The Experts below are selected from a list of 66 Experts worldwide ranked by ideXlab platform
Arnak S. Dalalyan - One of the best experts on this subject based on the ideXlab platform.
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Minimax testing of a Composite Null Hypothesis defined via a quadratic functional in the model of regression
Electronic journal of statistics, 2013Co-Authors: Laëtitia Comminges, Arnak S. DalalyanAbstract:We consider the problem of testing a particular type of Composite Null Hypothesis under a nonparametric multivariate regression model. For a given quadratic functional $Q$, the Null Hypothesis states that the regression function $f$ satisfies the constraint $Q[f]=0$, while the alternative corresponds to the functions for which $Q[f]$ is bounded away from zero. On the one hand, we provide minimax rates of testing and the exact separation constants, along with a sharp-optimal testing procedure, for diagonal and nonnegative quadratic functionals. We consider smoothness classes of ellipsoidal form and check that our conditions are fulfilled in the particular case of ellipsoids corresponding to anisotropic Sobolev classes. In this case, we present a closed form of the minimax rate and the separation constant. On the other hand, minimax rates for quadratic functionals which are neither positive nor negative makes appear two different regimes: ''regular'' and ''irregular''. In the ''regular" case, the minimax rate is equal to $n^{-1/4}$ while in the ''irregular'' case, the rate depends on the smoothness class and is slower than in the ''regular'' case. We apply this to the issue of testing the equality of norms of two functions observed in noisy environments.
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minimax testing of a Composite Null Hypothesis defined via a quadratic functional in the model of regression
Electronic Journal of Statistics, 2013Co-Authors: Laëtitia Comminges, Arnak S. DalalyanAbstract:We consider the problem of testing a particular type of Composite Null Hypothesis under a nonparametric multivariate regression model. For a given quadratic functional $Q$, the Null Hypothesis states that the regression function $f$ satisfies the constraint $Q[f]=0$, while the alternative corresponds to the functions for which $Q[f]$ is bounded away from zero. On the one hand, we provide minimax rates of testing and the exact separation constants, along with a sharp-optimal testing procedure, for diagonal and nonnegative quadratic functionals. We consider smoothness classes of ellipsoidal form and check that our conditions are fulfilled in the particular case of ellipsoids corresponding to anisotropic Sobolev classes. In this case, we present a closed form of the minimax rate and the separation constant. On the other hand, minimax rates for quadratic functionals which are neither positive nor negative makes appear two different regimes: “regular” and “irregular”. In the “regular" case, the minimax rate is equal to $n^{-1/4}$ while in the “irregular” case, the rate depends on the smoothness class and is slower than in the “regular” case. We apply this to the problem of testing the equality of Sobolev norms of two functions observed in noisy environments.
Nilanjan Chatterjee - One of the best experts on this subject based on the ideXlab platform.
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a powerful method for pleiotropic analysis under Composite Null Hypothesis identifies novel shared loci between type 2 diabetes and prostate cancer
PLOS Genetics, 2020Co-Authors: Debashree Ray, Nilanjan ChatterjeeAbstract:There is increasing evidence that pleiotropy, the association of multiple traits with the same genetic variants/loci, is a very common phenomenon. Cross-phenotype association tests are often used to jointly analyze multiple traits from a genome-wide association study (GWAS). The underlying methods, however, are often designed to test the global Null Hypothesis that there is no association of a genetic variant with any of the traits, the rejection of which does not implicate pleiotropy. In this article, we propose a new statistical approach, PLACO, for specifically detecting pleiotropic loci between two traits by considering an underlying Composite Null Hypothesis that a variant is associated with none or only one of the traits. We propose testing the Null Hypothesis based on the product of the Z-statistics of the genetic variants across two studies and derive a Null distribution of the test statistic in the form of a mixture distribution that allows for fractions of variants to be associated with none or only one of the traits. We borrow approaches from the statistical literature on mediation analysis that allow asymptotic approximation of the Null distribution avoiding estimation of nuisance parameters related to mixture proportions and variance components. Simulation studies demonstrate that the proposed method can maintain type I error and can achieve major power gain over alternative simpler methods that are typically used for testing pleiotropy. PLACO allows correlation in summary statistics between studies that may arise due to sharing of controls between disease traits. Application of PLACO to publicly available summary data from two large case-control GWAS of Type 2 Diabetes and of Prostate Cancer implicated a number of novel shared genetic regions: 3q23 (ZBTB38), 6q25.3 (RGS17), 9p22.1 (HAUS6), 9p13.3 (UBAP2), 11p11.2 (RAPSN), 14q12 (AKAP6), 15q15 (KNL1) and 18q23 (ZNF236).
