Abstract
Using the fact that a multivariate random sample of n observations also generates n nearest neighbour distance (NND) univariate observations and from these NND observations, a set of n auxiliary observations can be obtained and with these auxiliary observations when combined with the original multivariate observations of the random sample, a class of pseudodistance Dh is allowed to be used and inference methods can be developed using this class of pseudodistances. The Dh estimators obtained from this class can achieve high efficiencies and have robustness properties. Model testing also can be handled in a unified way by means of goodness-of-fit tests statistics derived from this class which have an asymptotic normal distribution. These properties make the developed inference methods relatively simple to implement and appear to be suitable for analyzing multivariate data which are often encountered in applications.
Highlights
Using the fact that a multivariate random sample of n observations generates n nearest neighbour distance (NND) univariate observations and from these NND observations, a set of n auxiliary observations can be obtained and with these auxiliary observations when combined with the original multivariate observations of the random sample, a class of pseudodistance Dh is allowed to be used and inference methods can be developed using this class of pseudodistances
Model testing can be handled in a unified way by means of goodness-of-fit tests statistics derived from this class which have an asymptotic normal distribution
For the parametric set-up g ( x ) ∈{ fθ },θ = (θ1,θm )′ and let the vector θ0 denote the true vector of parameters, we would like to have statistical methods for estimating the vector θ0 if the parametric model { fθ } can be assumed and inference methods to validate the assumption of the model { fθ } by means of various goodness-of-fit statistics
Summary
For statistical inferences methods for continuous multivariate models, we often assume to have a random sample of size n of multivariate observations x1, , xn which are independent and identically distributed as the d-dimensional vector of random variable x with a d-dimensional density function g ( x)
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