N Rao Chaganty - Profile on Academia.edu (original) (raw)
Papers by N Rao Chaganty
Letters to the Editor: Chaganty, N. R. (1993), "Comment," the American Statistician, 47,158: Comments by Bancroft and Neudecker and Liu with response by Chaganty and Vaish
A Note on "A Matrix Formulation on How Deviant an Observation Can Be
Linear Algebra and its Applications, Sep 1, 2004
Let X be distributed as matrix normal with mean M and covariance matrix W ⊗ V, where W and V are ... more Let X be distributed as matrix normal with mean M and covariance matrix W ⊗ V, where W and V are nonnegative definite (nnd) matrices. In this paper we present a simple version of the Cochran's theorem for matrix quadratic forms in X. The theorem is used to characterize the class of nnd matrices W such that the matrix quadratic forms that occur in multivariate analysis of variance are independent and Wishart except for a scale factor.
What can go wrong when ignoring correlation bounds in the use of generalized estimating equations
Statistics in Medicine, Aug 4, 2010
The analysis of repeated measure or clustered data is often complicated by the presence of correl... more The analysis of repeated measure or clustered data is often complicated by the presence of correlation. Further complications arise for discrete responses, where the marginal probability-dependent Fréchet bounds impose feasibility limits on the correlation that are often more restrictive than the positive definite range. Some popular statistical methods, such as generalized estimating equations (GEE), ignore these bounds, and as such can generate erroneous estimates and lead to incorrect inferential results. In this paper, we discuss two alternative strategies: (i) using QIC to select a data-driven correlation value within the Fréchet bounds, and (ii) the use of likelihood-based latent variable modeling, such as multivariate probit, to get around the problem all together. We provide two examples of the repercussions of incorrectly using existing GEE software in the presence of correlated binary responses.
of Biometrics on “ Joint Regression Analysis for Discrete Longitudinal Data ” by Madsen and Fang From
Madsen and Fang (2010) recently presented their work using an approximate Gaussian copula in the ... more Madsen and Fang (2010) recently presented their work using an approximate Gaussian copula in the analysis of binary repeated measure data. In that work, they compared their estimation method to the generalized estimating equation (GEE) approach, finding among other things that the GEE estimator was more efficient than the maximum likelihood (ML) estimator in certain situations. We would like to inform readers of several points. The authors state (p. 2, Section 4) that they fit the GEE2 “alternating logistic regression” model assuming “an exchangeable correlation structure.” The alternating logistic regression model (Carey, Zeger, and Diggle, 1993) incorporates dependence using pairwise odds ratios, not correlations. The authors should have stated that they are using GEE with a working exchangeable correlation structure. We have verified this by obtaining identical results running SAS PROC GENMOD using GEE with exchangeable correlation. The authors present results from an analysis of...
In health and social science and other fields where count data analysis is important, zeroinflate... more In health and social science and other fields where count data analysis is important, zeroinflated models have been employed when the frequency of zero count is high (inflated). Due to multiple reasons, there are scenarios in which an additional count value of k > 0 occurs with high frequency. The zero-and k-inflated Poisson distribution model (ZkIP) is more appropriate for such situations. The ZkIP model is a mixture distribution with three components: degenerate distributions at 0 and k count and a Poisson distribution. In this article, we propose an alternative and computationally fast expectation-maximization (EM) algorithm to obtain the parameter estimates for grouped zero and k-inflated count data. The asymptotic standard errors are derived using the complete data approach. We compare the zero-and k-inflated Poisson model with its zero-inflated and non-inflated counterparts. The best model is selected based on commonly used criteria. The theoretical results are supplemented with the analysis of two real-life datasets from health sciences.
In health and social science and other fields where count data analysis is important, zeroinflate... more In health and social science and other fields where count data analysis is important, zeroinflated models have been employed when the frequency of zero count is high (inflated). Due to multiple reasons, there are scenarios in which an additional count value of k > 0 occurs with high frequency. The zero-and k-inflated Poisson distribution model (ZkIP) is more appropriate for such situations. The ZkIP model is a mixture distribution with three components: degenerate distributions at 0 and k count and a Poisson distribution. In this article, we propose an alternative and computationally fast expectation-maximization (EM) algorithm to obtain the parameter estimates for grouped zero and k-inflated count data. The asymptotic standard errors are derived using the complete data approach. We compare the zero-and k-inflated Poisson model with its zero-inflated and non-inflated counterparts. The best model is selected based on commonly used criteria. The theoretical results are supplemented with the analysis of two real-life datasets from health sciences.
