Results 1  10
of
12
Quasi Maximum Likelihood Estimation of Structural Equation Models With Multiple Interaction and Quadratic Effects
"... The development of statistically efficient and computationally practicable estimation methods for the analysis of structural equation models with multiple nonlinear effects has been called for by substantive researchers in psychology, marketing research, and sociology. But the development of efficie ..."
Abstract

Cited by 14 (0 self)
 Add to MetaCart
(Show Context)
The development of statistically efficient and computationally practicable estimation methods for the analysis of structural equation models with multiple nonlinear effects has been called for by substantive researchers in psychology, marketing research, and sociology. But the development of efficient methods is complicated by the fact that a nonlinear model structure implies specifically nonnormal multivariate distributions for the indicator variables. In this paper, nonlinear structural equation models with quadratic forms are introduced and a new QuasiMaximum Likelihood method for simultaneous estimation of model parameters is developed with the focus on statistical efficiency and computational practicability. The QuasiML method is based on an approximation of the nonnormal density function of the joint indicator vector by a product of a normal and a conditionally normal density. The results of MonteCarlo studies for the new QuasiML method indicate that the parameter estimation is almost as efficient as ML estimation, whereas ML estimation is only computationally practical for elementary models. Also, the QuasiML method outperforms other currently available methods with respect to efficiency. It is demonstrated in a MonteCarlo study that the QuasiML method permits computationally feasible and very efficient analysis of models with multiple latent nonlinear effects. Finally, the applicability of the QuasiML method is illustrated by an empirical example of an aging study in psychology. Key words: structural equation modeling, quadratic form of normal variates, latent interaction effect, moderator effect, QuasiML estimation, variance function model. 1 1.
The phylogenetic KantorovichRubinstein metric for environmental sequence samples. Arxiv preprint arXiv:1005.1699
, 2010
"... Abstract. Using modern technology, it is now common to survey microbial communities by sequencing DNA or RNA extracted in bulk from a given environment. Comparative methods are needed that indicate the extent to which two communities differ given data sets of this type. UniFrac, a method built aroun ..."
Abstract

Cited by 8 (2 self)
 Add to MetaCart
(Show Context)
Abstract. Using modern technology, it is now common to survey microbial communities by sequencing DNA or RNA extracted in bulk from a given environment. Comparative methods are needed that indicate the extent to which two communities differ given data sets of this type. UniFrac, a method built around a somewhat ad hoc phylogeneticsbased distance between two communities, is one of the most commonly used tools for these analyses. We provide a foundation for such methods by establishing that if one equates a metagenomic sample with its empirical distribution on a reference phylogenetic tree, then the weighted UniFrac distance between two samples is just the classical KantorovichRubinstein (KR) distance between the corresponding empirical distributions. We demonstrate that this KR distance and extensions of it that arise from incorporating uncertainty in the location of sample points can be written as a readily computable integral over the tree, we develop Lp Zolotarevtype generalizations of the metric, and we show how the pvalue of the resulting natural permutation test of the null hypothesis “no difference between the two communities ” can be approximated using a functional of a Gaussian process indexed by the tree. We relate the L2 case to an ANOVAtype decomposition and find that the distribution of its associated Gaussian functional is that of a computable linear combination of independent χ2 1 random variables. 1.
On the Description of Spectrogram Probabilities with a ChiSquared Law
 IEEE Transactions on Signal Processing
"... law of probability always be used to describe a spectrogram coefficient distribution? If not, would a "chisquared description " lead to an acceptable amount of error when detection problems are to be faced in the timefrequency domain? The two questions prompted the study reported in this ..."
Abstract

