Ebook: Local Variance Estimation for Uncensored and Censored Observations

Paola Gloria Ferrario develops and investigates several methods of nonparametric local variance estimation. The first two methods use regression estimations (plug-in), achieving least squares estimates as well as local averaging estimates (partitioning or kernel type). Furthermore, the author uses a partitioning method for the estimation of the local variance based on first and second nearest neighbors (instead of regression estimation). Approaching specific problems of application fields, all the results are extended and generalised to the case where only censored observations are available. Further, simulations have been executed comparing the performance of two different estimators (R-Code available!). As a possible application of the given theory the author proposes a survival analysis of patients who are treated for a specific illness.

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Paola Gloria Ferrario develops and investigates several methods of nonparametric local variance estimation. The first two methods use regression estimations (plug-in), achieving least squares estimates as well as local averaging estimates (partitioning or kernel type). Furthermore, the author uses a partitioning method for the estimation of the local variance based on first and second nearest neighbors (instead of regression estimation). Approaching specific problems of application fields, all the results are extended and generalised to the case where only censored observations are available. Further, simulations have been executed comparing the performance of two different estimators (R-Code available!). As a possible application of the given theory the author proposes a survival analysis of patients who are treated for a specific illness.

Contents

· Least Squares Estimation of the Local Variance via Plug-In

· Local Averaging Estimation of the Local Variance via Plug-In

· Partitioning Estimation of the Local Variance via Nearest Neighbors

· Estimation of the Local Variance under Censored Observations

Target Groups

· Researchers and graduate students in the fields of mathematics and statistics

· Practitioners in the fields of medicine, reliability, finance, and insurance

Author

Paola Gloria Ferrario received her doctorate degree (doctor rerum naturalium) from the University of Stuttgart, Germany, in 2012, after having studied Mathematical Engineering at the Polytechnic of Milano, Italy. She taught mathematics to students of economics at University of Hohenheim and now works as a researcher at the University of L?beck, Germany.

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Paola Gloria Ferrario develops and investigates several methods of nonparametric local variance estimation. The first two methods use regression estimations (plug-in), achieving least squares estimates as well as local averaging estimates (partitioning or kernel type). Furthermore, the author uses a partitioning method for the estimation of the local variance based on first and second nearest neighbors (instead of regression estimation). Approaching specific problems of application fields, all the results are extended and generalised to the case where only censored observations are available. Further, simulations have been executed comparing the performance of two different estimators (R-Code available!). As a possible application of the given theory the author proposes a survival analysis of patients who are treated for a specific illness.

Contents

· Least Squares Estimation of the Local Variance via Plug-In

· Local Averaging Estimation of the Local Variance via Plug-In

· Partitioning Estimation of the Local Variance via Nearest Neighbors

· Estimation of the Local Variance under Censored Observations

Target Groups

· Researchers and graduate students in the fields of mathematics and statistics

· Practitioners in the fields of medicine, reliability, finance, and insurance

Author

Paola Gloria Ferrario received her doctorate degree (doctor rerum naturalium) from the University of Stuttgart, Germany, in 2012, after having studied Mathematical Engineering at the Polytechnic of Milano, Italy. She taught mathematics to students of economics at University of Hohenheim and now works as a researcher at the University of L?beck, Germany.

Content:
Front Matter....Pages i-xvii
Introduction....Pages 1-17
Least Squares Estimation via Plug-In....Pages 19-29
Local Averaging Estimation via Plug-In....Pages 31-51
Partitioning Estimation via Nearest Neighbors....Pages 53-78
Local Variance Estimation for Censored Observations....Pages 79-116
Simulations....Pages 117-127
Back Matter....Pages 129-130

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Paola Gloria Ferrario develops and investigates several methods of nonparametric local variance estimation. The first two methods use regression estimations (plug-in), achieving least squares estimates as well as local averaging estimates (partitioning or kernel type). Furthermore, the author uses a partitioning method for the estimation of the local variance based on first and second nearest neighbors (instead of regression estimation). Approaching specific problems of application fields, all the results are extended and generalised to the case where only censored observations are available. Further, simulations have been executed comparing the performance of two different estimators (R-Code available!). As a possible application of the given theory the author proposes a survival analysis of patients who are treated for a specific illness.

Contents

· Least Squares Estimation of the Local Variance via Plug-In

· Local Averaging Estimation of the Local Variance via Plug-In

· Partitioning Estimation of the Local Variance via Nearest Neighbors

· Estimation of the Local Variance under Censored Observations

Target Groups

· Researchers and graduate students in the fields of mathematics and statistics

· Practitioners in the fields of medicine, reliability, finance, and insurance

Author

Paola Gloria Ferrario received her doctorate degree (doctor rerum naturalium) from the University of Stuttgart, Germany, in 2012, after having studied Mathematical Engineering at the Polytechnic of Milano, Italy. She taught mathematics to students of economics at University of Hohenheim and now works as a researcher at the University of L?beck, Germany.

Content:
Front Matter....Pages i-xvii
Introduction....Pages 1-17
Least Squares Estimation via Plug-In....Pages 19-29
Local Averaging Estimation via Plug-In....Pages 31-51
Partitioning Estimation via Nearest Neighbors....Pages 53-78
Local Variance Estimation for Censored Observations....Pages 79-116
Simulations....Pages 117-127
Back Matter....Pages 129-130
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