Abstract: In this article, experimental situations are considered
where a main effects plan is to be used to study m two-level factors
using n runs which are partitioned into b blocks, not necessarily
of same size. Assuming the block sizes to be even for all blocks,
for the case n ≡ 2 (mod 4), optimal designs are obtained with
respect to type 1 and type 2 optimality criteria in the class of designs
providing estimation of all main effects orthogonal to the block
effects. In practice, such orthogonal estimation of main effects is
often a desirable condition. In the wider class of all available m two
level even sized blocked main effects plans, where the factors do not
occur at high and low levels equally often in each block, E-optimal
designs are also characterized. Simple construction methods based on
Hadamard matrices and Kronecker product for these optimal designs
are presented.
Abstract: The detection of outliers is very essential because of
their responsibility for producing huge interpretative problem in
linear as well as in nonlinear regression analysis. Much work has
been accomplished on the identification of outlier in linear
regression, but not in nonlinear regression. In this article we propose
several outlier detection techniques for nonlinear regression. The
main idea is to use the linear approximation of a nonlinear model and
consider the gradient as the design matrix. Subsequently, the
detection techniques are formulated. Six detection measures are
developed that combined with three estimation techniques such as the
Least-Squares, M and MM-estimators. The study shows that among
the six measures, only the studentized residual and Cook Distance
which combined with the MM estimator, consistently capable of
identifying the correct outliers.