We propose the maximin efficiency robust test（MERT） for multiple nuisance parameters based on theories about the maximin efficiency robust test for only one nuisance parameter and investigate some theoretical proper...We propose the maximin efficiency robust test（MERT） for multiple nuisance parameters based on theories about the maximin efficiency robust test for only one nuisance parameter and investigate some theoretical properties about this robust test.We explore some theoretical properties about the power of the MERT for multiple nuisance parameters in a specified scenario intuitively further more.We also propose a meaningful example from statistical genetic field to which the MERT for multiple nuisance parameters can be well applied.Extensive simulation studies are conducted to testify the robustness of the MERT for multiple nuisance parameters.展开更多
Consider a distribution with several parameters whose exact values are unknown and need to be estimated using the maximum-likelihood technique. Under a regular case of estimation, it is fairly routine to construct a c...Consider a distribution with several parameters whose exact values are unknown and need to be estimated using the maximum-likelihood technique. Under a regular case of estimation, it is fairly routine to construct a confidence region for all such parameters, based on the natural logarithm of the corresponding likelihood function. In this article, we investigate the case of doing this for only some of these parameters, assuming that the remaining (so called nuisance) parameters are of no interest to us. This is to be done at a chosen level of confidence, maintaining the usual accuracy of this procedure (resulting in about 1% error for samples of size , and further decreasing with 1/n). We provide a general solution to this problem, demonstrating it by many explicit examples.展开更多
A nuisance parameter is introduced to the semimartingale regression model proposed by Aalen(1980), and we construct two estimators for this nuisance parameter based on the results ofparametric estimation which were gi...A nuisance parameter is introduced to the semimartingale regression model proposed by Aalen(1980), and we construct two estimators for this nuisance parameter based on the results ofparametric estimation which were given by Mckeague (1986) using the method of sieves. Theconsistency of the estimators is also provided.展开更多
We discuss formulas and techniques for finding maximum-likelihood estimators of parameters of autoregressive (with particular emphasis on Markov and Yule) models, computing their asymptotic variance-covariance matrix ...We discuss formulas and techniques for finding maximum-likelihood estimators of parameters of autoregressive (with particular emphasis on Markov and Yule) models, computing their asymptotic variance-covariance matrix and displaying the resulting confidence regions;Monte Carlo simulation is then used to establish the accuracy of the corresponding level of confidence. The results indicate that a direct application of the Central Limit Theorem yields errors too large to be acceptable;instead, we recommend using a technique based directly on the natural logarithm of the likelihood function, verifying its substantially higher accuracy. Our study is then extended to the case of estimating only a subset of a model’s parameters, when the remaining ones (called nuisance) are of no interest to us.展开更多
基金supported by the Natural Science Foundation of China(11401240,11471135)the self-determined research funds of CCNU from the colleges’basic research of MOE(CCNU15A05038,CCNU15ZD011)
文摘We propose the maximin efficiency robust test（MERT） for multiple nuisance parameters based on theories about the maximin efficiency robust test for only one nuisance parameter and investigate some theoretical properties about this robust test.We explore some theoretical properties about the power of the MERT for multiple nuisance parameters in a specified scenario intuitively further more.We also propose a meaningful example from statistical genetic field to which the MERT for multiple nuisance parameters can be well applied.Extensive simulation studies are conducted to testify the robustness of the MERT for multiple nuisance parameters.
文摘Consider a distribution with several parameters whose exact values are unknown and need to be estimated using the maximum-likelihood technique. Under a regular case of estimation, it is fairly routine to construct a confidence region for all such parameters, based on the natural logarithm of the corresponding likelihood function. In this article, we investigate the case of doing this for only some of these parameters, assuming that the remaining (so called nuisance) parameters are of no interest to us. This is to be done at a chosen level of confidence, maintaining the usual accuracy of this procedure (resulting in about 1% error for samples of size , and further decreasing with 1/n). We provide a general solution to this problem, demonstrating it by many explicit examples.
文摘A nuisance parameter is introduced to the semimartingale regression model proposed by Aalen(1980), and we construct two estimators for this nuisance parameter based on the results ofparametric estimation which were given by Mckeague (1986) using the method of sieves. Theconsistency of the estimators is also provided.
文摘We discuss formulas and techniques for finding maximum-likelihood estimators of parameters of autoregressive (with particular emphasis on Markov and Yule) models, computing their asymptotic variance-covariance matrix and displaying the resulting confidence regions;Monte Carlo simulation is then used to establish the accuracy of the corresponding level of confidence. The results indicate that a direct application of the Central Limit Theorem yields errors too large to be acceptable;instead, we recommend using a technique based directly on the natural logarithm of the likelihood function, verifying its substantially higher accuracy. Our study is then extended to the case of estimating only a subset of a model’s parameters, when the remaining ones (called nuisance) are of no interest to us.
