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�ݺ�ߣshows by User: LuMao1 / http://www.slideshare.net/images/logo.gif �ݺ�ߣshows by User: LuMao1 / Thu, 12 Nov 2015 00:29:51 GMT �ݺ�ߣShare feed for �ݺ�ߣshows by User: LuMao1 Problem_Session_Notes /slideshow/problemsessionnotes-55019002/55019002 4d4927e1-e0bc-470a-98b2-a3669cf116c4-151112002951-lva1-app6892
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]]> Thu, 12 Nov 2015 00:29:51 GMT /slideshow/problemsessionnotes-55019002/55019002 LuMao1@slideshare.net(LuMao1) Problem_Session_Notes LuMao1 <img style="border:1px solid #C3E6D8;float:right;" alt="" src="https://cdn.slidesharecdn.com/ss_thumbnails/4d4927e1-e0bc-470a-98b2-a3669cf116c4-151112002951-lva1-app6892-thumbnail.jpg?width=120&height=120&fit=bounds" /><br>

Problem_Session_Notes from Lu Mao

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0 Strategies for setting futility analyses at multiple time points in clinical trials /slideshow/strategies-for-setting-futility-analyses/40567723 strategiesforsettingfutilityanalyses-141021181131-conversion-gate02
To be added later.]]>
To be added later.]]> Tue, 21 Oct 2014 18:11:31 GMT /slideshow/strategies-for-setting-futility-analyses/40567723 LuMao1@slideshare.net(LuMao1) Strategies for setting futility analyses at multiple time points in clinical trials LuMao1 To be added later. <img style="border:1px solid #C3E6D8;float:right;" alt="" src="https://cdn.slidesharecdn.com/ss_thumbnails/strategiesforsettingfutilityanalyses-141021181131-conversion-gate02-thumbnail.jpg?width=120&height=120&fit=bounds" /><br> To be added later.

Strategies for setting futility analyses at multiple time points in clinical trials from Lu Mao

