共查询到20条相似文献,搜索用时 31 毫秒
1.
P. Kabaila 《Acta Appl Math》2003,78(1-3):185-192
We consider the problem of constructing a 1– upper confidence limit for the scalar parameter 0 in the presence of the nuisance parameter vector 0, when the data are discrete. The 'profile plug-in' upper confidence limit is introduced by Kabaila and Lloyd. This confidence limit is based on computing a P-value
from an estimator
of 0, replacing the nuisance parameter by the profile maximum likelihood estimate
for known, and equating to . Theoretical and numerical evidence for the good coverage properties of this confidence limit is presented by Kabaila and Lloyd. An upper confidence limit should be assessed not only by its coverage properties but also by how large this confidence limit is. We measure how large the profile plug-in upper limit is by using a large sample approximation to it. This large sample approximation is used to delineate further the good properties of this confidence limit. 相似文献
2.
O. E. Barndorff-Nielsen 《Annals of the Institute of Statistical Mathematics》1995,47(3):461-464
Frequently, corresponding to a given estimating equation it would be desirable to have a scalar combinant having parametric derivative equal to the estimating function since such a combinant may serve as a quasi log likelihood. In general this cannot be achieved but it is nevertheless possible to define a quasi profile log likelihood and also a quasi directed likelihood, for an arbitrary one-dimensional parameter of interest and with the standard kind of distributional limit behaviour. 相似文献
3.
Gran Kauermann 《Journal of multivariate analysis》2002,82(2):471
We consider the profile score function in models with smooth and parametric components. If local respectively weighted likelihood estimation is used for fitting the smooth component, the resulting profile likelihood estimate for the parametric component is asymptotically efficient as shown in T. A. Severini and W. H. Wong (1992, Ann. Statist.20, 1768–1802). However, as in solely parametric models the profile score function is not unbiased. We propose a small sample bias adjustment which results by extending the correction suggested in P. McCullagh and R. Tibshirani (1990, J. Roy. Statist. Soc. Ser. B52, 325–344) to the framework of semiparametric models. 相似文献
4.
Paul Kabaila 《Computational Statistics》2005,20(3):401-414
Suppose that the data have a discrete distribution determined by (∞, ψ) where θ is the scalar parameter of interest and ψ
is a nuisance parameter vector. The Buehler 1 - α upper confidence limit for θ is as small as possible, subject to the constraints
that (a) its coverage probability is at least 1 - α and (b) it is a nondecreasing function of a pre-specified statisticT. This confidence limit has important biostatistical and reliability applications. The main result of the paper is that for
a wide class of models (including binomial and Poisson), parameters of interest 9 and statisticsT (which possess what we call the “logical ordering” property) there is a dramatic increase in the ease with which this upper
confidence limit can be computed. This result is illustrated numerically for θ a difference of binomial probabilities. Kabaila
& Lloyd (2002) also show that ifT is poorly chosen then an assumption required for the validity of the formula for this confidence limit may not be satisfied.
We show that for binomial data this assumption must be satisfied whenT possesses the “logical ordering” property. 相似文献
5.
Fabrizio Solari Brunero Liseo Dongchu Sun 《Annals of the Institute of Statistical Mathematics》2008,60(3):483-498
We consider the standard one-way ANOVA model; it is well-known that classical statistical procedures are based on a scalar
non-centrality parameter. In this paper we explore both marginal likelihood and integrated likelihood functions for this parameter
and we show that they exactly lead to the same answer. On the other hand, we prove that a fully Bayesian testing procedure
may provide different conclusions, depending on what is considered to be the real quantity of interest in the model or, said
differently, which are the competing hypotheses. We illustrate these issues via a real data example. 相似文献
6.
N. Sartori 《Annals of the Institute of Statistical Mathematics》2003,55(1):187-195
Higher-order likelihood methods often give very accurate results. A way to evaluate accuracy is the comparison of the solutions
with the exact ones of the classical theory, when these exist. To this end, we consider inference for a scalar regression
parameter in the normal regression setting. In particular, we compare confidence intervals computed from the likelihood and
its higher-order modifications with the ones based on the Studentt distribution. It is shown that higher-order likelihood methods give accurate approximations to exact results. 相似文献
7.
