Pub Date : 2008-08-01DOI: 10.1142/S0219024908004919
H. Dette, D. Ziggel
In this paper a new and very simple method for monotone estimation of discount curves is proposed. The main idea of this approach is a simple modification of the commonly used (unconstrained) Mc-Culloch Spline. We construct an integrated density estimate from the predicted values of the discount curve. It can be shown that this statistic is an estimate of the inverse of the discount function and the final estimate can easily be obtained by a numerical inversion. The resulting procedure is extremely simple and we have implemented it in Excel and VBA, respectively. The performance is illustrated by three examples, in which the curve was previously estimated with an unconstrained McCulloch Spline.
{"title":"Discount curve estimation by monotonizing McCulloch Splines","authors":"H. Dette, D. Ziggel","doi":"10.1142/S0219024908004919","DOIUrl":"https://doi.org/10.1142/S0219024908004919","url":null,"abstract":"In this paper a new and very simple method for monotone estimation of discount curves is proposed. The main idea of this approach is a simple modification of the commonly used (unconstrained) Mc-Culloch Spline. We construct an integrated density estimate from the predicted values of the discount curve. It can be shown that this statistic is an estimate of the inverse of the discount function and the final estimate can easily be obtained by a numerical inversion. The resulting procedure is extremely simple and we have implemented it in Excel and VBA, respectively. The performance is illustrated by three examples, in which the curve was previously estimated with an unconstrained McCulloch Spline.","PeriodicalId":10841,"journal":{"name":"CTIT technical reports series","volume":"29 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2008-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91089557","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A drawback of robust statistical techniques is the increased computational effort often needed compared to non robust methods. Robust estimators possessing the exact fit property, for example, are NP-hard to compute. This means thatunder the widely believed assumption that the computational complexity classes NP and P are not equalthere is no hope to compute exact solutions for large high dimensional data sets. To tackle this problem, search heuristics are used to compute NP-hard estimators in high dimensions. Here, an evolutionary algorithm that is applicable to different robust estimators is presented. Further, variants of this evolutionary algorithm for selected estimatorsmost prominently least trimmed squares and least median of squaresare introduced and shown to outperform existing popular search heuristics in difficult data situations. The results increase the applicability of robust methods and underline the usefulness of evolutionary computation for computational statistics.
{"title":"Evolutionary algorithms for robust methods","authors":"Robin Nunkesser, Oliver Morell","doi":"10.17877/DE290R-12759","DOIUrl":"https://doi.org/10.17877/DE290R-12759","url":null,"abstract":"A drawback of robust statistical techniques is the increased computational effort often needed compared to non robust methods. Robust estimators possessing the exact fit property, for example, are NP-hard to compute. This means thatunder the widely believed assumption that the computational complexity classes NP and P are not equalthere is no hope to compute exact solutions for large high dimensional data sets. To tackle this problem, search heuristics are used to compute NP-hard estimators in high dimensions. Here, an evolutionary algorithm that is applicable to different robust estimators is presented. Further, variants of this evolutionary algorithm for selected estimatorsmost prominently least trimmed squares and least median of squaresare introduced and shown to outperform existing popular search heuristics in difficult data situations. The results increase the applicability of robust methods and underline the usefulness of evolutionary computation for computational statistics.","PeriodicalId":10841,"journal":{"name":"CTIT technical reports series","volume":"61 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2008-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72761979","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2008-01-01DOI: 10.3929/ETHZ-A-006824756
Boris Danev, Srdjan Capkun
Identification of wireless sensor nodes based on the physical characteristics of their radio transmissions can potentially provide additional layer of security in all-wireless multi-hop sensor networks. Reliable identification can be means for detection and/or prevention of wormhole, Sybil and replication attacks, and for complementing cryptographic message authentication protocols. In this paper, we propose an improved method for capturing and analysis of sensor node radio signals for reliable and accurate recognition. We investigate the performance accuracy of our approach in terms of parameters such as distance, antenna polarization, voltage and show that it achieves recognition with EER=0.24%. We also propose and perform practical attacks on the recognition to further evaluate the robustness of the proposed method under security threats.
{"title":"Physical-layer Identification of Wireless Sensor Nodes; ; Technical Report;","authors":"Boris Danev, Srdjan Capkun","doi":"10.3929/ETHZ-A-006824756","DOIUrl":"https://doi.org/10.3929/ETHZ-A-006824756","url":null,"abstract":"Identification of wireless sensor nodes based on the physical characteristics of their radio transmissions can potentially provide additional layer of security in all-wireless multi-hop sensor networks. Reliable identification can be means for detection and/or prevention of wormhole, Sybil and replication attacks, and for complementing cryptographic message authentication protocols. In this paper, we propose an improved method for capturing and analysis of sensor node radio signals for reliable and accurate recognition. We investigate the performance accuracy of our approach in terms of parameters such as distance, antenna polarization, voltage and show that it achieves recognition with EER=0.24%. We also propose and perform practical attacks on the recognition to further evaluate the robustness of the proposed method under security threats.","PeriodicalId":10841,"journal":{"name":"CTIT technical reports series","volume":"7 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2008-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89216216","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Almost sure convergence for ratios of delta functions establishes global and local strong consistency for a variety of estimates and data generations. For instance, the empirical probability function from independent identically distributed random vectors, the empirical distribution for univariate independent identically distributed observations, and the kernel hazard rate estimate for right-censored and left-truncated data are covered. The convergence rates derive from the Bennett-Hoeffding inequality.
