scholarly journals Generalized Inferences about the Mean Vector of Several Multivariate Gaussian Processes

2015 ◽  
Vol 2015 ◽  
pp. 1-9
Author(s):  
Pilar Ibarrola ◽  
Ricardo Vélez
Keyword(s):  
Gaussian Processes ◽  
Confidence Region ◽  
Confidence Regions ◽  
Covariance Matrices ◽  
Nuisance Parameters ◽  
Vector Parameter ◽  
Multivariate Gaussian ◽  
The Mean ◽  
Unknown Vector ◽  
Mean Vector

We consider in this paper the problem of comparing the means of several multivariate Gaussian processes. It is assumed that the means depend linearly on an unknown vector parameterθand that nuisance parameters appear in the covariance matrices. More precisely, we deal with the problem of testing hypotheses, as well as obtaining confidence regions forθ. Both methods will be based on the concepts of generalizedpvalue and generalized confidence region adapted to our context.

Structured Antedependence Models for Functional Mapping of Multiple Longitudinal Traits

2005 ◽  
Vol 4 (1) ◽  
Author(s):  
Wei Zhao ◽  
Wei Hou ◽  
Ramon C. Littell ◽  
Rongling Wu
Keyword(s):  
Genetic Correlations ◽  
Covariance Matrices ◽  
Growth Trajectories ◽  
Relative Importance ◽  
Hybrid Progeny ◽  
Linkage Groups ◽  
Stem Height ◽  
Pleiotropic Qtl ◽  
The Mean ◽  
Mean Vector

In this article, we present a statistical model for mapping quantitative trait loci (QTL) that determine growth trajectories of two correlated traits during ontogenetic development. This model is derived within the maximum likelihood context, incorporated by mathematical aspects of growth processes to model the mean vector and by structured antedependence (SAD) models to approximate time-dependent covariance matrices for longitudinal traits. It provides a quantitative framework for testing the relative importance of two mechanisms, pleiotropy and linkage, in contributing to genetic correlations during ontogeny. This model has been employed to map QTL affecting stem height and diameter growth trajectories in an interspecific hybrid progeny of Populus, leading to the successful discovery of three pleiotropic QTL on different linkage groups. The implications of this model for genetic mapping within a broader context are discussed.

scholarly journals The Location Parameter Estimation of Spherically Distributions with Known Covariance Matrices

2020 ◽  
Vol 8 (2) ◽  
pp. 499-506
Author(s):  
Mahmoud Afshari ◽  
Hamid Karamikabir
Keyword(s):  
Location Parameter ◽  
Covariance Matrices ◽  
Spherically Symmetric ◽  
Shrinkage Estimators ◽  
Parameter Vector ◽  
Symmetric Distributions ◽  
The Mean ◽  
Simulation Results ◽  
Balance Error ◽  
Mean Vector

This paper presents shrinkage estimators of the location parameter vector for spherically symmetric distributions. We suppose that the mean vector is non-negative constraint and the components of diagonal covariance matrix is known.We compared the present estimator with natural estimator by using risk function.We show that when the covariance matrices are known, under the balance error loss function, shrinkage estimator has the smaller risk than the natural estimator. Simulation results are provided to examine the shrinkage estimators.

Application of Confidence Regions to Ice Ridge Keel Data Statistical Assessment

2017 ◽  
Author(s):  
Petr Zvyagin ◽  
Jaakko Heinonen
Keyword(s):  
Confidence Region ◽  
Random Variable ◽  
Confidence Regions ◽  
Small Sample ◽  
Unknown Parameters ◽  
Minimum Area ◽  
Statistical Assessment ◽  
Gulf Of Bothnia ◽  
The Mean ◽  
Small Sample Sizes

Sets of measurements of underwater ridge parts usually contain a limited amount of data. Outcomes need to be made while relying on small sample sizes. In this event, the chance of making inaccurate estimations increases. This paper proposes to use stochastic confidence regions in the estimation of the unknown parameters of keel depths. A model for a random variable with a lognormal distribution for keel depths is assumed. Regions for the mean and standard deviation of keel depths are obtained from Mood’s and minimum-area confidence regions for parameters of the normally distributed random variable. Conservative safety probability of non-exceeding the critical keel depth in one random interaction of the ridge with structure is estimated. An algorithm for statistically assessment of ice ridge keel data by means of confidence region building is here offered. The assessment of a set of ridge keel depths for the Gulf of Bothnia (Baltic Sea) is performed.

scholarly journals Fixed–size confidence regions for the mean vector of a multinormal distribution

1986 ◽  
Vol 5 (2) ◽  
pp. 139-168 ◽  
Author(s):  
N. Mukhopadhyay ◽  
J.S. Al-Mousawi
Keyword(s):  
Confidence Regions ◽  
Fixed Size ◽  
The Mean ◽  
Mean Vector

scholarly journals On Sequential Fixed-Size Confidence Regions for the Mean Vector

1997 ◽  
Vol 60 (2) ◽  
pp. 233-251 ◽  
Author(s):  
S. Datta ◽  
N. Mukhopadhyay
Keyword(s):  
Confidence Regions ◽  
Fixed Size ◽  
The Mean ◽  
Mean Vector

scholarly journals Mean Empirical Likelihood Inference for Response Mean with Data Missing at Random

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Hanji He ◽  
Guangming Deng
Keyword(s):  
Empirical Likelihood ◽  
Missing At Random ◽  
Confidence Regions ◽  
Likelihood Inference ◽  
High Dimensional ◽  
Finite Sample ◽  
The Mean ◽  
Data Missing ◽  
Consistency And Asymptotic Normality ◽  
The Impact

We extend the mean empirical likelihood inference for response mean with data missing at random. The empirical likelihood ratio confidence regions are poor when the response is missing at random, especially when the covariate is high-dimensional and the sample size is small. Hence, we develop three bias-corrected mean empirical likelihood approaches to obtain efficient inference for response mean. As to three bias-corrected estimating equations, we get a new set by producing a pairwise-mean dataset. The method can increase the size of the sample for estimation and reduce the impact of the dimensional curse. Consistency and asymptotic normality of the maximum mean empirical likelihood estimators are established. The finite sample performance of the proposed estimators is presented through simulation, and an application to the Boston Housing dataset is shown.

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