An Introduction to Applied Multivariate Statistics.

Srivastava, Mukul; Carter, E. M.

doi:10.2307/2530797

Cited by 54 publications

(62 citation statements)

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“…Maximum likelihood estimators for the parameters in the MLNM(ABC) are given by (e.g. see Srivastava and Khatri (1979) or yon Rosen (1989))…”

Section: Mlnm(abc)mentioning

confidence: 99%

Residuals in the growth curve model

Rosen

1995

Ann Inst Stat Math

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A b s t r a c t .Residuals for the Growth Curve model will be discussed. In univariate linear models as well as the ordinary multivariate analysis of variance model residuals are based on the difference between the observations and the mean whereas for the Growth Curve model we have three different residuals all showing various aspects useful for validating analysis. For these residuals some basic properties are established.

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“…Maximum likelihood estimators for the parameters in the MLNM(ABC) are given by (e.g. see Srivastava and Khatri (1979) or yon Rosen (1989))…”

Section: Mlnm(abc)mentioning

confidence: 99%

Residuals in the growth curve model

Rosen

1995

Ann Inst Stat Math

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“…Transforming Z = X 1/2 2 X 1 X 1/2 2 and X 2 = X 2 , with Jacobian J(X 1 , X 2 → Z, X 2 ) = det(X 2 ) −(m+1)/2 , we obtain the joint p.d.f. of Z and X 2 as [19] Matrix-variate Gauss hypergeometric distribution 353 P. Since X 1 and X 2 are independent, their joint p.d.f.…”

Section: Quadratic Formsmentioning

confidence: 99%

Matrix-Variate Gauss Hypergeometric Distribution

Gupta

Nagar

2012

J. Aust. Math. Soc.

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In this paper, we propose a matrix-variate generalization of the Gauss hypergeometric distribution and study several of its properties. We also derive probability density functions of the product of two independent random matrices when one of them is Gauss hypergeometric. These densities are expressed in terms of Appell's first hypergeometric function F 1 and Humbert's confluent hypergeometric function Φ 1 of matrix arguments.

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“…The maximum likelihood estimator can be used. The properties of this estimator can be found in [91]. In case there are missing points in the training examples, one can make use of the expectation maximization algorithm [18,80].…”

Section: Parameter Estimationmentioning

confidence: 99%

“…The estimation of the parameters of the Gaussian distribution is straightforward using the maximum likelihood estimator [91]. The object localization problem is treated as a graph search problem with an objective function integrating the performance of part detectors and the object configuration.…”

Section: Part-based Learningmentioning

confidence: 99%