Parsimonious Covariance Matrix Estimation for Longitudinal Data

Smith, Michael S.; Kohn, Robert

doi:10.1198/016214502388618942

Cited by 167 publications

(144 citation statements)

References 22 publications

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“…From the model identity y t = X t β t + A −1 t Λ t e t and using the lower triangular form of A t , we deduceỹ (Pinheiro and Bates 1996;Pourahmadi 1999;Smith and Kohn 2002). The construction has also appeared in time-varying covariance matrix modeling in VAR contexts (Cogley and Sargent 2005;Primiceri 2005;Lopes et al 2012) which is one point of departure here; this section uses the above Cholesky structure and embeds it in a novel LTM framework, combining models for stochastic time-variation in variance matrices with the natural threshold-based sparsity inducing mechanism to shrink subsets of the lower-triangle of A t to zero adaptively and dynamically.…”

Section: Time-varying Covariance Matrixmentioning

confidence: 99%

Bayesian Analysis of Latent Threshold Dynamic Models

Nakajima

West

2013

Journal of Business & Economic Statistics

130

146

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Chapter 1 overviews the idea of the latent threshold approach and outlines the dissertation. Chapter 2 introduces the new approach to dynamic sparsity using latent threshold modeling and also discusses Bayesian analysis and computation for model fitting. Chapter 3 describes latent threshold multivariate models for a wide range of applications in the real data analysis that follows. Chapter 4 provides US and Japanese macroeconomic data analysis using latent threshold VAR models. Chapter 5 analyzes time series of foreign currency exchange rates (FX) using latent threshold dynamic factor models. Chapter 6 provides a study of electroencephalographic iv (EEG) time series using latent threshold factor process models. Chapter 7 develops a new framework of dynamic network modeling for multivariate time series using the latent threshold approach. Finally, Chapter 8 concludes the dissertation with open questions and future works.

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Section: Time-varying Covariance Matrixmentioning

confidence: 99%

Bayesian Analysis of Latent Threshold Dynamic Models

Nakajima

West

2013

Journal of Business & Economic Statistics

130

146

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“…In the first step (I) we generate the indicators γ lm one at a time from γ lm |γ \lm ,z N , σ 2 ε , y by applying the efficient sampling scheme of Smith and Kohn (2002). γ \lm denotes the sequence γ where γ lm is excluded and y are the data.…”

Section: Bayesian Estimation According To the Principle Of Adaptive Pmentioning

confidence: 99%

The Use of Score Tests for Inference on Variance Components

Verbeke¹,

Molenberghs²

2003

Biometrics

203

144

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Summary Whenever inference for variance components is required, the choice between one‐sided and two‐sided tests is crucial. This choice is usually driven by whether or not negative variance components are permitted. For two‐sided tests, classical inferential procedures can be followed, based on likelihood ratios, score statistics, or Wald statistics. For one‐sided tests, however, one‐sided test statistics need to be developed, and their null distribution derived. While this has received considerable attention in the context of the likelihood ratio test, there appears to be much confusion about the related problem for the score test. The aim of this paper is to illustrate that classical (two‐sided) score test statistics, frequently advocated in practice, cannot be used in this context, but that well‐chosen one‐sided counterparts could be used instead. The relation with likelihood ratio tests will be established, and all results are illustrated in an analysis of continuous longitudinal data using linear mixed models.

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“…(See Fig. 1a) If we were to consider the features of each sample as a time-series, the elements in L can be seen rowwise as parameters in autoregressive processes of the same order as the row r. Several authors in the time series literature have noted this [3], [4]. We will use this fact to transform the task of approximating covariance matrices into a sequence of regressions.…”

Section: Parameter Sparsing In Full Dimensionmentioning

confidence: 99%

Improving Hyperspectral Classifiers: The Difference Between Reducing Data Dimensionality and Reducing Classifier Parameter Complexity

Berge

Solberg

2007

Image Analysis

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Abstract. Hyperspectral data is usually high dimensional, and there is often a scarcity of available ground truth pixels . Thus the task of applying even a simple classifier such as the Gaussian Maximum Likelihood (GML) classifier usually forces the analyst to reduce the complexity of the implicit parameter estimation task. For decades, the common perception in the literature has been that the solution to this has been to reduce data dimensionality. However, as can be seen from a result by Cover [1], reducing dimensionality increases the risk of making the classification problem more complex.Using the simple GML classifier we compare state of the art dimensionality reduction strategies with a recently proposed strategy for sparsing of parameter estimates in full dimension [2]. Results show that reducing parameter estimation complexity by fitting sparse models in full dimension have a slight edge on the common approaches.

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Parsimonious Covariance Matrix Estimation for Longitudinal Data

Cited by 167 publications

References 22 publications

Bayesian Analysis of Latent Threshold Dynamic Models

Bayesian Analysis of Latent Threshold Dynamic Models

The Use of Score Tests for Inference on Variance Components

Improving Hyperspectral Classifiers: The Difference Between Reducing Data Dimensionality and Reducing Classifier Parameter Complexity

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