Asymptotic Robustness Study of the Polychoric Correlation Estimation.
Ontology highlight
ABSTRACT:
SUBMITTER: Jin S
PROVIDER: S-EPMC5591612 | biostudies-literature |
REPOSITORIES: biostudies-literature
Similar Datasets
Project description:Here, we address the consequences of the extension in the space of a simple model of a system that is closed to efficient causation: the (M,R)-system model. To do so, we use a diffusion term to describe the collective motion of the nutrients' concentration across the compartmentalized space that defines the organism. We show that the non-trivial stable steady state remains despite such generalization, as long as the system is small enough to deal with the transport of the precursors to feed the entire protocell and dispose of a sufficient concentration of it in its surroundings. Such consideration explains the emergence of a bifurcation with two parameters that we characterize. Finally, we show that the robustness of the system under catastrophic losses of catalysts also remains, preserving the original's model character.
| S-EPMC7511346 | biostudies-literature
Project description:Distance correlation has become an increasingly popular tool for detecting the nonlinear dependence between a pair of potentially high-dimensional random vectors. Most existing works have explored its asymptotic distributions under the null hypothesis of independence between the two random vectors when only the sample size or the dimensionality diverges. Yet its asymptotic null distribution for the more realistic setting when both sample size and dimensionality diverge in the full range remains largely underdeveloped. In this paper, we fill such a gap and develop central limit theorems and associated rates of convergence for a rescaled test statistic based on the bias-corrected distance correlation in high dimensions under some mild regularity conditions and the null hypothesis. Our new theoretical results reveal an interesting phenomenon of blessing of dimensionality for high-dimensional distance correlation inference in the sense that the accuracy of normal approximation can increase with dimensionality. Moreover, we provide a general theory on the power analysis under the alternative hypothesis of dependence, and further justify the capability of the rescaled distance correlation in capturing the pure nonlinear dependency under moderately high dimensionality for a certain type of alternative hypothesis. The theoretical results and finite-sample performance of the rescaled statistic are illustrated with several simulation examples and a blockchain application.
| S-EPMC8491772 | biostudies-literature
Project description:We develop purely nonparametric methods for the analysis of repeated measures designs with missing values. Hypotheses are formulated in terms of purely nonparametric treatment effects. In particular, data can have different shapes even under the null hypothesis and therefore, a solution to the nonparametric Behrens-Fisher problem in repeated measures designs will be presented. Moreover, global testing and multiple contrast test procedures as well as simultaneous confidence intervals for the treatment effects of interest will be developed. All methods can be applied for the analysis of metric, discrete, ordinal, and even binary data in a unified way. Extensive simulation studies indicate a satisfactory control of the nominal type-I error rate, even for small sample sizes and a high amount of missing data (up to 30%). We apply the newly developed methodology to a real data set, demonstrating its application and interpretation.
| S-EPMC8721540 | biostudies-literature
Project description:BACKGROUND: When multiple endpoints are of interest in evidence synthesis, a multivariate meta-analysis can jointly synthesise those endpoints and utilise their correlation. A multivariate random-effects meta-analysis must incorporate and estimate the between-study correlation (rhoB). METHODS: In this paper we assess maximum likelihood estimation of a general normal model and a generalised model for bivariate random-effects meta-analysis (BRMA). We consider two applied examples, one involving a diagnostic marker and the other a surrogate outcome. These motivate a simulation study where estimation properties from BRMA are compared with those from two separate univariate random-effects meta-analyses (URMAs), the traditional approach. RESULTS: The normal BRMA model estimates rhoB as -1 in both applied examples. Analytically we show this is due to the maximum likelihood estimator sensibly truncating the between-study covariance matrix on the boundary of its parameter space. Our simulations reveal this commonly occurs when the number of studies is small or the within-study variation is relatively large; it also causes upwardly biased between-study variance estimates, which are inflated to compensate for the restriction on rhoB. Importantly, this does not induce any systematic bias in the pooled estimates and produces conservative standard errors and mean-square errors. Furthermore, the normal BRMA is preferable to two normal URMAs; the mean-square error and standard error of pooled estimates is generally smaller in the BRMA, especially given data missing at random. For meta-analysis of proportions we then show that a generalised BRMA model is better still. This correctly uses a binomial rather than normal distribution, and produces better estimates than the normal BRMA and also two generalised URMAs; however the model may sometimes not converge due to difficulties estimating rhoB. CONCLUSION: A BRMA model offers numerous advantages over separate univariate synthesises; this paper highlights some of these benefits in both a normal and generalised modelling framework, and examines the estimation of between-study correlation to aid practitioners.
