Nonparametric methods play a central role in modern empirical work. While they provide inference procedures that are more robust to parametric misspecification bias, they may be quite sensitive to tuning parameter choices. We study the effects of bias correction on confidence interval coverage in the context of kernel density and local polynomial regression estimation, and prove that bias corre...

The paper is concerned with best constants in Markov-type inequalities between the norm of a higher derivative of a polynomial and the norm of the polynomial itself. The norm of the polynomial is taken in L2 with the Gegenbauer weight corresponding to a parameter α , while the derivative is measured in L2 with the Gegenbauer weight for a parameter β . Under the assumption that β −α is an intege...

A novel semi-blind defocused image deconvolution technique is proposed, which is based on multivariate local polynomial regression and iterative Wiener filtering. In this technique, firstly a multivariate local polynomial regression model is trained in wavelet domain to estimate defocus parameter. After obtaining the point spread function (PSF ) parameter, iterative wiener filter is adopted to ...

An analytical polynomial expression, for accurate and computationally efficient frequency estimation of a single real sinusoid under Additive White Gaussian Noise (AWGN), is derived proposed in this paper. The method, which can be easily adapted time estimation, based on transforming the problem as solution fourth order (quartic) expressed powers trigonometric function containing unknown freque...

The paper considers a linear matrix inequality (LMI) that depends on a parameter varying in a compact topological space. It turns out that if a strict LMI continuously depends on a parameter and is feasible for any value of that parameter, then it has a solution which continuously depends on the parameter. The result holds true for LMIs that arise in S-procedure and Yakubovich lemma. It is show...

Simple monomial inflationary scenarios have been ruled out by recent observations. In this work we revisit the next simplest scenario, a single--field model where scalar potential is polynomial of degree four which features concave ``almost'' saddle point. We focus on trans--Planckian field values. reparametrize potential, greatly simplifies procedure for finding acceptbale parameters. This all...