{"title":"Strong consistency for delta sequence ratios","authors":"Wladyslaw Poniatowski, R. Weißbach","doi":"10.17877/DE290R-12770","DOIUrl":"https://doi.org/10.17877/DE290R-12770","url":null,"abstract":"Almost sure convergence for ratios of delta functions establishes global and local strong consistency for a variety of estimates and data generations. For instance, the empirical probability function from independent identically distributed random vectors, the empirical distribution for univariate independent identically distributed observations, and the kernel hazard rate estimate for right-censored and left-truncated data are covered. The convergence rates derive from the Bennett-Hoeffding inequality.","PeriodicalId":10841,"journal":{"name":"CTIT technical reports series","volume":"337 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2008-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75931567","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2008-01-01DOI: 10.3929/ETHZ-A-006733631
Rolf Adelsberger, R. Ziegler, M. Levoy, M. Gross
Using photographic flash for candid shots often results in an unevenly lit scene, in which objects in the back appear dark. We describe a spatially adaptive photographic flash system, in which the intensity of illumination varies depending on the depth and reflectivity of features in the scene. We adapt to changes in depth using a single-shot method, and to changes in reflectivity using a multi-shot method. The single-shot method requires only a depth image, whereas the multi-shot method requires at least one color image in addition to the depth data. To reduce noise in our depth images, we present a novel filter that takes into account the amplitude-dependent noise distribution of observed depth values. To demonstrate our ideas, we have built a prototype consisting of a depth camera, a flash light, an LCD and a lens. By attenuating the flash using the LCD, a variety of illumination effects can be achieved.
{"title":"Spatially adaptive photographic flash","authors":"Rolf Adelsberger, R. Ziegler, M. Levoy, M. Gross","doi":"10.3929/ETHZ-A-006733631","DOIUrl":"https://doi.org/10.3929/ETHZ-A-006733631","url":null,"abstract":"Using photographic flash for candid shots often results in an unevenly lit scene, in which objects in the back appear dark. We describe a spatially adaptive photographic flash system, in which the intensity of illumination varies depending on the depth and reflectivity of features in the scene. We adapt to changes in depth using a single-shot method, and to changes in reflectivity using a multi-shot method. The single-shot method requires only a depth image, whereas the multi-shot method requires at least one color image in addition to the depth data. To reduce noise in our depth images, we present a novel filter that takes into account the amplitude-dependent noise distribution of observed depth values. To demonstrate our ideas, we have built a prototype consisting of a depth camera, a flash light, an LCD and a lens. By attenuating the flash using the LCD, a variety of illumination effects can be achieved.","PeriodicalId":10841,"journal":{"name":"CTIT technical reports series","volume":"79 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2008-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75381518","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The Michaelis-Menten model has and continues to be one of the most widely used models in many diverse fields. In the biomedical sciences, the model continues to be ubiquitous in biochemistry, enzyme kinetics studies, nutrition science and in the pharmaceutical sciences. Despite its wide ranging applications across disciplines, design issues for this model are given short shrift. This paper focuses on design issues and provides a variety of optimal designs of this model. In addition, we evaluate robustness properties of the optimal designs under a variation in optimality criteria. To facilitate use of optimal design ideas in practice, we design a web site for generating and comparing dfferent types of tailor-made optimal designs and user-supplied designs for the Michaelis-Menten and related models.
{"title":"Robustness of optimal designs for the Michaelis-Menten model under a variation of criteria","authors":"H. Dette, C. Kiss, W. Wong","doi":"10.17877/DE290R-14159","DOIUrl":"https://doi.org/10.17877/DE290R-14159","url":null,"abstract":"The Michaelis-Menten model has and continues to be one of the most widely used models in many diverse fields. In the biomedical sciences, the model continues to be ubiquitous in biochemistry, enzyme kinetics studies, nutrition science and in the pharmaceutical sciences. Despite its wide ranging applications across disciplines, design issues for this model are given short shrift. This paper focuses on design issues and provides a variety of optimal designs of this model. In addition, we evaluate robustness properties of the optimal designs under a variation in optimality criteria. To facilitate use of optimal design ideas in practice, we design a web site for generating and comparing dfferent types of tailor-made optimal designs and user-supplied designs for the Michaelis-Menten and related models.","PeriodicalId":10841,"journal":{"name":"CTIT technical reports series","volume":"11 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2008-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72622666","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper we are concerned with shape restricted estimation in inverse regression problems with convolution-type operator. We use increasing rearrangements to compute increasingand convex estimates from an (in principle arbitrary) unconstrained estimate of the unknown regression function. An advantage of our approach is that it is not necessary that prior shape information is known to be valid on the complete domain of the regression function. Instead, it is sufficient if it holds on some compact interval. A simulation study shows that the shape restricted estimate on the respective interval is significantly less sensitive to moderate undersmoothing than the unconstrained estimate, which substantially improves applicability of estimates based on data-driven bandwidth estimators. Finally, we demonstrate the application of the increasing estimator by the estimation of the luminosity profile of an elliptical galaxy. Here, a major interest is in reconstructing the central peak of the profile, which, due to its small size, requires to select the bandwidth as small as possible.
