Dr. Yichuan Zhao is a Full Professor of Statistics, Georgia State University, Atlanta. He has a joint appointment as Associate Member of the Neuroscience Institute and he is also an affiliated faculty member of School of Public Health at Georgia State University. Dr. Zhao has a B.S. and an M.S. in Mathematics from Peking University, and an M.S. in Stochastics and Operations Research from Utrecht University. He received his Ph.D. in Statistics from the Department of Statistics at Florida State University. His current research interest focuses on survival analysis, empirical likelihood method, nonparametric statistics, statistical analysis of ROC curves, high-dimensional data analysis, bioinformatics, Monte Carlo methods, and statistical modeling of fuzzy systems. He has published 100 research articles in Statistics and Biostatistics research fields. Dr. Zhao has organized the Workshop Series on Biostatistics and Bioinformatics since its initiation in 2012. The ICSA Springer Book from the workshop can be found through New Frontiers of Biostatistics and Bioinformatics. He also organized the 25th ICSA Applied Statistics Symposium in Atlanta as chairs of organizing committee and program committee to great success. The ICSA Springer Book from the Symposium reflects new challenges in the contemporary data era, see the book: New Advances in Statistics and Data Science for details. A Springer Book reflects statistical modeling in biomedical research, see the book: Statistical Modeling in Biomedical Research . A Springer Book reflects advanced statistical methods for health research, see the book: Modern Statistical Methods for Health Research. He served on program committee of numerous statistical conferences, and is currently serving on the editorial board, for several statistical journals including Electronic Journal of Statistics and Journal of Applied Statistics. Dr. Zhao is a Fellow of the American Statistical Association and an elected member of the International Statistical Institute.
New Frontiers of Biostatistics and Bioinformatics, 2018
In this paper, a general regression model with responses missing at random is considered. From an... more In this paper, a general regression model with responses missing at random is considered. From an imputed rank-based objective function, a rank-based estimator is derived and its asymptotic distribution is established under mild conditions. Inference based on the normal approximation approach results in under coverage or over coverage issues. In order to address these issues, we propose an empirical likelihood approach based on the rank-based objective function, from which its asymptotic distribution is established. Extensive Monte Carlo simulation experiments under different settings of error distributions with different response probabilities are considered. The simulation results show that the proposed approach has better performance for the regression parameters compared to the normal approximation approach and its least-squares counterpart. Finally, a data example is provided to illustrate our method.
Journal of Statistical Planning and Inference, 2021
In constructing a confidence interval for the mean difference of two independent populations, we ... more In constructing a confidence interval for the mean difference of two independent populations, we may encounter the problem of having a low coverage probability when there are many zeros in the data, and the non-zero values are highly positively skewed. The violation of the normality assumption makes parametric methods inefficient in such cases. In this paper, jackknife empirical likelihood (JEL) and adjusted jackknife empirical likelihood (AJEL) methods are proposed to construct a nonparametric confidence interval for the mean difference of two independent zero-inflated skewed populations. The JEL and AJEL confidence intervals are compared with the confidence intervals by normal approximation and empirical likelihood proposed by Zhou and Zhou (2005). Simulation studies are performed to assess the new methods. Two real-life datasets are also used as an illustration of the proposed methodologies.
Left truncation and right truncation coexist in a truncated sample. Earlier researches focused on... more Left truncation and right truncation coexist in a truncated sample. Earlier researches focused on left truncation. Lagakos et al. (Biometrika 75:515–523, 1988) proposed to transform right truncated data to left truncated data and then apply the methods developed for left truncation. Interpretation of survival quantities, such as the hazard rate function, in reverse-time is not natural. Though it is most interpretable, researchers seldom use the forward-time hazard function. In this book chapter we studied the nonparametric inference for the hazard rate function with right truncated data. Kernel smoothing techniques were used to get smoothed estimates of hazard rates. Three commonly used kernels, uniform, Epanechnikov, and biweight kernels were applied on the AIDS data to illustrate the proposed methods.
Generalized additive partially linear models enjoy the simplicity of GLMs and the flexibility of ... more Generalized additive partially linear models enjoy the simplicity of GLMs and the flexibility of GAMs because they combine both parametric and nonparametric components. Based on spline-backfitted kernel estimator, we propose empirical likelihood (EL)-based pointwise confidence intervals and simultaneous confidence bands (SCBs) for the nonparametric component functions to make statistical inference. Simulation study strongly supports the asymptotic theory and shows that EL-based SCBs are much easier for implementation and have better performance than Wald-type SCBs. We apply the proposed method to a university retention study and provide SCBs for the effect of the students information.
2005 IEEE International Conference on Granular Computing, 2005
In recent years, the type-2 fuzzy sets theory has been used to model and minimize the effects of ... more In recent years, the type-2 fuzzy sets theory has been used to model and minimize the effects of uncertainties in rule-base fuzzy logic system. In order to make the type-2 fuzzy logic system reasonable and reliable, a new simple statistical linear method to decide interval-valued fuzzy membership functions and a new probability type reduce reasoning method for the interval-valued fuzzy logic system are proposed in this paper. An example of statistical interval-valued FLS is performed and results show that the developed method is more accurate to design a fuzzy logic system than type-1 method and computation is efficient.