Cited by 4 (0 self)
 Add to MetaCart
(Show Context)
law of probability always be used to describe a spectrogram coefficient distribution? If not, would a "chisquared description " lead to an acceptable amount of error when detection problems are to be faced in the timefrequency domain? The two questions prompted the study reported in this paper. After deriving the probability distribution of spectrogram coefficients in the context of a noncentred Gaussian correlated signal, the KullbackLeibler divergence is first used to evaluate to what extent the nonwhiteness of the signal and the Fourier analysis window impact the probability distribution of the spectrogram. To complete the analysis, a detection task formulated as a binary hypothesis test is considered. We evaluate the error committed on the probability of false alarm when the likelihood ratio test is expressed with chisquared laws. From these results, a chisquared description of the spectrogram distribution appears accurate when the analysis window used to construct the spectrogram decreases to zero at its boundaries, regardless of the level of correlation contained in the signal. When other analysis windows are used, the length of the window and the correlation contained in the analysed signal impact the validity of the chisquared description. Index Terms—Spectrogram probability distribution, Chisquared law, KullbackLeibler divergence, TimeFrequency statistical detection. I.
Sum OutageRate Maximization for MIMO Interference Channels
"... Abstract—In this paper, the weighted sum outagerate maximization for timeinvariant multipleinput multipleoutput (MIMO) interference channels is considered. The cumulative distribution function (CDF) of outage events in MIMO interference channels is characterized under the assumption of Gaussian ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
(Show Context)
Abstract—In this paper, the weighted sum outagerate maximization for timeinvariant multipleinput multipleoutput (MIMO) interference channels is considered. The cumulative distribution function (CDF) of outage events in MIMO interference channels is characterized under the assumption of Gaussian distribution for channel uncertainty. Based on the derived expression for the outage probability an iterative beam design algorithm for maximizing the weighted sum outagerate under outage constraints is newly proposed. Numerical results show that the proposed algorithm shows good sum outagerate performance. I.
EFFECT OF SOME ESTIMATORS ON A LARGE SAMPLE APPROXIMATION TO THE NONNULL DISTRIBUTION OF THE
, 1985
"... m 1111122 ..."
Measuring the Reliability of the Average Estimated Variance
"... In this dissertation an attempt is made to provide tools for evaluating the reliability of decisions based on the AEV for model selection in the general linear model setting. criterion The traditional distribution theory approach to such an evaluation is shown to be intractable due to the complex na ..."
Abstract
 Add to MetaCart
In this dissertation an attempt is made to provide tools for evaluating the reliability of decisions based on the AEV for model selection in the general linear model setting. criterion The traditional distribution theory approach to such an evaluation is shown to be intractable due to the complex nature of the joint distribution of the AEV's. A perturbation/conditional risk approach is developed which utilizes the idea of perturbing the observed data and determining the proportion of decisions based on perturbed data which differ from the decision based on the original data. The,proportion of changed decisions is shown to be a conditional risk function for an appropriately defined loss function.
21(5) Replace (1 ~ by (1 _ ~)2 •
"... the Office of Naval Research under Contract No. NR042031 for research in probability and statistics at Chapel Hill. Reproduction for any purpose of the United States Government is permitted. ..."
Abstract
 Add to MetaCart
the Office of Naval Research under Contract No. NR042031 for research in probability and statistics at Chapel Hill. Reproduction for any purpose of the United States Government is permitted.
Outage Probability and OutageBased Robust Beamforming for MIMO Interference Channels with Imperfect Channel State Information
"... Abstract—In this paper, the outage probability and outagebased beam design for multipleinput multipleoutput (MIMO) interference channels are considered. First, closedform expressions for the outage probability in MIMO interference channels are derived under the assumption of Gaussiandistribute ..."
Abstract
 Add to MetaCart
(Show Context)
Abstract—In this paper, the outage probability and outagebased beam design for multipleinput multipleoutput (MIMO) interference channels are considered. First, closedform expressions for the outage probability in MIMO interference channels are derived under the assumption of Gaussiandistributed channel state information (CSI) error, and the asymptotic behavior of the outage probability as a function of several system parameters is examined by using the Chernoff bound. It is shown that the outage probability decreases exponentially with respect to the quality of CSI measured by the inverse of the mean square error of CSI. Second, based on the derived outage probability expressions, an iterative beam design algorithm for maximizing the sum outage rate is proposed. Numerical results show that the proposed beam design algorithm yields significantly better sum outage rate performance than conventional algorithms such as interference alignment developed under the assumption of perfect CSI. Index Terms—Multiuser MIMO, interference channels, channel uncertainty, outage probability, Chernoff bound, interference alignment. I.