| 1. |
- Ahmad, M. Rauf, et al.
(författare)
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A U-statistics Based Approach to Mean Testing for High Dimensional Multivariate Data Under Non-normality
- 2011
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- A test statistic is considered for testing a hypothesis for the mean vector for multivariate data, when the dimension of the vector, p, may exceed the number of vectors, n, and the underlying distribution need not necessarily be normal. With n, p large, and under mild assumptions, the statistic is shown to asymptotically follow a normal distribution. A by product of the paper is the approximate distribution of a quadratic form, based on the reformulation of well-known Box's approximation, under high-dimensional set up.
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| 2. |
- Ahmad, M. Rauf, et al.
(författare)
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Some Tests of Covariance Matrices for High Dimensional Multivariate Data
- 2011
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- Test statistics for sphericity and identity of the covariance matrix are presented, when the data are multivariate normal and the dimension, p, can exceed the sample size, n. Using the asymptotic theory of U-statistics, the test statistics are shown to follow an approximate normal distribution for large p, also when p >> n. The statistics are derived under very general conditions, particularly avoiding any strict assumptions on the traces of the unknown covariance matrix. Neither any relationship between n and p is assumed. The accuracy of the statistics is shown through simulation results, particularly emphasizing the case when p can be much larger than n. The validity of the commonly used assumptions for high-dimensional set up is also briefly discussed.
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| 3. |
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| 4. |
- Cengiz, Cigdem, et al.
(författare)
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High-dimensional profile analysis
- 2020
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- The three tests of profile analysis: test of parallelism, test of level and test of flatness have been studied. Likelihood ratio tests have been derived. Firstly, a traditional setting, where the sample size is greater than the dimension of the parameter space, is considered. Then, all tests have been derived in a high-dimensional setting. In high-dimensional data analysis, it is required to use some techniques to tackle the problems which arise with the dimensionality. We propose a dimension reduction method using scores which was first proposed by Läuter et al. (1996).
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| 5. |
- Filipiak, Katarzyna, et al.
(författare)
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Estimation under inequality constraints in univariate and multivariate linear models
- 2024
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- In this paper least squares and maximum likelihood estimates under univariate and multivariate linear models with a priori information related to maximum effects in the models are determined. Both loss functions (the least squares and negative log-likelihood) and the constraints are convex, so the convex optimization theory can be utilized to obtain estimates, which in this paper are called Safety belt estimates. In particular, the complementary slackness condition, common in convex optimization, implies two alternative types of solutions, strongly dependent on the data and the restriction.It is experimentally shown that, despite of the similarity to the ridge regression estimation under the univariate linear model, the Safety belt estimates behave usually better than estimates obtained via ridge regression. Moreover, concerning the multivariate model, the proposed technique represents a completely novel approach.
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| 6. |
- Gauraha, Niharika, et al.
(författare)
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Conditional Independence Models which are Totally Ordered
- 2018
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- The totally ordered conditional independence (TOCI) model N(K) is defined to be the set of all normal distributions on RI such that for each adjacent pair (Ki, Ki+1) K, the components of a multivariate normal vector x RI, indexed by the set difference { Ki+1 \ Ki } are mutually conditionally independent given the variables indexed by Ki. Here K = {K1 … Kq } is a totally ordered set of subsets of a finite index set I. It is shown that TOCI models constitute a proper subset of lattice conditional independence (LCI) models. It follows that like LCI models, for the TOCI models the likelihood function and parameter space can be factored into the products of conditional likelihood functions and disjoint parameter spaces, respectively, where each conditional likelihood function corresponds to an ordinary multivariate normal regression model.
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| 7. |
- Imori, Shinpei, et al.
(författare)
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On the mean and dispersion of the Moore-Penrose generalized inverse of a Wishart matrix
- 2019
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- The Moore-Penrose inverse of a singular Wishart matrix is studied. When the scale matrix equals the identity matrix the mean and dispersion matrices of the Moore-Penrose inverse are known. When the scale matrix has an arbitrary structure no exact results are available. We complement the existing literature by deriving upper and lower bounds for the expectation and an upper bound for the dispersion of the Moore-Penrose inverse. The results show that the bounds become large when the number of rows (columns) of the Wishart matrix are close to the degrees of freedom of the distribution.
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| 8. |
- Li, Ying, et al.
(författare)
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A Two Step Model for Linear Prediction with Group Effect
- 2011
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- In this article, we consider prediction of a univariate response from background data. The data may have a near-collinear structure and additionally group effects are assumed to exist. A two step estimation procedure is proposed. The first step is to summarize the information in the predictors via a bilinear model. The bilinear model has a Krylov structured within individual design matrix, which is the link to classical partial least squares (PLS) analysis and a between individual design matrix which handles group effects. The second step is the prediction step where a conditional expectation approach is used. The two step approach gives new insight in PLS. Explicit maximum likelihood estimator of the dispersion matrix and mean for the predictors are derived under the assumption that the covariance between the response and explanatory variable is known. It is shown that the mean square error of the two step approach is always smaller than PLS.
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| 9. |
- Liang, Yuli, et al.
(författare)
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Hierarchical Models with Block Circular Covariance Structures
- 2013
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- Hierarchical linear models with a block circular covariance structure are considered. Sufficient conditions for obtaining explicit and unique estimators for the variance-covariance components are derived. Different restricted models are discussed and maximum likelihood estimators are presented.
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| 10. |
- Ngailo, Edward, 1982-, et al.
(författare)
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Approximation of misclassification probabilities in linear discriminant analysis with repeated measurements
- 2020
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- In this paper, we propose approximations for the probabilities of misclassification in linear discriminant analysis when means follow a growth curve structure. The discriminant function can classify a new observation vector of p repeated measurements into one of two multivariate normal populations with equal covariance matrix. We derive certain relations of the statistics under consideration in order to obtain approximations of the misclassification errors. Finally, we perform Monte Carlo simulations to evaluate the performance of proposed results.
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