{"title":"Shape constrained estimators in inverse regression models with convolution-type operator","authors":"M. Birke, N. Bissantz","doi":"10.17877/DE290R-15931","DOIUrl":"https://doi.org/10.17877/DE290R-15931","url":null,"abstract":"In this paper we are concerned with shape restricted estimation in inverse regression problems with convolution-type operator. We use increasing rearrangements to compute increasingand convex estimates from an (in principle arbitrary) unconstrained estimate of the unknown regression function. An advantage of our approach is that it is not necessary that prior shape information is known to be valid on the complete domain of the regression function. Instead, it is sufficient if it holds on some compact interval. A simulation study shows that the shape restricted estimate on the respective interval is significantly less sensitive to moderate undersmoothing than the unconstrained estimate, which substantially improves applicability of estimates based on data-driven bandwidth estimators. Finally, we demonstrate the application of the increasing estimator by the estimation of the luminosity profile of an elliptical galaxy. Here, a major interest is in reconstructing the central peak of the profile, which, due to its small size, requires to select the bandwidth as small as possible.","PeriodicalId":10841,"journal":{"name":"CTIT technical reports series","volume":"41 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2007-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74156219","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We develop a test of the hypothesis that the spectral densities of a number m, m ≥ 2, not necessarily independent time series are equal. The test proposed is based on an appropriate L2-distance measure between the nonparametrically estimated individual spectral densities and an overall, ’pooled’ spectral density, the later being obtained using the whole set of m time series considered. The limiting distribution of the test statistic under the null hypothesis of equal spectral densities is derived and a novel frequency domain bootstrap method is presented in order to approximate more accurately this distribution. The asymptotic distribution of the test and its power properties for fixed alternatives are investigated. Some simulations are presented and a real-life data example is discussed.
{"title":"Testing equality of spectral densities","authors":"H. Dette, Efstathios Paroditis","doi":"10.17877/DE290R-14177","DOIUrl":"https://doi.org/10.17877/DE290R-14177","url":null,"abstract":"We develop a test of the hypothesis that the spectral densities of a number m, m ≥ 2, not necessarily independent time series are equal. The test proposed is based on an appropriate L2-distance measure between the nonparametrically estimated individual spectral densities and an overall, ’pooled’ spectral density, the later being obtained using the whole set of m time series considered. The limiting distribution of the test statistic under the null hypothesis of equal spectral densities is derived and a novel frequency domain bootstrap method is presented in order to approximate more accurately this distribution. The asymptotic distribution of the test and its power properties for fixed alternatives are investigated. Some simulations are presented and a real-life data example is discussed.","PeriodicalId":10841,"journal":{"name":"CTIT technical reports series","volume":"11 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2007-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82395062","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In the common nonparametric regression model we consider the problem of constructing optimal designs, if the unknown curve is estimated by a smoothing spline. A new basis for the space of natural splines is derived, and the local minimax property for these splines is used to derive two optimality criteria for the construction of optimal designs. The first criterion determines the design for a most precise estimation of the coefficients in the spline representation and corresponds to D-optimality, while the second criterion is the G-criterion and corresponds to an accurate prediction of the curve. Several properties of the optimal designs are derived. In general D- and G-optimal designs are not equivalent. Optimal designs are determined numerically and compared with the uniform design.
{"title":"Optimal designs for smoothing splines","authors":"H. Dette, V. Melas, A. Pepelyshev","doi":"10.17877/DE290R-206","DOIUrl":"https://doi.org/10.17877/DE290R-206","url":null,"abstract":"In the common nonparametric regression model we consider the problem of constructing optimal designs, if the unknown curve is estimated by a smoothing spline. A new basis for the space of natural splines is derived, and the local minimax property for these splines is used to derive two optimality criteria for the construction of optimal designs. The first criterion determines the design for a most precise estimation of the coefficients in the spline representation and corresponds to D-optimality, while the second criterion is the G-criterion and corresponds to an accurate prediction of the curve. Several properties of the optimal designs are derived. In general D- and G-optimal designs are not equivalent. Optimal designs are determined numerically and compared with the uniform design.","PeriodicalId":10841,"journal":{"name":"CTIT technical reports series","volume":"32 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2007-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78602550","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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