  In this paper, we introduce reduced-bias estimators for the estimation of the
tail index of a Pareto-type distribution. This is achieved through the use of a
regularised weighted least squares with an exponential regression model for
log-spacings of top order statistics. The asymptotic properties of the proposed
estimators are investigated analytically and found to be asymptotically
unbiased, consistent and normally distributed. Also, the finite sample
behaviour of the estimators are studied through a simulations theory. The
proposed estimators were found to yield low bias and MSE. In addition, the
proposed estimators are illustrated through the estimation of the tail index of
the underlying distribution of claims from the insurance industry.