Journal of Statistical Planning and Inference, 2018
Abstract The bivariate survival function plays an important role in multivariate survival analysi... more Abstract The bivariate survival function plays an important role in multivariate survival analysis. Using the idea of influence functions, we develop empirical likelihood confidence intervals for the bivariate survival function in the presence of univariate censoring. It is shown that the empirical log-likelihood ratio has an asymptotic standard chi-squared distribution with one degree of freedom. A comprehensive simulation study shows that the proposed method outperforms both the traditional normal approximation method and the adjusted empirical likelihood method in most cases. The Diabetic Retinopathy Data are analyzed for illustration of the proposed procedure.
ABSTRACT The Gini index has been widely used as a measure of income (or wealth) inequality in soc... more ABSTRACT The Gini index has been widely used as a measure of income (or wealth) inequality in social sciences. To construct a confidence interval for the difference of two Gini indices from the paired samples, Wang and Zhao [‘Jackknife Empirical Likelihood for Comparing Two Gini Indices’, The Canadian Journal of Statistics, 44(1), 102–119] used a profile jackknife empirical likelihood. However, the computing cost with the profile empirical likelihood could be very expensive. In this paper, we propose an alternative approach of the jackknife empirical likelihood method to reduce the computational cost. We also investigate the adjusted jackknife empirical likelihood and the bootstrap-calibrated jackknife empirical likelihood to improve coverage accuracy for small samples. Simulations show that the proposed methods perform better than Wang and Zhao's methods in terms of coverage accuracy and computational time. Real data applications demonstrate that the proposed methods work very well in practice.
For a continuous scale biomarker of binary disease status, the Youden index is a frequently used ... more For a continuous scale biomarker of binary disease status, the Youden index is a frequently used measurement of diagnostic accuracy in the context of the receiver operating characteristic curve and provides an optimal threshold for making diagnosis. The majority of existing inference methods for the Youden index are either parametric or bootstrap based. In the current paper, the empirical likelihood method for the Youden index is derived via defining novel smoothed estimating equations, and Wilks’ theorem for the empirical likelihood ratio statistic is established. Extensive simulation studies suggest that the chi-square calibrated empirical likelihood interval estimators are robust to model assumptions, enjoy computational efficiency and perform better than the bootstrap procedure almost uniformly across a variety of scenarios in terms of coverage probabilities.
Communications in Statistics - Simulation and Computation, 2015
ABSTRACT In this article, we apply the empirical likelihood method to make inference on the bivar... more ABSTRACT In this article, we apply the empirical likelihood method to make inference on the bivariate survival function of paired failure times by estimating the survival function of censored time with the Kaplan–Meier estimator. Adjusted empirical likelihood (AEL) confidence intervals for the bivariate survival function are developed. We conduct a simulation study to compare the proposed AEL method with other methods. The simulation study shows the proposed AEL method has better performance than other existing methods. We illustrate the proposed method by analyzing the skin graft data.
Journal of Statistical Planning and Inference, 2012
The transformation model plays an important role in survival analysis. In this paper, we investig... more The transformation model plays an important role in survival analysis. In this paper, we investigate the linear transformation model based on new empirical likelihood. Motivated by Fine et al.(1998) and Yu et al.(2011), we introduce the truncated survival time t0 and ...
New Frontiers of Biostatistics and Bioinformatics, 2018
In this paper, a general regression model with responses missing at random is considered. From an... more In this paper, a general regression model with responses missing at random is considered. From an imputed rank-based objective function, a rank-based estimator is derived and its asymptotic distribution is established under mild conditions. Inference based on the normal approximation approach results in under coverage or over coverage issues. In order to address these issues, we propose an empirical likelihood approach based on the rank-based objective function, from which its asymptotic distribution is established. Extensive Monte Carlo simulation experiments under different settings of error distributions with different response probabilities are considered. The simulation results show that the proposed approach has better performance for the regression parameters compared to the normal approximation approach and its least-squares counterpart. Finally, a data example is provided to illustrate our method.
Journal of Statistical Planning and Inference, 2021
In constructing a confidence interval for the mean difference of two independent populations, we ... more In constructing a confidence interval for the mean difference of two independent populations, we may encounter the problem of having a low coverage probability when there are many zeros in the data, and the non-zero values are highly positively skewed. The violation of the normality assumption makes parametric methods inefficient in such cases. In this paper, jackknife empirical likelihood (JEL) and adjusted jackknife empirical likelihood (AJEL) methods are proposed to construct a nonparametric confidence interval for the mean difference of two independent zero-inflated skewed populations. The JEL and AJEL confidence intervals are compared with the confidence intervals by normal approximation and empirical likelihood proposed by Zhou and Zhou (2005). Simulation studies are performed to assess the new methods. Two real-life datasets are also used as an illustration of the proposed methodologies.