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0 Rates of convergence in M-Estimation with an example from current status data /slideshow/m-estimation/40564262 mestimation-141021161623-conversion-gate02
In many statistical problems, estimators are derived from maximizing a data-dependent function of the parameter, usually in the form of an empirical average., e.g. the maximum likelihood and the least squares. For asymptotic studies, ordinary calculus fails if the parameter is non-Euclidean or has an infinite-dimensional component. In such cases, it becomes useful to capitalize on general M-estimation theorems formulated in terms of Banach-space-valued parameters. Although these theorems are constructed using sophisticated empirical processes results and arguments, the idea is usually simple enough to grasp. For example, if the objective function converges in probability to a limit function, then the estimator should also tend in probability to the maximizer of that limit function (consistency). Now, if a centered and re-scaled objective function that takes a centered and re-scaled parameter as argument converges weakly to a tight limit process, then the centered and re-scaled estimator should also tend weakly to the (hopefully tight) maximizer of that tight limit process. Along this line, it is clear that the proper re-scaling rate on the parameter (argument) should render the standardized objective function (in the form of an empirical process) asymptotically tight. Therefore, it is not surprising that the re-scaling rate is intimately related to the "modulus of continuity" of the empirical process. This is essentially the spirit of rate theorems such as Theorem 3.2.5 of van der Vaart and Wellner (1996) and Theorem 7.4 of van de Geer (2000), where technical tools such as the “peeling device” are employed to make the mathematics go through. This presentation tries to deliver the intuitive ideas behind the general M-estimation theory. For a complete and rigorous treatment, please refer to the relevant parts of Vaart and Wellner (1996) and van de Geer (2000), among others. An application with one-sample estimation in current status data is briefly described. For details, please refer to Groeneboom and Wellner, J. A. (1992). The slides were originally presented in the class STOR 831 Advanced Probability in Fall 2013 at UNC Chapel Hill as a final project. ]]>
In many statistical problems, estimators are derived from maximizing a data-dependent function of the parameter, usually in the form of an empirical average., e.g. the maximum likelihood and the least squares. For asymptotic studies, ordinary calculus fails if the parameter is non-Euclidean or has an infinite-dimensional component. In such cases, it becomes useful to capitalize on general M-estimation theorems formulated in terms of Banach-space-valued parameters. Although these theorems are constructed using sophisticated empirical processes results and arguments, the idea is usually simple enough to grasp. For example, if the objective function converges in probability to a limit function, then the estimator should also tend in probability to the maximizer of that limit function (consistency). Now, if a centered and re-scaled objective function that takes a centered and re-scaled parameter as argument converges weakly to a tight limit process, then the centered and re-scaled estimator should also tend weakly to the (hopefully tight) maximizer of that tight limit process. Along this line, it is clear that the proper re-scaling rate on the parameter (argument) should render the standardized objective function (in the form of an empirical process) asymptotically tight. Therefore, it is not surprising that the re-scaling rate is intimately related to the "modulus of continuity" of the empirical process. This is essentially the spirit of rate theorems such as Theorem 3.2.5 of van der Vaart and Wellner (1996) and Theorem 7.4 of van de Geer (2000), where technical tools such as the “peeling device” are employed to make the mathematics go through. This presentation tries to deliver the intuitive ideas behind the general M-estimation theory. For a complete and rigorous treatment, please refer to the relevant parts of Vaart and Wellner (1996) and van de Geer (2000), among others. An application with one-sample estimation in current status data is briefly described. For details, please refer to Groeneboom and Wellner, J. A. (1992). The slides were originally presented in the class STOR 831 Advanced Probability in Fall 2013 at UNC Chapel Hill as a final project. ]]> Tue, 21 Oct 2014 16:16:23 GMT /slideshow/m-estimation/40564262 LuMao1@slideshare.net(LuMao1) Rates