Zhiwei Zhang Howard E. Rockette 《Annals of the Institute of Statistical Mathematics》2006,58(4):687-706
We consider parameter estimation in parametric regression models with covariates missing at random. This problem admits a
semiparametric maximum likelihood approach which requires no parametric specification of the selection mechanism or the covariate
distribution. The semiparametric maximum likelihood estimator (MLE) has been found to be consistent. We show here, for some
specific models, that the semiparametric MLE converges weakly to a zero-mean Gaussian process in a suitable space. The regression
parameter estimate, in particular, achieves the semiparametric information bound, which can be consistently estimated by perturbing
the profile log-likelihood. Furthermore, the profile likelihood ratio statistic is asymptotically chi-squared. The techniques
used here extend to other models. 相似文献
8.
9.
Tsung-Yin Wang Jau-Chuan Ke Kuo-Hsiung Wang Siu-Chuen Ho 《Mathematical Methods of Operations Research》2006,63(2):371-384
This paper studies maximum likelihood estimates as well as confidence intervals of an M/M/R queue with heterogeneous servers under steady-state conditions. We derive the maximum likelihood estimates of the mean arrival rate and the three unequal mean service rates for an M/M/3 queue with heterogeneous servers, and then extend the results to an M/M/R queue with heterogeneous servers. We also develop the confidence interval formula for the parameter ρ, the probability of empty system P
0, and the expected number of customers in the system E[N], of an M/M/R queue with heterogeneous servers 相似文献
10.
Heleno Bolfarine Lisbeth K. Cordani 《Annals of the Institute of Statistical Mathematics》1993,45(3):531-540
In this paper, we consider the estimation of the slope parameter of a simple structural linear regression model when the reliability ratio (Fuller (1987),Measurement Error Models, Wiley, New York) is considered to be known. By making use of an orthogonal transformation of the unknown parameters, the maximum likelihood estimator of and its asymptotic distribution are derived. Likelihood ratio statistics based on the profile and on the conditional profile likelihoods are proposed. An exact marginal posterior distribution of , which is shown to be at-distribution is obtained. Results of a small Monte Carlo study are also reported.The first author acknowledges partial finantial suport from CNPq-BRASIL. 相似文献
11.
在缺失样本下,构造了线性模型中参数的调整的经验似然置信域,数值模拟表明调整的经验似然置信域有较好的覆盖率和精度. 相似文献
12.
This paper introduces a profile empirical likelihood and a profile conditionally empirical likelihood to estimate the parameter
of interest in the presence of nuisance parameters respectively for the parametric and semiparametric models. It is proven
that these methods propose some efficient estimators of parameters of interest in the sense of least-favorable efficiency.
Particularly, for the decomposable semiparametric models, an explicit representation for the estimator of parameter of interest
is derived from the proposed nonparametric method. These new estimations are different from and more efficient than the existing
estimations. Some examples and simulation studies are given to illustrate the theoretical results.
The first author is supported by NNSF projects (10371059 and 10171051) of China. The second author is supported by a grant
from The Research Grants Council of the Hong Kong Special Administrative Region, China (#HKU7060/04P). The third author is
supported by the University Research Committee of the University of Hong Kong and a grant from the Research Grants Council
of the Hong Kong Special Administrative Region, China (Project No. HKU7323/01M). 相似文献
13.
Stein shrinkage and second-order efficiency for semiparametric estimation of the shift 总被引:1,自引:1,他引:0
A. S. Dalalyan 《Mathematical Methods of Statistics》2007,16(1):42-62
The problem of estimating the shift (or, equivalently, the center of symmetry) of an unknown symmetric and periodic function
f observed in Gaussian white noise is considered. Using the blockwise Stein method, a penalized profile likelihood with a data-driven
penalization is introduced so that the estimator of the center of symmetry is defined as the maximizer of the penalized profile
likelihood. This estimator has the advantage of being independent of the functional class to which the signal f is assumed to belong and, furthermore, is shown to be semiparametrically adaptive and efficient.
