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Multivariate Exponential Analysis from the Minimal Number of Samples [article]

Annie Cuyt, Wen-shin Lee
2017 arXiv   pre-print
The problem of multivariate exponential analysis or sparse interpolation has received a lot of attention, especially with respect to the number of samples required to solve it unambiguously.  ...  In this paper we show how to bring the number of samples down to the absolute minimum of (d+1)n where d is the dimension of the problem and n is the number of exponential terms.  ...  Acknowledgements This work was partially supported by a Research Grant of the FWO-Flanders (Flemish Science Foundation).  ... 
arXiv:1610.06329v4 fatcat:2qvw6htfjnfhdmbjnogosngmkm

Multivariate exponential analysis from the minimal number of samples

Annie Cuyt, Wen-shin Lee
2017 Advances in Computational Mathematics  
The problem of multivariate exponential analysis or sparse interpolation has received a lot of attention, especially with respect to the number of samples required to solve it unambiguously.  ...  In this paper we show how to bring the number of samples down to the absolute minimum of (d +1)n where d is the dimension of the problem and n is the number of exponential terms.  ...  Acknowledgements This work was partially supported by a Research Grant of the FWO-Flanders (Flemish Science Foundation).  ... 
doi:10.1007/s10444-017-9570-8 fatcat:n3msdtsv2zdbxeenksh3wupouu

A new alternative Hotelling's T2 control chart using MEWMA to monitor minimal mean deviation

Kunyun Wang, Qianqian Li, Guangdong Li, I. Barukčić
2021 MATEC Web of Conferences  
It indicated the smaller forgetting factor is more sensitive to minimal mean value deviation and that average run length tended to become bigger gradually along with increase of sample sizes N when production  ...  A new alternative control chart was constructed after the original products data are processed by using multivariate exponentially weighted moving average for cumulating failure effects because T2 control  ...  cumulates failure effects according to multivariate exponentially weighted moving average to detect process minimal deviation quickly. m n × samples are extracted from production process.  ... 
doi:10.1051/matecconf/202133609021 fatcat:j5bxbzmynvcx7gcui7mm4acfre

Analyzing Data utilized in Process Control and Continuous Improvement

Jeffrey E. Jarrett
2016 International Journal of Economics & Management Sciences  
A number of authors have extended this analysis to the multivariate case.  ...  The residuals from the analysis should be normally distributed. In practice, large sample data with moderate departures from normality do not seriously affect the results.  ... 
doi:10.4172/2162-6359.1000328 fatcat:glpr4wshandwhe26m2hpbzmrvu

Page 1357 of Mathematical Reviews Vol. 52, Issue 4 [page]

1976 Mathematical Reviews  
Other varia- tions of the problem are also considered. K. S. Miller (New York) Wijsman, R. A. 9532 Stopping time in sequential samples from multivariate exponential families.  ...  Multivariate analysis, III (Proc. Third Internat. Sympos. on Multivariate Analysis, Wright State Univ., Dayton, Ohio, 1972), pp. 171-179. Academic Press, New York, 1973.  ... 

Page 2324 of Mathematical Reviews Vol. , Issue 95d [page]

1995 Mathematical Reviews  
order asymptotic theory for discriminant analysis in exponential families of distributions.  ...  They are exactly the same, although the collapsibility approach used by Lee restricts the number of models to be considered.  ... 

Decomposing Textures using Exponential Analysis

Yuan Hou, Annie Cuyt, Wen-shin Lee, Deepayan Bhowmik
2021 ICASSP 2021 - 2021 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)  
Exponential analysis offers the advantage of sparsity in the model and continuity in the parameters.  ...  Decomposition is integral to most image processing algorithms and often required in texture analysis. We present a new approach using a recent 2-dimensional exponential analysis technique.  ...  Moreover, the minimal number of 3η = 2η + η required samples for an η-term model of the form (1) is often again overestimated by N + n with N ≥ 2η and n ≥ η.  ... 
doi:10.1109/icassp39728.2021.9413909 fatcat:xqre4krtrjcndipmhnrrkyue2u

Page 3172 of Mathematical Reviews Vol. , Issue 86g [page]

1986 Mathematical Reviews  
Then 1 — Fy, is estimated by the Kaplan-Meier estimator obtained from the totality of the observations, where those from the ith sample are rescaled by 6;.  ...  Failures are assumed to follow an exponential distribution with an unknown mean, and we concentrate on estimation of the number of faults v.  ... 