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a powerful method for pleiotropic analysis under Composite Null Hypothesis identifies novel shared loci between type 2 diabetes and prostate cancer
bioRxiv, 2020Co-Authors: Debashree Ray, Nilanjan ChatterjeeAbstract:SO_SCPLOWUMMARYC_SCPLOWThere is increasing evidence that pleiotropy, the association of multiple traits with the same genetic variants/loci, is a very common phenomenon. Cross-phenotype association tests are often used to jointly analyze multiple traits from a GWAS. The underlying methods, however, are often designed to test the global Null Hypothesis that there is no association of a genetic variant with any of the traits, the rejection of which does not implicate pleiotropy. In this article, we propose a new statistical approach, PLACO, for specifically detecting pleiotropic loci between two traits by considering an underlying Composite Null Hypothesis that a variant is associated with none or only one of the traits. We propose testing the Null Hypothesis based on the product of the Z-statistics of the SNPs across two studies and derive a Null distribution of the test statistic in the form of a mixture distribution that allows for fractions of SNPs to be associated with none or only one of the traits. We borrow approaches from the statistical literature on mediation analysis that allow asymptotic approximation of the Null distribution avoiding estimation of nuisance parameters related to mixture proportions and variance components. Simulation studies demonstrate that the proposed method can maintain type I error and can achieve major power gain over alternative simpler methods that are typically used for testing pleiotropy. PLACO allows correlation in summary statistics between studies that may arise due to sharing of controls between disease traits. Application of PLACO to publicly available summary data from two large case-control GWAS of Type 2 Diabetes and of Prostate Cancer implicated a number of novel shared genetic regions near ZBTB38 (3q23), RGS17 (6q25.3), HAUS6 (9p22.1), UBAP2 (9p13.3), RAPSN (11p11.2), AKAP6 (14q12), KNL1 (15q15) and ZNF236 (18q23).
Laëtitia Comminges - One of the best experts on this subject based on the ideXlab platform.
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Minimax testing of a Composite Null Hypothesis defined via a quadratic functional in the model of regression
Electronic journal of statistics, 2013Co-Authors: Laëtitia Comminges, Arnak S. DalalyanAbstract:We consider the problem of testing a particular type of Composite Null Hypothesis under a nonparametric multivariate regression model. For a given quadratic functional $Q$, the Null Hypothesis states that the regression function $f$ satisfies the constraint $Q[f]=0$, while the alternative corresponds to the functions for which $Q[f]$ is bounded away from zero. On the one hand, we provide minimax rates of testing and the exact separation constants, along with a sharp-optimal testing procedure, for diagonal and nonnegative quadratic functionals. We consider smoothness classes of ellipsoidal form and check that our conditions are fulfilled in the particular case of ellipsoids corresponding to anisotropic Sobolev classes. In this case, we present a closed form of the minimax rate and the separation constant. On the other hand, minimax rates for quadratic functionals which are neither positive nor negative makes appear two different regimes: ''regular'' and ''irregular''. In the ''regular" case, the minimax rate is equal to $n^{-1/4}$ while in the ''irregular'' case, the rate depends on the smoothness class and is slower than in the ''regular'' case. We apply this to the issue of testing the equality of norms of two functions observed in noisy environments.
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minimax testing of a Composite Null Hypothesis defined via a quadratic functional in the model of regression
Electronic Journal of Statistics, 2013Co-Authors: Laëtitia Comminges, Arnak S. DalalyanAbstract:We consider the problem of testing a particular type of Composite Null Hypothesis under a nonparametric multivariate regression model. For a given quadratic functional $Q$, the Null Hypothesis states that the regression function $f$ satisfies the constraint $Q[f]=0$, while the alternative corresponds to the functions for which $Q[f]$ is bounded away from zero. On the one hand, we provide minimax rates of testing and the exact separation constants, along with a sharp-optimal testing procedure, for diagonal and nonnegative quadratic functionals. We consider smoothness classes of ellipsoidal form and check that our conditions are fulfilled in the particular case of ellipsoids corresponding to anisotropic Sobolev classes. In this case, we present a closed form of the minimax rate and the separation constant. On the other hand, minimax rates for quadratic functionals which are neither positive nor negative makes appear two different regimes: “regular” and “irregular”. In the “regular" case, the minimax rate is equal to $n^{-1/4}$ while in the “irregular” case, the rate depends on the smoothness class and is slower than in the “regular” case. We apply this to the problem of testing the equality of Sobolev norms of two functions observed in noisy environments.
Debashree Ray - One of the best experts on this subject based on the ideXlab platform.