Moreover, the second-order term of the risk expansion of the proposed estimator is proved to behave at least as well as the
second-order term of the risk of the best possible estimator using monotone smoothing filter. Under mild assumptions, this
estimator is shown to be second-order minimax sharp adaptive over the whole scale of Sobolev balls with smoothness β > 1. Thus, these results extend those of [10], where second-order asymptotic minimaxity is proved for an estimator depending
on the functional class containing f and β ≥ 2 is required.
相似文献
14.
The problem of estimation of an interest parameter in the presence of a nuisance parameter, which is either location or scale, is studied. Two estimators are considered: the usual maximum likelihood estimator and the estimator based on maximization of the integrated likelihood function. The estimators are compared, asymptotically, with respect to the bias and with respect to the mean squared error. The examples are given. 相似文献
15.
Empirical likelihood(EL) ratio statistic on θ = g(x) is constructed based on the inverse probability weighted imputation approach in a nonparametric regression model Y = g(x) + ε(x ∈ [0,1]p) with fixed designs and missing responses,which asymptotically has χ12 distribution.This result is used to obtain a EL based confidence interval on θ. 相似文献
16.
17.
针对响应变量缺失下的半参数回归模型,构造模型中未知参数的经验对数似然比统计量,证明了所提出的统计量具有渐近χ2分布,由此构造未知参数的置信域,并就置信域的覆盖概率及区间长度方面,通过模拟研究与最小二乘法进行优劣比较. 相似文献
18.
A. G. Belov 《Computational Mathematics and Modeling》2009,20(4):383-396
We investigate OLS parameter estimation for a linear paired model in the case of a passive experiment with errors in both
variables. The explicit form of the OLS estimates is obtained, their equivalence to maximum likelihood estimates is demonstrated
in the presence of normal errors, and estimate consistency is proved. The OLS estimates are compared analytically and numerically
with known parameter estimates of “direct,” “orthogonal,” and “diagonal” regression models. 相似文献
19.
Empirical likelihood for partial linear models 总被引:2,自引:0,他引:2
In this paper the empirical likelihood method due to Owen (1988,Biometrika,75, 237–249) is applied to partial linear random models. A nonparametric version of Wilks' theorem is derived. The theorem is
then used to construct confidence regions of the parameter vector in the partial linear models, which has correct asymptotic
coverage. A simulation study is conducted to compare the empirical likelihood and normal approximation based method.
Research supported by NNSF of China and a grant to the first author for his excellent Ph.D. dissertation work in China.
Research supported by Hong Kong RGC CERG No. HKUST6162/97P. 相似文献
20.
Andrew M. Raim Nagaraj K. Neerchal Jorge G. Morel 《Journal of computational and graphical statistics》2018,27(3):587-601
Finite mixture distributions arise in sampling a heterogeneous population. Data drawn from such a population will exhibit extra variability relative to any single subpopulation. Statistical models based on finite mixtures can assist in the analysis of categorical and count outcomes when standard generalized linear models (GLMs) cannot adequately express variability observed in the data. We propose an extension of GLMs where the response follows a finite mixture distribution and the regression of interest is linked to the mixture’s mean. This approach may be preferred over a finite mixture of regressions when the population mean is of interest; here, only one regression must be specified and interpreted in the analysis. A technical challenge is that the mixture’s mean is a composite parameter that does not appear explicitly in the density. The proposed model maintains its link to the regression through a certain random effects structure and is completely likelihood-based. We consider typical GLM cases where means are either real-valued, constrained to be positive, or constrained to be on the unit interval. The resulting model is applied to two example datasets through Bayesian analysis. Supporting the extra variation is seen to improve residual plots and produce widened prediction intervals reflecting the uncertainty. Supplementary materials for this article are available online. 相似文献