| S-EPMC1800862 | biostudies-other
Project description:Adaptive measurement of change (AMC) is a psychometric method for measuring intra-individual change on one or more latent traits across testing occasions. Three hypothesis tests-a Z test, likelihood ratio test, and score ratio index-have demonstrated desirable statistical properties in this context, including low false positive rates and high true positive rates. However, the extant AMC research has assumed that the item parameter values in the simulated item banks were devoid of estimation error. This assumption is unrealistic for applied testing settings, where item parameters are estimated from a calibration sample before test administration. Using Monte Carlo simulation, this study evaluated the robustness of the common AMC hypothesis tests to the presence of item parameter estimation error when measuring omnibus change across four testing occasions. Results indicated that item parameter estimation error had at most a small effect on false positive rates and latent trait change recovery, and these effects were largely explained by the computerized adaptive testing item bank information functions. Differences in AMC performance as a function of item parameter estimation error and choice of hypothesis test were generally limited to simulees with particularly low or high latent trait values, where the item bank provided relatively lower information. These simulations highlight how AMC can accurately measure intra-individual change in the presence of item parameter estimation error when paired with an informative item bank. Limitations and future directions for AMC research are discussed.
| S-EPMC9228691 | biostudies-literature
Project description:Within vision research retinotopic mapping and the more general receptive field estimation approach constitute not only an active field of research in itself but also underlie a plethora of interesting applications. This necessitates not only good estimation of population receptive fields (pRFs) but also that these receptive fields are consistent across time rather than dynamically changing. It is therefore of interest to maximize the accuracy with which population receptive fields can be estimated in a functional magnetic resonance imaging (fMRI) setting. This, in turn, requires an adequate estimation framework providing the data for population receptive field mapping. More specifically, adequate decisions with regard to stimulus choice and mode of presentation need to be made. Additionally, it needs to be evaluated whether the stimulation protocol should entail mean luminance periods and whether it is advantageous to average the blood oxygenation level dependent (BOLD) signal across stimulus cycles or not. By systematically studying the effects of these decisions on pRF estimates in an empirical as well as simulation setting we come to the conclusion that a bar stimulus presented at random positions and interspersed with mean luminance periods is generally most favorable. Finally, using this optimal estimation framework we furthermore tested the assumption of temporal consistency of population receptive fields. We show that the estimation of pRFs from two temporally separated sessions leads to highly similar pRF parameters.
| S-EPMC4252088 | biostudies-literature
Project description:Many statistical methods gain robustness and flexibility by sacrificing convenient computational structures. In this paper, we illustrate this fundamental tradeoff by studying a semi-parametric graph estimation problem in high dimensions. We explain how novel computational techniques help to solve this type of problem. In particular, we propose a nonparanormal neighborhood pursuit algorithm to estimate high dimensional semiparametric graphical models with theoretical guarantees. Moreover, we provide an alternative view to analyze the tradeoff between computational efficiency and statistical error under a smoothing optimization framework. Though this paper focuses on the problem of graph estimation, the proposed methodology is widely applicable to other problems with similar structures. We also report thorough experimental results on text, stock, and genomic datasets.
| S-EPMC4219653 | biostudies-literature
Project description:Motivated by the problem of construction of gene co-expression network, we propose a statistical framework for estimating high-dimensional partial correlation matrix by a three-step approach. We first obtain a penalized estimate of a partial correlation matrix using ridge penalty. Next we select the non-zero entries of the partial correlation matrix by hypothesis testing. Finally we re-estimate the partial correlation coefficients at these non-zero entries. In the second step, the null distribution of the test statistics derived from penalized partial correlation estimates has not been established. We address this challenge by estimating the null distribution from the empirical distribution of the test statistics of all the penalized partial correlation estimates. Extensive simulation studies demonstrate the good performance of our method. Application on a yeast cell cycle gene expression data shows that our method delivers better predictions of the protein-protein interactions than the Graphic Lasso.
| S-EPMC4239206 | biostudies-literature
Project description:In this paper, we propose a computationally efficient approach -space(Sparse PArtial Correlation Estimation)- for selecting non-zero partial correlations under the high-dimension-low-sample-size setting. This method assumes the overall sparsity of the partial correlation matrix and employs sparse regression techniques for model fitting. We illustrate the performance of space by extensive simulation studies. It is shown that space performs well in both non-zero partial correlation selection and the identification of hub variables, and also outperforms two existing methods. We then apply space to a microarray breast cancer data set and identify a set of hub genes which may provide important insights on genetic regulatory networks. Finally, we prove that, under a set of suitable assumptions, the proposed procedure is asymptotically consistent in terms of model selection and parameter estimation.
| S-EPMC2770199 | biostudies-literature
Project description:Existing monocular depth estimation driving datasets are limited in the number of images and the diversity of driving conditions. The images of datasets are commonly in a low resolution and the depth maps are sparse. To overcome these limitations, we produce a Synthetic Digital City Dataset (SDCD) which was collected under 6 different weather driving conditions, and 6 common adverse perturbations caused by the data transmission. SDCD provides a total of 930 K high-resolution RGB images and corresponding perfect observed depth maps. The evaluation shows that depth estimation models which are trained on SDCD provide a clearer, smoother, and more precise long-range depth estimation compared to those trained on one of the best-known driving datasets KITTI. Moreover, we provide a benchmark to investigate the performance of depth estimation models in different adverse driving conditions. Instead of collecting data from the real world, we generate the SDCD under severe driving conditions with perfect observed data in the digital world, enhancing depth estimation for autonomous driving.
| S-EPMC10944538 | biostudies-literature