Journal of statistical theory and practice, Nov 26, 2020
The construction of multivariate models for analyzing family data can be challenging due to the v... more The construction of multivariate models for analyzing family data can be challenging due to the various dependencies between family members. These models typically have parameters that are subject to intricate and stringent constraints, which make it more difficult to arrive at a proper estimation of these model parameters. Recently, vines and pair-copula constructions have been utilized in order to simplify construction of multivariate models for both continuous and discrete data. The pair-copula models break down the hierarchy of dependence into vines and employ bivariate or pair-copulas as "building bricks" to generate appropriate multivariate distributions. This paper discusses pair-copula methods to model the convoluted dependence structure and proposes using a C-Vine type copula to model the dependence among family members. Analysis of actual, real-world family data is presented to illustrate our models and estimation procedures.
Journal of Multivariate Analysis, Dec 1, 1986
An earlier paper by the authors (Chaganty and Sethuraman, Ann. of Probab. 13 (1985). 97-114) esta... more An earlier paper by the authors (Chaganty and Sethuraman, Ann. of Probab. 13 (1985). 97-114) established large deviation local limit theorems for arbitrary sequences of real valued random variables. This work showed clearly the connection between the Cramer series and large deviation rates. In this article we present large deviation local limit theorems for arbitrary multidimensional random variables based solely on conditions imposed on their moment generating functions. These results generalize the theorems of W. Richter (Theory Probab. Appl. 3 (1958), 1OO106) for sums of independent and identically distributed random vectors.
IFR results for repairable systems
Naval Research Logistics Quarterly, Dec 1, 1983
Consider a k-out-of-n system with independent repairable components. Assume that the repair and f... more Consider a k-out-of-n system with independent repairable components. Assume that the repair and failure distributions are exponential with parameters {μ1, ,μn} and {λ1, ,λn}, respectively. In this article we show that if λi – μi = Δ for all i then the life distribution of the system is increasing failure rate (IFR).
S2a. SECURITY CLASSIFICATION AUTHOG 6 ,,~jJJ 3. 01STftlBUTION/AVAILA"ILTY OF REPORT 2b. ECLSSIICA... more S2a. SECURITY CLASSIFICATION AUTHOG 6 ,,~jJJ 3. 01STftlBUTION/AVAILA"ILTY OF REPORT 2b. ECLSSIICA1ONIOWNRAD EA Approved for public release; 2b. ECLASIFA~iO/DOWGRA10W EU Rdistribution unlimited. 4. PERFORMING ORGANtIZATION REPORT NUMB"(5) S. MONITORING ORGANIZATION REPORT NUMBER(S) ARO 24834.2-MA Ga B. NAME OF PERFORMING ORGANIZATION 6b. OFFICE SYMBOL 7a. NAME OF MONITORING ORGANIZATION Old Dominion University (If eppkiablo) U .Am eerhOfc 6_ c. ADDRESS (city. state, aMd ZIP Cods) 7b. ADDRESS (City, State, and ZIP Code) NoflV.25806 P. 0. Box 12211 = Nofolk VA 35080369Research Triangle Park, NC 27709-2211 Ba. NAME OF FUNDING ISPONSORING Bb. OFFICE SYMBOL 9. PROCUREMENT INSTRUMENT IDENTIFICATION NUMBER ORGAIZATON if OP*&b1*)DAAL03-88-C-0076 8c-ADDRESS (City, Stats, and ZIPCo*s) 10. SOURCE OF FUNDING NUMBERSTAKWR UI P0.Bx121PROGRAM PROJECT TKWOKUI ELMN O O. NACCESSION NO.
On inequalities for outlier detection in statistical data analysis
Consider a k-out-of-n system with Independent repairable components. Assume that the repair and f... more Consider a k-out-of-n system with Independent repairable components. Assume that the repair and failure distributions are exponential with parameters n,...,Un and nI...,). It is shown that if A 1 -j 1 -A for all 1, then the distribution of system life is in1.
