We study nonparametric inference of stochastic models driven by stable Lévy processes. We introduce a nonparametric estimator of the stable index that achieves the parametric √ n rate of convergence. For the volatility function, due to the heavy-tailedness, the classical least-squares method is not applicable. We then propose a nonparametric least-absolute-deviation or median-quantile estimator...

Abstract: We show that with a class of penalty functions, numerical problems associated with the implementation of the penalized least square estimators are equivalent to the exact cover by 3-sets problem, which belongs to a class of NP-hard problems. We then extend this NP-hardness result to the cases of penalized least absolute deviation regression and penalized support vector machines. We di...

Given a set of objects and a symmetric matrix of dissimilarities between them, Unidimensional Scaling is the problem of finding a representation by locating points on a continuum. Approximating dissimilarities by the absolute value of the difference between coordinates on a line constitutes a serious computational problem. This paper presents an algorithm that implements Simulated Annealing in ...

We explore the extension of James-Stein type estimators in a direction that enables them to preserve their superiority when the sample size goes to infinity. Instead of shrinking a base estimator towards a fixed point, we shrink it towards a data-dependent point. We provide an analytic expression for the asymptotic risk and bias of James-Stein type estimators shrunk towards a data-dependent poi...

For a GARCH(1,1) sequence or an AR(1) model with ARCH(1) errors, it is known that the observations have a heavy tail and the tail index is determined by an estimating equation. Therefore, one can estimate the tail index by solving the estimating equation with unknown parameters replaced by quasi maximum likelihood estimation (QMLE), and profile empirical likelihood method can be employed to eff...

We explore the extension of James-Stein type estimators in a direction that enables them to preserve their superiority when the sample size goes to infinity. Instead of shrinking a base estimator towards a fixed point, we shrink it towards a data-dependent point. We provide an analytic expression for the asymptotic risk and bias of James-Stein type estimators shrunk towards a data-dependent poi...

Powell's(1984) Censored Least Absolute Deviations (CLAD) estimator for the censored linear regression model has been regarded as a desirable alternative to maximum likelihood estimation methods due to its robustness to conditional heteroscedasticity and distributional misspeci ̄cation of the error term. However, the CLAD estimation procedure has failed in certain empirical applications (e.g. Hon...

Homogeneity analysis is a technique for making graphical representations of categorical multivariate data sets. Such data sets can also be represented by the adjacency matrix of a bipartite graph. Homogeneity analysis optimizes a weighted least-squares criterion and the optimal graph layout is computed by an alternating least squares algorithm. Heiser Comput. Statist. Data Anal. (1987) 337, loo...