Abstract In this paper we consider generalized Hardy spaces in the octonionic setting associated to arbitrary Lipschitz domains where unit normal field exists almost everywhere. First discuss some basic properties and explain structural differences associative Clifford analysis setting. The non-associativity requires special attention definition of an appropriate inner product hence a Szegö pro...

We introduce a simple iterative technique for bounding derivatives of solutions of Stein equations Lf = h−Eh(Z), where L is a linear differential operator and Z is the limit random variable. Given bounds on just the solutions or certain lower order derivatives of the solution, the technique allows one to deduce bounds for derivatives of any order, in terms of supremum norms of derivatives of th...

In this paper we prove $$L^p$$ estimates for Stein’s square functions associated with Fourier–Bessel expansions. Furthermore, transference results from series to Hankel transforms. Actually, these are vector-valued multipliers discrete continuous in the Bessel setting. As a consequence, deduce sharpness of range p -boundedness corresponding property Hankel–Stein functions. Finally, that ones ha...

This paper revisits the methodology of Stein (1975, 1986) for estimating a covariance matrix in the setting where the number of variables can be of the same magnitude as the sample size. Stein proposed to keep the eigenvectors of the sample covariance matrix but to shrink the eigenvalues. By minimizing an unbiased estimator of risk, Stein derived an ‘optimal’ shrinkage transformation. Unfortuna...

The estimation problem in multivariate linear calibration with elliptical errors is considered under a loss function which can be derived from the Kullback-Leibler distance. First, we discuss the problem under normal errors and we give unbiased estimate of risk of an alternative estimator by means of the Stein and Stein-Haff identities for multivariate normal distribution. From the unbiased est...