Multidimensional strong large deviation theorems
Journal of Statistical Planning and Inference, Nov 1, 1996
In this paper we obtain some local limit theorems for arbitrary sequences of random vectors. The ... more In this paper we obtain some local limit theorems for arbitrary sequences of random vectors. The local limit theorems give conditions on the characteristic functions of random vectors for their pseudo-density function to converge uniformly on bounded sets. We then use these theorems to obtain strong large deviation results for an arbitrary sequence of random vectors. Thus our paper establishes the connection between the local limit theorems and the strong limit theorems. We apply our results to the multivariate F-distribution.
Subjective Probability Models for Lifetimes. Fabio Spizzichino
Journal of the American Statistical Association, 2003
Thia documnent Mow bi..napovd08 0 EIM pub1ic wolocab and sale; its d1kUa in uunited.
In this paper we present a survey of large deviation local limit theorems for random vectors. We ... more In this paper we present a survey of large deviation local limit theorems for random vectors. We then establish a more extensive large deviation local limit theorem that requires somewhat weaker conditions even in the special cases proved earlier.
[Let's Make a Deal: The Player's Dilemma]: Rejoinder
The American Statistician, Nov 1, 1991
An empirically adjusted weighted ordered p-values meta-analysis method for large-scale simultaneous significance testing in genomic experiments
Research Methods in Medicine & Health Sciences
Background Meta-analysis is a popular approach for combining results from multiple studies invest... more Background Meta-analysis is a popular approach for combining results from multiple studies investigating the same questions. Meta-analysis has gained wide popularity in genomic analysis due to the availability of large volumes of genomic study results from public databases. In genomic meta-analysis, researchers, often, tend to combine p-values related to significance testing of a gene from multiple studies where thousands of genes are tested simultaneously. The traditional p-value combination approaches aim to find genes which are differentially expressed in at least one of studies. An alternative form of meta-analysis has, recently, gained popularity where the aim is to find genes that are consistently differentially expressed in a large number, possibly a majority, of studies. An approach based on weighted ordered p-values (WOP) has been developed, in the recent past, to perform the latter type of meta-analysis. Methods In this article, we discuss the limitations of the WOP meta-a...
Letters to the Editor: Chaganty, N. R. (1993), "Comment," the American Statistician, 47,158: Comments by Bancroft and Neudecker and Liu with response by Chaganty and Vaish
A Note on "A Matrix Formulation on How Deviant an Observation Can Be
Linear Algebra and its Applications, Sep 1, 2004
Let X be distributed as matrix normal with mean M and covariance matrix W ⊗ V, where W and V are ... more Let X be distributed as matrix normal with mean M and covariance matrix W ⊗ V, where W and V are nonnegative definite (nnd) matrices. In this paper we present a simple version of the Cochran's theorem for matrix quadratic forms in X. The theorem is used to characterize the class of nnd matrices W such that the matrix quadratic forms that occur in multivariate analysis of variance are independent and Wishart except for a scale factor.
What can go wrong when ignoring correlation bounds in the use of generalized estimating equations
Statistics in Medicine, Aug 4, 2010
The analysis of repeated measure or clustered data is often complicated by the presence of correl... more The analysis of repeated measure or clustered data is often complicated by the presence of correlation. Further complications arise for discrete responses, where the marginal probability-dependent Fréchet bounds impose feasibility limits on the correlation that are often more restrictive than the positive definite range. Some popular statistical methods, such as generalized estimating equations (GEE), ignore these bounds, and as such can generate erroneous estimates and lead to incorrect inferential results. In this paper, we discuss two alternative strategies: (i) using QIC to select a data-driven correlation value within the Fréchet bounds, and (ii) the use of likelihood-based latent variable modeling, such as multivariate probit, to get around the problem all together. We provide two examples of the repercussions of incorrectly using existing GEE software in the presence of correlated binary responses.
of Biometrics on “ Joint Regression Analysis for Discrete Longitudinal Data ” by Madsen and Fang From
Madsen and Fang (2010) recently presented their work using an approximate Gaussian copula in the ... more Madsen and Fang (2010) recently presented their work using an approximate Gaussian copula in the analysis of binary repeated measure data. In that work, they compared their estimation method to the generalized estimating equation (GEE) approach, finding among other things that the GEE estimator was more efficient than the maximum likelihood (ML) estimator in certain situations. We would like to inform readers of several points. The authors state (p. 2, Section 4) that they fit the GEE2 “alternating logistic regression” model assuming “an exchangeable correlation structure.” The alternating logistic regression model (Carey, Zeger, and Diggle, 1993) incorporates dependence using pairwise odds ratios, not correlations. The authors should have stated that they are using GEE with a working exchangeable correlation structure. We have verified this by obtaining identical results running SAS PROC GENMOD using GEE with exchangeable correlation. The authors present results from an analysis of...
