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On the Normalized Cut

100%

Nadarajah S.

2008

tom Vol. 86, nr 1-2

169-173

In the recent paper by Soundararajan and Sarkar (2003), the normalized cut, a graph partitioning measure for perceptual organization, was shown to be a sum of two beta distributed random variables and expressions derived for its mean and mode. Here, it is pointed out that the given expression for the mode is incorrect. The correct expression is derived and the implications of the error discussed.

Explicit expressions for moments of F order statistics

100%

Nadarajah S.

2007

tom Vol. 40, nr 4

815-818

For the first time, explicit closed form expressions are derived for moments of order statistics from the F distribution.

Normal maximum likelihood, weighted least squares, and ridge regression estimates

63%

Withers C. S. , Nadarajah S.

Probability and Mathematical Statistics

2012

tom Vol. 32, Fasc. 1

11--24

There have been many papers published (in almost every statistics related journal) suggesting that normal maximum likelihood is superior or inferior to weighted least squares and other approaches. In this note, we show that the three main estimation methods (normal maximum likelihood, weighted least squares and ridge regression) all have the same asymptotic covariance and that there is no gain in efficiency among them. We also show how the bias of these estimators can be reduced and conduct a simulation study to illustrate the magnitude of bias reduction.

Unbiased estimates for linear regression with roundoff error

63%

Withers C. S. , Nadarajah S.

Probability and Mathematical Statistics

2011

tom Vol. 31, Fasc. 2

177--182

We consider the linear regression model, where the residuals have zero mean and an otherwise unspecified distribution F. Suppose that least squares estimates are formed by using rounded values of the dependent variables.We show that these are still unbiased, and that unbiased estimates for the moments and cumulants of F are given by applying Sheppard’s corrections to their estimates.

The Linear Combination of Logistic and Gumbel Random Variables

63%

Nadarajah S. , Kotz S.

2006

tom Vol. 74, nr 2,3

341-350

The exact distribution of the linear combination aX +bY is derived when X and Y are independent logistic and Gumbel random variables. A measure of entropy of the linear combination is investigated. Computer programs are provided for generating tabulations of the percentage points associated with the linear combination. The work is motivated by problems in automation, control, fuzzy sets, neurocomputing and other areas of computer science.

Charlier and edgeworth expansions for distributions and densities in terms of bell polynomials

63%

Withers C. S. , Nadarajah S.

tom Vol. 29, Fasc. 2

271--280

We show that the coefficients of the Charlier differential series for distributions and densities are simply Bell polynomials in the cumulants. The same is true for the Edgeworth expansions of distributions and densities of sample means. We use this to obtain higher order extensions of these well-known series.

Minimax estimation of the mean matrix of the matrix-variate normal distribution

51%

Zinodiny S. , Rezaei S. , Nadarajah S.

Probability and Mathematical Statistics

2016

tom Vol. 36, Fasc. 2

187--200

In this paper, the problem of estimating the mean matrix Θ of a matrix-variate normal distribution with the covariance matrix V⊗ Im is considered under the loss functions, ω tr((δ − X)′ Q(δ − X)) + (1 − ω) tr((δ − Θ)′ Q(δ − Θ)) and k[1−e−tr((δ − Θ)′ Γ−1(δ − Θ))]. We construct a class of empirical Bayes estimators which are better than the maximum likelihood estimator under the first loss function for m > p + 1 and hence show that the maximum likelihood estimator is inadmissible. For the case Q = V = Ip, we find a general class of minimax estimators. Also we give a class of estimators that improve on the maximum likelihood estimator under the second loss function for m > p + 1 and hence show that the maximum likelihood estimator is inadmissible.