Left truncation and right truncation coexist in a truncated sample. Earlier researches focused on... more Left truncation and right truncation coexist in a truncated sample. Earlier researches focused on left truncation. Lagakos et al. (Biometrika 75:515–523, 1988) proposed to transform right truncated data to left truncated data and then apply the methods developed for left truncation. Interpretation of survival quantities, such as the hazard rate function, in reverse-time is not natural. Though it is most interpretable, researchers seldom use the forward-time hazard function. In this book chapter we studied the nonparametric inference for the hazard rate function with right truncated data. Kernel smoothing techniques were used to get smoothed estimates of hazard rates. Three commonly used kernels, uniform, Epanechnikov, and biweight kernels were applied on the AIDS data to illustrate the proposed methods.
Generalized additive partially linear models enjoy the simplicity of GLMs and the flexibility of ... more Generalized additive partially linear models enjoy the simplicity of GLMs and the flexibility of GAMs because they combine both parametric and nonparametric components. Based on spline-backfitted kernel estimator, we propose empirical likelihood (EL)-based pointwise confidence intervals and simultaneous confidence bands (SCBs) for the nonparametric component functions to make statistical inference. Simulation study strongly supports the asymptotic theory and shows that EL-based SCBs are much easier for implementation and have better performance than Wald-type SCBs. We apply the proposed method to a university retention study and provide SCBs for the effect of the students information.
2005 IEEE International Conference on Granular Computing, 2005
In recent years, the type-2 fuzzy sets theory has been used to model and minimize the effects of ... more In recent years, the type-2 fuzzy sets theory has been used to model and minimize the effects of uncertainties in rule-base fuzzy logic system. In order to make the type-2 fuzzy logic system reasonable and reliable, a new simple statistical linear method to decide interval-valued fuzzy membership functions and a new probability type reduce reasoning method for the interval-valued fuzzy logic system are proposed in this paper. An example of statistical interval-valued FLS is performed and results show that the developed method is more accurate to design a fuzzy logic system than type-1 method and computation is efficient.
Journal of Statistical Planning and Inference, 2018
Abstract The bivariate survival function plays an important role in multivariate survival analysi... more Abstract The bivariate survival function plays an important role in multivariate survival analysis. Using the idea of influence functions, we develop empirical likelihood confidence intervals for the bivariate survival function in the presence of univariate censoring. It is shown that the empirical log-likelihood ratio has an asymptotic standard chi-squared distribution with one degree of freedom. A comprehensive simulation study shows that the proposed method outperforms both the traditional normal approximation method and the adjusted empirical likelihood method in most cases. The Diabetic Retinopathy Data are analyzed for illustration of the proposed procedure.
ABSTRACT The Gini index has been widely used as a measure of income (or wealth) inequality in soc... more ABSTRACT The Gini index has been widely used as a measure of income (or wealth) inequality in social sciences. To construct a confidence interval for the difference of two Gini indices from the paired samples, Wang and Zhao [‘Jackknife Empirical Likelihood for Comparing Two Gini Indices’, The Canadian Journal of Statistics, 44(1), 102–119] used a profile jackknife empirical likelihood. However, the computing cost with the profile empirical likelihood could be very expensive. In this paper, we propose an alternative approach of the jackknife empirical likelihood method to reduce the computational cost. We also investigate the adjusted jackknife empirical likelihood and the bootstrap-calibrated jackknife empirical likelihood to improve coverage accuracy for small samples. Simulations show that the proposed methods perform better than Wang and Zhao's methods in terms of coverage accuracy and computational time. Real data applications demonstrate that the proposed methods work very well in practice.
For a continuous scale biomarker of binary disease status, the Youden index is a frequently used ... more For a continuous scale biomarker of binary disease status, the Youden index is a frequently used measurement of diagnostic accuracy in the context of the receiver operating characteristic curve and provides an optimal threshold for making diagnosis. The majority of existing inference methods for the Youden index are either parametric or bootstrap based. In the current paper, the empirical likelihood method for the Youden index is derived via defining novel smoothed estimating equations, and Wilks’ theorem for the empirical likelihood ratio statistic is established. Extensive simulation studies suggest that the chi-square calibrated empirical likelihood interval estimators are robust to model assumptions, enjoy computational efficiency and perform better than the bootstrap procedure almost uniformly across a variety of scenarios in terms of coverage probabilities.
Communications in Statistics - Simulation and Computation, 2015
ABSTRACT In this article, we apply the empirical likelihood method to make inference on the bivar... more ABSTRACT In this article, we apply the empirical likelihood method to make inference on the bivariate survival function of paired failure times by estimating the survival function of censored time with the Kaplan–Meier estimator. Adjusted empirical likelihood (AEL) confidence intervals for the bivariate survival function are developed. We conduct a simulation study to compare the proposed AEL method with other methods. The simulation study shows the proposed AEL method has better performance than other existing methods. We illustrate the proposed method by analyzing the skin graft data.
Journal of Statistical Planning and Inference, 2012
The transformation model plays an important role in survival analysis. In this paper, we investig... more The transformation model plays an important role in survival analysis. In this paper, we investigate the linear transformation model based on new empirical likelihood. Motivated by Fine et al.(1998) and Yu et al.(2011), we introduce the truncated survival time t0 and ...
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Papers by Yichuan Zhao