In health and social science and other fields where count data analysis is important, zeroinflate... more In health and social science and other fields where count data analysis is important, zeroinflated models have been employed when the frequency of zero count is high (inflated). Due to multiple reasons, there are scenarios in which an additional count value of k > 0 occurs with high frequency. The zero-and k-inflated Poisson distribution model (ZkIP) is more appropriate for such situations. The ZkIP model is a mixture distribution with three components: degenerate distributions at 0 and k count and a Poisson distribution. In this article, we propose an alternative and computationally fast expectation-maximization (EM) algorithm to obtain the parameter estimates for grouped zero and k-inflated count data. The asymptotic standard errors are derived using the complete data approach. We compare the zero-and k-inflated Poisson model with its zero-inflated and non-inflated counterparts. The best model is selected based on commonly used criteria. The theoretical results are supplemented with the analysis of two real-life datasets from health sciences.
In health and social science and other fields where count data analysis is important, zeroinflate... more In health and social science and other fields where count data analysis is important, zeroinflated models have been employed when the frequency of zero count is high (inflated). Due to multiple reasons, there are scenarios in which an additional count value of k > 0 occurs with high frequency. The zero-and k-inflated Poisson distribution model (ZkIP) is more appropriate for such situations. The ZkIP model is a mixture distribution with three components: degenerate distributions at 0 and k count and a Poisson distribution. In this article, we propose an alternative and computationally fast expectation-maximization (EM) algorithm to obtain the parameter estimates for grouped zero and k-inflated count data. The asymptotic standard errors are derived using the complete data approach. We compare the zero-and k-inflated Poisson model with its zero-inflated and non-inflated counterparts. The best model is selected based on commonly used criteria. The theoretical results are supplemented with the analysis of two real-life datasets from health sciences.
Journal of statistical theory and practice, Nov 26, 2020
The construction of multivariate models for analyzing family data can be challenging due to the v... more The construction of multivariate models for analyzing family data can be challenging due to the various dependencies between family members. These models typically have parameters that are subject to intricate and stringent constraints, which make it more difficult to arrive at a proper estimation of these model parameters. Recently, vines and pair-copula constructions have been utilized in order to simplify construction of multivariate models for both continuous and discrete data. The pair-copula models break down the hierarchy of dependence into vines and employ bivariate or pair-copulas as "building bricks" to generate appropriate multivariate distributions. This paper discusses pair-copula methods to model the convoluted dependence structure and proposes using a C-Vine type copula to model the dependence among family members. Analysis of actual, real-world family data is presented to illustrate our models and estimation procedures.
Journal of Multivariate Analysis, Dec 1, 1986
An earlier paper by the authors (Chaganty and Sethuraman, Ann. of Probab. 13 (1985). 97-114) esta... more An earlier paper by the authors (Chaganty and Sethuraman, Ann. of Probab. 13 (1985). 97-114) established large deviation local limit theorems for arbitrary sequences of real valued random variables. This work showed clearly the connection between the Cramer series and large deviation rates. In this article we present large deviation local limit theorems for arbitrary multidimensional random variables based solely on conditions imposed on their moment generating functions. These results generalize the theorems of W. Richter (Theory Probab. Appl. 3 (1958), 1OO106) for sums of independent and identically distributed random vectors.
IFR results for repairable systems
Naval Research Logistics Quarterly, Dec 1, 1983
Consider a k-out-of-n system with independent repairable components. Assume that the repair and f... more Consider a k-out-of-n system with independent repairable components. Assume that the repair and failure distributions are exponential with parameters {μ1, ,μn} and {λ1, ,λn}, respectively. In this article we show that if λi – μi = Δ for all i then the life distribution of the system is increasing failure rate (IFR).
