Uniform in bandwidth consistency of kernel estimators of the tail index

We consider a class of kernel estimators [^(t)]_n,h\hat{\tau}_{n,h} of the tail index of a Pareto-type distribution, which generalizes and includes the classical Hill estimator [^(a)]_n,k\hat{a}_{n,k}. It is well-known that [^(a)]_n,k\hat{a}_{n,k} is a consistent estimator of the tail index if and only if k→ ∞ and k/n→0. Under suitable assumptions on the kernel, [^(t)] _n,h\hat{\tau} _{n,h} is consistent whenever the bandwidth is taken to be a sequence of non-random numbers satisfying h _n →0 and nh _n → ∞. We extend this result and prove the consistency uniformly over a certain range of bandwidths. This permits the treatment of estimators of the tail index based upon data-dependent bandwidths, which are often used in practice. In the process, we establish a uniform in bandwidth result for kernel-type regression estimators with a fixed design, which will likely be of separate interest.     

The use of a figure-of-eight coil for fibre optic respiratory plethysmography: Geometrical analysis and experimental characterisation

An optical fibre sensor based on the macro-bending loss effect has been redeveloped for thoracic and abdominal circumference measurements in non-invasive plethysmographic respiratory monitoring. A new geometrical analysis of the figure-of-eight transducer is presented, along with an optical analysis, and experimental results are presented which are in good agreement with these analyses. A comparison is made with earlier implementations of macrobending loss effect based transducers for respiratory measurement, and the newer sensor compares favourably, indicating a higher resolution and a simpler mechanical construction.     

Synthesis of multifunctional hydroxyethyl tetrazoles

A series of di-, tri-, and tetra-tetrazoloalkanes were synthesized from the corresponding nitrile and sodium azide. These were alkylated to give hydroxy terminated chains for possible use as high energy oligomers.     

Laurent-Padé approximants to four kinds of Chebyshev polynomial expansions. Part II: Clenshaw-Lord type approximants

Laurent-Padé (Chebyshev) rational approximantsP _m (w, w ⁻¹)/Q _n (w, w ⁻¹) of Clenshaw-Lord type [2,1] are defined, such that the Laurent series ofP _m /Q _n matches that of a given functionf(w, w ⁻¹) up to terms of orderw ^±(m+n) , based only on knowledge of the Laurent series coefficients off up to terms inw ^±(m+n) . This contrasts with the Maehly-type approximants [4,5] defined and computed in part I of this paper [6], where the Laurent series ofP _m matches that ofQ _n f up to terms of orderw ^±(m+n ), but based on knowledge of the series coefficients off up to terms inw ^±(m+2n). The Clenshaw-Lord method is here extended to be applicable to Chebyshev polynomials of the 1st, 2nd, 3rd and 4th kinds and corresponding rational approximants and Laurent series, and efficient systems of linear equations for the determination of the Padé-Chebyshev coefficients are obtained in each case. Using the Laurent approach of Gragg and Johnson [4], approximations are obtainable for allm≥0,n≥0. Numerical results are obtained for all four kinds of Chebyshev polynomials and Padé-Chebyshev approximants. Remarkably similar results of formidable accuracy are obtained by both Maehly-type and Clenshaw-Lord type methods, thus validating the use of either.     

Zur Theorie der Randwertaufgaben

Ohne ZusammenfassungDie vorliegende Arbeit bildet einen Auszug meiner in Göttingen (1903) erschienenen Dissertation. Einige Änderungen sind aber eingetreten, insbesondere wird dem Beweise der Existenz der ausgezeichneten Lösungen (§ 2) eine einfachere Gestalt gegeben.     

Excitation and relative differential oscillator strengths for trifluoromethyl sulphur pentafluoride, SF5CF3, in the UV–VUV region by electron energy loss spectroscopy

Electron energy loss spectroscopy (EELS) has been used to study the photo-absorption spectrum of trifluoromethyl sulphur pentafluoride (SF₅CF₃) for the first time. Comparison is made with the EELS spectrum of sulphur hexafluoride (SF₆). The photolysis of the compound is discussed with relevance to estimated lifetimes in the atmosphere. It is estimated that the lifetime of SF₅CF₃ is of the order of 1000 years.     

Mikroskopische chemische Reaktionen der S?uren von Chlor, Brom und Jod

Ohne Zusammenfassung