of convergence in M-Estimation with an example from current status data LuMao1 In many statistical problems, estimators are derived from maximizing a data-dependent function of the parameter, usually in the form of an empirical average., e.g. the maximum likelihood and the least squares. For asymptotic studies, ordinary calculus fails if the parameter is non-Euclidean or has an infinite-dimensional component. In such cases, it becomes useful to capitalize on general M-estimation theorems formulated in terms of Banach-space-valued parameters. Although these theorems are constructed using sophisticated empirical processes results and arguments, the idea is usually simple enough to grasp. For example, if the objective function converges in probability to a limit function, then the estimator should also tend in probability to the maximizer of that limit function (consistency). Now, if a centered and re-scaled objective function that takes a centered and re-scaled parameter as argument converges weakly to a tight limit process, then the centered and re-scaled estimator should also tend weakly to the (hopefully tight) maximizer of that tight limit process. Along this line, it is clear that the proper re-scaling rate on the parameter (argument) should render the standardized objective function (in the form of an empirical process) asymptotically tight. Therefore, it is not surprising that the re-scaling rate is intimately related to the "modulus of continuity" of the empirical process. This is essentially the spirit of rate theorems such as Theorem 3.2.5 of van der Vaart and Wellner (1996) and Theorem 7.4 of van de Geer (2000), where technical tools such as the “peeling device” are employed to make the mathematics go through. This presentation tries to deliver the intuitive ideas behind the general M-estimation theory. For a complete and rigorous treatment, please refer to the relevant parts of Vaart and Wellner (1996) and van de Geer (2000), among others. An application with one-sample estimation in current status data is briefly described. For details, please refer to Groeneboom and Wellner, J. A. (1992). The slides were originally presented in the class STOR 831 Advanced Probability in Fall 2013 at UNC Chapel Hill as a final project. <img style="border:1px solid #C3E6D8;float:right;" alt="" src="https://cdn.slidesharecdn.com/ss_thumbnails/mestimation-141021161623-conversion-gate02-thumbnail.jpg?width=120&height=120&fit=bounds" /><br> In many statistical problems, estimators are derived from maximizing a data-dependent function of the parameter, usually in the form of an empirical average., e.g. the maximum likelihood and the least squares. For asymptotic studies, ordinary calculus fails if the parameter is non-Euclidean or has an infinite-dimensional component. In such cases, it becomes useful to capitalize on general M-estimation theorems formulated in terms of Banach-space-valued parameters. Although these theorems are constructed using sophisticated empirical processes results and arguments, the idea is usually simple enough to grasp. For example, if the objective function converges in probability to a limit function, then the estimator should also tend in probability to the maximizer of that limit function (consistency). Now, if a centered and re-scaled objective function that takes a centered and re-scaled parameter as argument converges weakly to a tight limit process, then the centered and re-scaled estimator should also tend weakly to the (hopefully tight) maximizer of that tight limit process. Along this line, it is clear that the proper re-scaling rate on the parameter (argument) should render the standardized objective function (in the form of an empirical process) asymptotically tight. Therefore, it is not surprising that the re-scaling rate is intimately related to the "modulus of continuity" of the empirical process. This is essentially the spirit of rate theorems such as Theorem 3.2.5 of van der Vaart and Wellner (1996) and Theorem 7.4 of van de Geer (2000), where technical tools such as the “peeling device” are employed to make the mathematics go through. This presentation tries to deliver the intuitive ideas behind the general M-estimation theory. For a complete and rigorous treatment, please refer to the relevant parts of Vaart and Wellner (1996) and van de Geer (2000), among others. An application with one-sample estimation in current status data is briefly described. For details, please refer to Groeneboom and Wellner, J. A. (1992). The slides were originally presented in the class STOR 831 Advanced Probability in Fall 2013 at UNC Chapel Hill as a final project.