S2a. SECURITY CLASSIFICATION AUTHOG 6 ,,~jJJ 3. 01STftlBUTION/AVAILA"ILTY OF REPORT 2b. ECLSSIICA... more S2a. SECURITY CLASSIFICATION AUTHOG 6 ,,~jJJ 3. 01STftlBUTION/AVAILA"ILTY OF REPORT 2b. ECLSSIICA1ONIOWNRAD EA Approved for public release; 2b. ECLASIFA~iO/DOWGRA10W EU Rdistribution unlimited. 4. PERFORMING ORGANtIZATION REPORT NUMB"(5) S. MONITORING ORGANIZATION REPORT NUMBER(S) ARO 24834.2-MA Ga B. NAME OF PERFORMING ORGANIZATION 6b. OFFICE SYMBOL 7a. NAME OF MONITORING ORGANIZATION Old Dominion University (If eppkiablo) U .Am eerhOfc 6_ c. ADDRESS (city. state, aMd ZIP Cods) 7b. ADDRESS (City, State, and ZIP Code) NoflV.25806 P. 0. Box 12211 = Nofolk VA 35080369Research Triangle Park, NC 27709-2211 Ba. NAME OF FUNDING ISPONSORING Bb. OFFICE SYMBOL 9. PROCUREMENT INSTRUMENT IDENTIFICATION NUMBER ORGAIZATON if OP*&b1*)DAAL03-88-C-0076 8c-ADDRESS (City, Stats, and ZIPCo*s) 10. SOURCE OF FUNDING NUMBERSTAKWR UI P0.Bx121PROGRAM PROJECT TKWOKUI ELMN O O. NACCESSION NO.
On inequalities for outlier detection in statistical data analysis
Consider a k-out-of-n system with Independent repairable components. Assume that the repair and f... more Consider a k-out-of-n system with Independent repairable components. Assume that the repair and failure distributions are exponential with parameters n,...,Un and nI...,). It is shown that if A 1 -j 1 -A for all 1, then the distribution of system life is in1.
Multidimensional strong large deviation theorems
Journal of Statistical Planning and Inference, Nov 1, 1996
In this paper we obtain some local limit theorems for arbitrary sequences of random vectors. The ... more In this paper we obtain some local limit theorems for arbitrary sequences of random vectors. The local limit theorems give conditions on the characteristic functions of random vectors for their pseudo-density function to converge uniformly on bounded sets. We then use these theorems to obtain strong large deviation results for an arbitrary sequence of random vectors. Thus our paper establishes the connection between the local limit theorems and the strong limit theorems. We apply our results to the multivariate F-distribution.
Subjective Probability Models for Lifetimes. Fabio Spizzichino
Journal of the American Statistical Association, 2003
Thia documnent Mow bi..napovd08 0 EIM pub1ic wolocab and sale; its d1kUa in uunited.
In this paper we present a survey of large deviation local limit theorems for random vectors. We ... more In this paper we present a survey of large deviation local limit theorems for random vectors. We then establish a more extensive large deviation local limit theorem that requires somewhat weaker conditions even in the special cases proved earlier.
[Let's Make a Deal: The Player's Dilemma]: Rejoinder
The American Statistician, Nov 1, 1991
An empirically adjusted weighted ordered p-values meta-analysis method for large-scale simultaneous significance testing in genomic experiments
Research Methods in Medicine & Health Sciences
Background Meta-analysis is a popular approach for combining results from multiple studies invest... more Background Meta-analysis is a popular approach for combining results from multiple studies investigating the same questions. Meta-analysis has gained wide popularity in genomic analysis due to the availability of large volumes of genomic study results from public databases. In genomic meta-analysis, researchers, often, tend to combine p-values related to significance testing of a gene from multiple studies where thousands of genes are tested simultaneously. The traditional p-value combination approaches aim to find genes which are differentially expressed in at least one of studies. An alternative form of meta-analysis has, recently, gained popularity where the aim is to find genes that are consistently differentially expressed in a large number, possibly a majority, of studies. An approach based on weighted ordered p-values (WOP) has been developed, in the recent past, to perform the latter type of meta-analysis. Methods In this article, we discuss the limitations of the WOP meta-a...