2,n(x)—F1,m (x + δ)}, +δN(x) = {mF1,m (x + δ) + nF2,n(x)}/N, where F1,m and F2,n are the empirical distribution functions of two independent random samples (N = m + n), and where K2N = mn/N. First an estimator δN, is defined as a value of δ minimizing a functional H of the type of H1. A second estimator δ1N is also defined which is a linearized version of the first. Finite and asymptotic properties of these estimators are considered. It is also shown that most well-known test statistics of the Kolmogorov-Smirnov type are particular cases of such functionals H1. The asymptotic distribution and the asymptotic efficiency of some estimators are given. 相似文献
233.
Dankmar Bhning 《Statistical Methodology》2008,5(5):410-423
This note considers the variance estimation for population size estimators based on capture–recapture experiments. Whereas a diversity of estimators of the population size has been suggested, the question of estimating the associated variances is less frequently addressed. This note points out that the technique of conditioning can be applied here successfully which also allows us to identify sources of variation: the variance due to estimation of the model parameters and the binomial variance due to sampling n units from a population of size N. It is applied to estimators typically used in capture–recapture experiments in continuous time including the estimators of Zelterman and Chao and improves upon previously used variance estimators. In addition, knowledge of the variances associated with the estimators by Zelterman and Chao allows the suggestion of a new estimator as the weighted sum of the two. The decomposition of the variance into the two sources allows also a new understanding of how resampling techniques like the Bootstrap could be used appropriately. Finally, the sample size question for capture–recapture experiments is addressed. Since the variance of population size estimators increases with the sample size, it is suggested to use relative measures such as the observed-to-hidden ratio or the completeness of identification proportion for approaching the question of sample size choice. 相似文献
234.
For estimating the common mean of a bivariate normal distribution, Krishnamoorthy & Rohatgi (1989) proposed some estimators which dominate the maximum likelihood estimator in a large region of the parameter space. We consider some modifications of these estimators and study their risk performance. 相似文献
235.
Andrew L. Rukhin 《Journal of statistical planning and inference》1983,8(1):59-74
The estimation problem of a permutation parameter on the basis of a random sample of increasing size is considered. A necessary and sufficient condition for the existence of an estimator, asymptotically fully efficient for two different distributions families, is derived. We also study the application of this result to cyclic groups of order two and three. 相似文献
236.
Using the data from the AIDS Link to Intravenous Experiences cohort study as an example, an informative censoring model was
used to characterize the repeated hospitalization process of a group of patients. Under the informative censoring assumption,
the estimators of the baseline rate function and the regression parameters were shown to be related to a latent variable.
Hence, it becomes impractical to directly estimate the unknown quantities in the moments of the estimators for the bandwidth
selection of a smoothing estimator and the construction of confidence intervals, which are respectively based on the asymptotic
mean squared errors and the asymptotic distributions of the estimators. To overcome these difficulties, we develop a random
weighted bootstrap procedure to select appropriate bandwidths and to construct approximated confidence intervals. One can
see that our method is simple and faster to implement from a practical point of view, and is at least as accurate as other
bootstrap methods. In this article, it is shown that the proposed method is useful through the performance of a Monte Carlo
simulation. An application of our procedure is also illustrated by a recurrent event sample of intravenous drug users for
inpatient cares over time. 相似文献
237.
In biomedical studies, interest often focuses on the relationship between patients characteristics or some risk factors and both quality of life and survival time of subjects under study. In this paper, we propose a simultaneous modelling of both quality of life and survival time using the observed covariates. Moreover, random effects are introduced into the simultaneous models to account for dependence between quality of life and survival time due to unobserved factors. EM algorithms are used to derive the point estimates for the parameters in the proposed model and profile likelihood function is used to estimate their variances. The asymptotic properties are established for our proposed estimators. Finally, simulation studies are conducted to examine the finite-sample properties of the proposed estimators and a liver transplantation data set is analyzed to illustrate our approaches. 相似文献
238.
Kam-Wah Tsui 《Revue canadienne de statistique》1979,7(2):193-200
Let X1, …, Xp be independent random variables, all having the same distribution up to a possibly varying unspecified parameter, where each of the p distributions belongs to the family of one parameter discrete exponential distributions. The problem is to estimate the unknown parameters simultaneously. Hudson (1978) shows that the minimum variance unbiased estimator (MVUE) of the parameters is inadmissible under squared error loss, and estimators better than the MVUE are proposed. Essentially, these estimators shrink the MVUE towards the origin. In this paper, we indicate that estimators shifting the MVUE towards a point different from the origin or a point determined by the observations can be obtained. 相似文献
239.
In this article, we develop a cusum test for testing for parameter changes in linear processes based on Whittle's estimator. It is shown that under regularity conditions, the test statistic converges to the sup of a Brownian bridge. The result is particularly useful in handling the change point test in stationary ARMA processes. A simulation result is provided for illustration. 相似文献
240.