Mahalanobis distance under non-normality

Tiku, Moti L.
İslam, Muhammed Qamarul
Qumsiyeh, Sahar B.
We give a novel estimator of Mahalanobis distance D2 between two non-normal populations. We show that it is enormously more efficient and robust than the traditional estimator based on least squares estimators. We give a test statistic for testing that D2=0 and study its power and robustness properties.


İyigün, Cem (Cambridge University Press (CUP), 2008-01-01)
The probabilistic distance clustering method of [1] works well if the cluster sizes are approximately equal. We modify that method to deal with clusters of arbitrary size and for problems where the cluster sizes are themselves unknowns that need to be estimated. In the latter case, our method is a viable alternative to the expectation-maximization (EM) method.
A marginalized multilevel model for bivariate longitudinal binary data
Inan, Gul; İlk Dağ, Özlem (Springer Science and Business Media LLC, 2019-06-01)
This study considers analysis of bivariate longitudinal binary data. We propose a model based on marginalized multilevel model framework. The proposed model consists of two levels such that the first level associates the marginal mean of responses with covariates through a logistic regression model and the second level includes subject/time specific random intercepts within a probit regression model. The covariance matrix of multiple correlated time-specific random intercepts for each subject is assumed to ...
Representation of Multiplicative Seasonal Vector Autoregressive Moving Average Models
Yozgatlıgil, Ceylan (Informa UK Limited, 2009-11-01)
Time series often contain observations of several variables and multivariate time series models are used to represent the relationship between these variables. There are many studies on vector autoregressive moving average (VARMA) models, but the representation of multiplicative seasonal VARMA models has not been seriously studied. In a multiplicative vector model, such as a seasonal VARMA model, the representation is not unique because of the noncommutative property of matrix multiplication. In this articl...
The limiting distribution of the F-statistic from nonnormal universes
Gueven, Bilgehan (Informa UK Limited, 2006-12-01)
We consider a linear regression model with an unbalanced 1-fold nested error structure, where group effect and error are from nonnormal universes. The limiting distribution of the F-statistic in this model is derived, as the sample size is large and group sizes take values from a finite set of distinct integers. The result is used to approximate the F-distribution quantile and to test the significance of the random effect variance component. Results are also applicable to the F-statistic in the one-way rand...
Autoregressive models with short-tailed symmetric distributions
Akkaya, Ayşen (Informa UK Limited, 2008-01-01)
Symmetric short-tailed distributions do indeed occur in practice but have not received much attention particularly in the context of autoregression. We consider a family of such distributions and derive the modified maximum likelihood estimators of the parameters. We show that the estimators are efficient and robust. We develop hypothesis-testing procedures.
Citation Formats
M. L. Tiku, M. Q. İslam, and S. B. Qumsiyeh, “Mahalanobis distance under non-normality,” STATISTICS, pp. 275–290, 2010, Accessed: 00, 2020. [Online]. Available: