Abstract We use moderate deviations to study the signal detection problem for a diffusion model. We establish a moderate deviation principle for the log-likelihood function of the diffusion model. Then applying the mo...Abstract We use moderate deviations to study the signal detection problem for a diffusion model. We establish a moderate deviation principle for the log-likelihood function of the diffusion model. Then applying the moderate deviation estimates to hypothesis testing for signal detection problem we give a decision region such that its error probability of the second kind tends to zero with faster speed than the error probability of the first kind when the error probability of the first kind is approximated by e-ατ（T）, where α〉 0, τ（T） = o（T） and τ（T）→∞ as the observation time T goes to infinity.展开更多
Sample size determination is commonly encountered in modern medical studies for two inde- pendent binomial experiments. A new approach for calculating sample size is developed by combining Bayesian and frequentist ide...Sample size determination is commonly encountered in modern medical studies for two inde- pendent binomial experiments. A new approach for calculating sample size is developed by combining Bayesian and frequentist idea when a hypothesis test between two binomial proportions is conducted. Sample size is calculated according to Bayesian posterior decision function and power of the most powerful test under 0-1 loss function. Sample sizes are investigated for two cases that two proportions are equal to some fixed value or a random value. A simulation study and a real example are used to illustrate the proposed methodologies.展开更多
The authors consider the partially linear model relating a response Y to predictors （x, T） with a mean function x^Tβ0 ＋ g（T） when the x＇s are measured with an additive error. The estimators of parameter β0 are...The authors consider the partially linear model relating a response Y to predictors （x, T） with a mean function x^Tβ0 ＋ g（T） when the x＇s are measured with an additive error. The estimators of parameter β0 are derived by using the nearest neighbor-generalized randomly weighted least absolute deviation （LAD for short） method. The resulting estimator of the unknown vector 30 is shown to be consistent and asymptotically normal. In addition, the results facilitate the construction of confidence regions and the hypothesis testing for the unknown parameters. Extensive simulations are reported, showing that the proposed method works well in practical settings. The proposed methods are also applied to a data set from the study of an AIDS clinical trial group.展开更多
基金supported by National Natural Science Foundation of China (Grant Nos.10871153 and 11171262)the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 200804860048)
文摘Abstract We use moderate deviations to study the signal detection problem for a diffusion model. We establish a moderate deviation principle for the log-likelihood function of the diffusion model. Then applying the moderate deviation estimates to hypothesis testing for signal detection problem we give a decision region such that its error probability of the second kind tends to zero with faster speed than the error probability of the first kind when the error probability of the first kind is approximated by e-ατ（T）, where α〉 0, τ（T） = o（T） and τ（T）→∞ as the observation time T goes to infinity.
基金This research is supported by the National Natural Science Foundation of China under Grant Nos. 10761011, 10961026, Ph.D. Special Scientific Research Foundation of Chinese University under Grant No. 20060673002, and by program for New Century Excellent Talents in University （NCET-07-0737）.
文摘Sample size determination is commonly encountered in modern medical studies for two inde- pendent binomial experiments. A new approach for calculating sample size is developed by combining Bayesian and frequentist idea when a hypothesis test between two binomial proportions is conducted. Sample size is calculated according to Bayesian posterior decision function and power of the most powerful test under 0-1 loss function. Sample sizes are investigated for two cases that two proportions are equal to some fixed value or a random value. A simulation study and a real example are used to illustrate the proposed methodologies.
文摘The authors consider the partially linear model relating a response Y to predictors （x, T） with a mean function x^Tβ0 ＋ g（T） when the x＇s are measured with an additive error. The estimators of parameter β0 are derived by using the nearest neighbor-generalized randomly weighted least absolute deviation （LAD for short） method. The resulting estimator of the unknown vector 30 is shown to be consistent and asymptotically normal. In addition, the results facilitate the construction of confidence regions and the hypothesis testing for the unknown parameters. Extensive simulations are reported, showing that the proposed method works well in practical settings. The proposed methods are also applied to a data set from the study of an AIDS clinical trial group.