Stochastic collocation methods via L_1 minimization using randomized quadratures [article]

Ling Guo, Akil Narayan, Tao Zhou, Yuhang Chen
2016 arXiv   pre-print
In this work, we discuss the problem of approximating a multivariate function via ℓ_1 minimization method, using a random chosen sub-grid of the corresponding tensor grid of Gaussian points.  ...  We provide theoretical analysis on the validity of the approach.  ...  The number of samples we use is M , and is the number of points subsampled from the tensor-product Gaussian quadrature grid, coinciding with the number of rows of the matrix D. 5.1.1.  ... 
arXiv:1602.00995v2 fatcat:75pfrhgz7jcxnlu6uae7pnvnhm

Geostatistical and multivariate statistical methods for the assessment of polluted soils—merits and limitations

J.W. Einax, U. Soldt
1999 Chemometrics and Intelligent Laboratory Systems  
The first case study is characterized by a distinct spatial structure and a relatively large number of samples.  ...  Both geostatistical and multivariate statistical methods are well suited for the characterization of the state of pollution.  ...  Acknowledgements The authors wish to thank Dr. N. Simmleit of the Institute Fresenius, Fresenius Environment Consult,  ... 
doi:10.1016/s0169-7439(98)00152-x fatcat:gkqdp6qgfvee5gve47m36zmdye

GIVING MEANINGFUL INTERPRETATION TO ORDINATION AXES: ASSESSING LOADING SIGNIFICANCE IN PRINCIPAL COMPONENT ANALYSIS

Pedro R. Peres-Neto, Donald A. Jackson, Keith M. Somers
2003 Ecology  
ACKNOWLEDGMENTS We thank Pierre Legendre and two anonymous reviewers for comments on the manuscript and our simulation protocols.  ...  We adopted a similar solution as provided for the bootstrap samples in relation to the original sample in order to minimize this problem.  ...  the efficiency of this correction in minimizing type I error probabilities.  ... 
doi:10.1890/00-0634 fatcat:togyrr6aw5fcncs3offwshg4fu

Page 3 of The Journal of the Operational Research Society Vol. 58, Issue 3 [page]

2007 The Journal of the Operational Research Society  
In the sensitivity analysis of the number of initial samples for estimating the unknown in- control process mean vector and covariance matrix, the results of economic design of the VP 7° control chart  ...  appear fairly insensitive as long as the number of initial samples beyond the lower bound of the range recommended by Nedumaran and Pignatiello (1999).  ... 

New Test Statistics for MANOVA/Descriptive Discriminant Analysis

William T. Coombs, James Algina
1996 Educational and Psychological Measurement  
Departure from these basic ratios was minimized. FORM OF THE SAMPLE SIZE RATIO (NRF) When there were three groups, the sample size ratio was either of the form (a) m, = nz < n; or (b) m, <n, =n3.  ...  Statistics were more conservative when data were sampled from exponential distributions than when data were sampled from normal distributions.  ... 
doi:10.1177/0013164496056003002 fatcat:y5lurhgmsfbo7o3etmwntzuw4u

Implementation of Multivariate Exponential Power Distribution in Discrimination and Classification of Psychological Data and Other applications

A. A. Olosund ´ e, A. T. Soy´ınk ´ a´
2021 Journal of Education Society and Behavioural Science  
The present study employed a robust model for such cases in the context of discrimination and classification of multivariate psychological disorder data using multivariate exponential distribution as an  ...  Recent advances have shown that some multivariate psychological data are deviating from usual normal assumption either in the tails or kurtosis.  ...  We also appreciate the anonymous referees for offering useful suggestions that improved the quality of the paper.  ... 
doi:10.9734/jesbs/2021/v34i530327 fatcat:l33wpx555rhmpem22tkhj4zqx4

Open problems for tractability of multivariate integration

Henryk Woźniakowski
2003 Journal of Complexity  
We present a number of open problems regarding the tractability of multivariate integration for various spaces of functions in the worst case and randomized settings.  ...  In the worst case setting, we discuss two spaces. The first is a space of infinitely differentiable functions for which the tractability of multivariate integration is open.  ...  error of Q n;d : We stress that in the randomized setting, the minimal number nðe; F d Þ is at most equal to the minimal number of function values from the worst case setting.  ... 
doi:10.1016/s0885-064x(03)00016-5 fatcat:cjdz3qhwtfbpjnldign63dbtmi
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