Rates of convergence in M-Estimation with an example from current status data from Lu Mao

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0 Double Robustness: Theory and Applications with Missing Data /slideshow/dr-40559606/40559606 dr-141021142218-conversion-gate02
When data are missing at random (MAR), complete-case analysis with the full-data estimating equation is in general not valid. To correct the bias, we can employ the inverse probability weighting (IPW) technique on the complete cases. This requires modeling the missing pattern on the observed data (call it the $\pi$ model). The resulting IPW estimator, however, ignores information contained in cases with missing components, and is thus statistically inefficient. Efficiency can be improved by modifying the estimating equation along the lines of the semiparametric efficiency theory of Bickel et al. (1993). This modification usually requires modeling the distribution of the missing component on the observed ones (call it the $\mu$ model). Hence, when both the $\pi$ and the $\mu$ models are correct, the modified estimator is valid and is more efficient than the IPW one. In addition, the modified estimator is "doubly robust" in the sense that it is valid when either the $\pi$ model or the $\mu$ model is correct. Essential materials of the slides are extracted from the book "Semiparametric Theory and Missing Data" (Tsiatis, 2006). The slides were originally presented in the class BIOS 773 Statistical Analysis with Missing Data in Spring 2013 at UNC Chapel Hill as a final project.]]>
When data are missing at random (MAR), complete-case analysis with the full-data estimating equation is in general not valid. To correct the bias, we can employ the inverse probability weighting (IPW) technique on the complete cases. This requires modeling the missing pattern on the observed data (call it the $\pi$ model). The resulting IPW estimator, however, ignores information contained in cases with missing components, and is thus statistically inefficient. Efficiency can be improved by modifying the estimating equation along the lines of the semiparametric efficiency theory of Bickel et al. (1993). This modification usually requires modeling the distribution of the missing component on the observed ones (call it the $\mu$ model). Hence, when both the $\pi$ and the $\mu$ models are correct, the modified estimator is valid and is more efficient than the IPW one. In addition, the modified estimator is "doubly robust" in the sense that it is valid when either the $\pi$ model or the $\mu$ model is correct. Essential materials of the slides are extracted from the book "Semiparametric Theory and Missing Data" (Tsiatis, 2006). The slides were originally presented in the class BIOS 773 Statistical Analysis with Missing Data in Spring 2013 at UNC Chapel Hill as a final project.]]> Tue, 21 Oct 2014 14:22:18 GMT /slideshow/dr-40559606/40559606 LuMao1@slideshare.net(LuMao1) Double Robustness: Theory and Applications with Missing Data LuMao1 When data are missing at random (MAR), complete-case analysis with the full-data estimating equation is in general not valid. To correct the bias, we can employ the inverse probability weighting (IPW) technique on the complete cases. This requires modeling the missing pattern on the observed data (call it the $\pi$ model). The resulting IPW estimator, however, ignores information contained in cases with missing components, and is thus statistically inefficient. Efficiency can be improved by modifying the estimating equation along the lines of the semiparametric efficiency theory of Bickel et al. (1993). This modification usually requires modeling the distribution of the missing component on the observed ones (call it the $\mu$ model). Hence, when both the $\pi$ and the $\mu$ models are correct, the modified estimator is valid and is more efficient than the IPW one. In addition, the modified estimator is "doubly robust" in the sense that it is valid when either the $\pi$ model or the $\mu$ model is correct. Essential materials of the slides are extracted from the book "Semiparametric Theory and Missing Data" (Tsiatis, 2006). The slides were originally presented in the class BIOS 773 Statistical Analysis with Missing Data in Spring 2013 at UNC Chapel Hill as a final project. <img style="border:1px solid #C3E6D8;float:right;" alt="" src="https://cdn.slidesharecdn.com/ss_thumbnails/dr-141021142218-conversion-gate02-thumbnail.jpg?width=120&height=120&fit=bounds" /><br> When data are missing at random (MAR), complete-case analysis with the full-data estimating equation is in general not valid. To correct the bias, we can employ the inverse probability weighting (IPW) technique on the complete cases. This requires modeling the missing pattern on the observed data (call it the $\pi$ model). The resulting IPW estimator, however, ignores information contained in cases with missing components, and is thus statistically inefficient. Efficiency can be improved by modifying the estimating equation along the lines of the semiparametric efficiency theory of Bickel et al. (1993). This modification usually requires modeling the distribution of the missing component on the observed ones (call it the $\mu$ model). Hence, when both the $\pi$ and the $\mu$ models are correct, the modified estimator is valid and is more efficient than the IPW one. In addition, the modified estimator is "doubly robust" in the sense that it is valid when either the $\pi$ model or the $\mu$ model is correct. Essential materials of the slides are extracted from the book "Semiparametric Theory and Missing Data" (Tsiatis, 2006). The slides were originally presented in the class BIOS 773 Statistical Analysis with Missing Data in Spring 2013 at UNC Chapel Hill as a final project.

Double Robustness: Theory and Applications with Missing Data from Lu Mao

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0 https://cdn.slidesharecdn.com/profile-photo-LuMao1-48x48.jpg?cb=1475260958 https://cdn.slidesharecdn.com/ss_thumbnails/4d4927e1-e0bc-470a-98b2-a3669cf116c4-151112002951-lva1-app6892-thumbnail.jpg?width=320&height=320&fit=bounds slideshow/problemsessionnotes-55019002/55019002 Problem_Session_Notes https://cdn.slidesharecdn.com/ss_thumbnails/strategiesforsettingfutilityanalyses-141021181131-conversion-gate02-thumbnail.jpg?width=320&height=320&fit=bounds slideshow/strategies-for-setting-futility-analyses/40567723 Strategies for setting... https://cdn.slidesharecdn.com/ss_thumbnails/mestimation-141021161623-conversion-gate02-thumbnail.jpg?width=320&height=320&fit=bounds slideshow/m-estimation/40564262 Rates of convergence i...