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a powerful method for pleiotropic analysis under Composite Null Hypothesis identifies novel shared loci between type 2 diabetes and prostate cancer
PLOS Genetics, 2020Co-Authors: Debashree Ray, Nilanjan ChatterjeeAbstract:There is increasing evidence that pleiotropy, the association of multiple traits with the same genetic variants/loci, is a very common phenomenon. Cross-phenotype association tests are often used to jointly analyze multiple traits from a genome-wide association study (GWAS). The underlying methods, however, are often designed to test the global Null Hypothesis that there is no association of a genetic variant with any of the traits, the rejection of which does not implicate pleiotropy. In this article, we propose a new statistical approach, PLACO, for specifically detecting pleiotropic loci between two traits by considering an underlying Composite Null Hypothesis that a variant is associated with none or only one of the traits. We propose testing the Null Hypothesis based on the product of the Z-statistics of the genetic variants across two studies and derive a Null distribution of the test statistic in the form of a mixture distribution that allows for fractions of variants to be associated with none or only one of the traits. We borrow approaches from the statistical literature on mediation analysis that allow asymptotic approximation of the Null distribution avoiding estimation of nuisance parameters related to mixture proportions and variance components. Simulation studies demonstrate that the proposed method can maintain type I error and can achieve major power gain over alternative simpler methods that are typically used for testing pleiotropy. PLACO allows correlation in summary statistics between studies that may arise due to sharing of controls between disease traits. Application of PLACO to publicly available summary data from two large case-control GWAS of Type 2 Diabetes and of Prostate Cancer implicated a number of novel shared genetic regions: 3q23 (ZBTB38), 6q25.3 (RGS17), 9p22.1 (HAUS6), 9p13.3 (UBAP2), 11p11.2 (RAPSN), 14q12 (AKAP6), 15q15 (KNL1) and 18q23 (ZNF236).
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a powerful method for pleiotropic analysis under Composite Null Hypothesis identifies novel shared loci between type 2 diabetes and prostate cancer
bioRxiv, 2020Co-Authors: Debashree Ray, Nilanjan ChatterjeeAbstract:SO_SCPLOWUMMARYC_SCPLOWThere is increasing evidence that pleiotropy, the association of multiple traits with the same genetic variants/loci, is a very common phenomenon. Cross-phenotype association tests are often used to jointly analyze multiple traits from a GWAS. The underlying methods, however, are often designed to test the global Null Hypothesis that there is no association of a genetic variant with any of the traits, the rejection of which does not implicate pleiotropy. In this article, we propose a new statistical approach, PLACO, for specifically detecting pleiotropic loci between two traits by considering an underlying Composite Null Hypothesis that a variant is associated with none or only one of the traits. We propose testing the Null Hypothesis based on the product of the Z-statistics of the SNPs across two studies and derive a Null distribution of the test statistic in the form of a mixture distribution that allows for fractions of SNPs to be associated with none or only one of the traits. We borrow approaches from the statistical literature on mediation analysis that allow asymptotic approximation of the Null distribution avoiding estimation of nuisance parameters related to mixture proportions and variance components. Simulation studies demonstrate that the proposed method can maintain type I error and can achieve major power gain over alternative simpler methods that are typically used for testing pleiotropy. PLACO allows correlation in summary statistics between studies that may arise due to sharing of controls between disease traits. Application of PLACO to publicly available summary data from two large case-control GWAS of Type 2 Diabetes and of Prostate Cancer implicated a number of novel shared genetic regions near ZBTB38 (3q23), RGS17 (6q25.3), HAUS6 (9p22.1), UBAP2 (9p13.3), RAPSN (11p11.2), AKAP6 (14q12), KNL1 (15q15) and ZNF236 (18q23).
Sivagowry Sriananthakumar - One of the best experts on this subject based on the ideXlab platform.
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using point optimal test of a simple Null Hypothesis for testing a Composite Null Hypothesis via maximized monte carlo approach
Econometric Reviews, 2019Co-Authors: Sivagowry SriananthakumarAbstract:ABSTRACTKing’s Point Optimal (PO) test of a simple Null Hypothesis is useful in a number of ways, for example it can be used to trace the power envelope against which existing tests can be compared...
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using point optimal test of a simple Null Hypothesis for testing a Composite Null Hypothesis via maximized monte carlo approach
Econometric Reviews, 2019Co-Authors: Sivagowry SriananthakumarAbstract:King’s Point Optimal (PO) test of a simple Null Hypothesis is useful in a number of ways, for example it can be used to trace the power envelope against which existing tests can be compared. Howeve...
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a new approximate point optimal test of a Composite Null Hypothesis
Journal of Econometrics, 2006Co-Authors: Sivagowry Sriananthakumar, Maxwell L KingAbstract:In this paper, we use the generalized Neyman-Pearson lemma to introduce a new approximate point optimal test that can be used for testing a Composite Null Hypothesis against a Composite alternative. The new test involves finding multiple critical values. Two methods for obtaining these critical values are outlined. We report simulations of the application of this test to two Composite non-nested testing problems, namely testing for first-order moving average (MA(1)) errors against first-order autoregressive (AR(1)) errors in the linear regression model and testing for AR(1) errors against integrated MA(1) (IMA(1,1)) errors in the linear model. We compare the performance of the new test with Silvapulle and King's (1991) approximate point optimal test and some asymptotic tests and find that the new test has a clear advantage over the other tests, particularly for the second testing problem.