Asymptotic distribution theory of statistical functionals: The compact derivative approach for robust estimators

Summary Derivatives of statistical functionals have been used to derive the asymptotic distributions ofL-,M- andR-estimators. This approach is often heuristic because the types of derivatives chosen have serious limitations. The Gateaux derivative is too weak and the Fréchet derivative is too strong. In between lies the compact derivative. This paper obtains strong results in a rigorous manner using the compact derivative onC ₀(R). This choice of space allows results for a broader class of functionals than previous choices, and the fact that is often tight provides the compact set required. A major result is the derivation of the compact derivative of the inverse c.d.f. when the range space is endowed with the uniform norm. It has applications to the asymptotic theory ofL-,M- andR-estimators. We illustrate the power of this result by applications toL-estimators in settings including the one sample problem, data grouped by quantiles, and censored survival time data.     

Diorganotin(IV) complexes of dideprotonated pyridoxine (PN, vitamin B6). The crystal structures of [SnEt2(PN-2H)] · CH3OH, [SnEt2(PN-2H)(DMSO)] and [SnBu2(PN-2H)]

The reactions of dimethyl-, diethyl- and dibutyltin(IV) oxides with pyridoxine (PN) in toluene/ethanol led to the formation of compounds [SnR₂(PN-2H)] which were characterized by EI and FAB mass spectrometry and by IR, Raman, Mössbauer and ¹H, ¹³C and ¹¹⁹Sn NMR spectroscopy. The structures of [SnEt₂(PN-2H)] · CH₃OH, [SnBu₂(PN-2H)] and [SnEt₂(PN-2H)(DMSO)] were determined by X-ray diffractometry. The first two contain dimeric [SnR₂(PN-2H)]₂ units in which two bridging-chelating pyridoxinate anions link the Sn atoms, while in [SnEt₂(PN-2H)(DMSO)] the DMSO coordinates to the tin atom via its O atom in a similar dimeric unit.     

A mild, one-pot synthesis of disubstituted benzimidazoles from 2-nitroanilines

A one-pot synthesis of disubstituted benzimidazoles from 2-nitroanilines is described. Hydrogenation of N-substituted 2-nitroanilines with palladium on carbon as catalyst in the presence of trimethyl orthoformate and catalytic pyridinium p-toluenesulfonate (PPTS) at room temperature provided good to excellent yields of the corresponding disubstituted benzimidazoles.     

On the existence of periodic solutions for the equation\ddot x + f(x)\dot x + g(x) = 0

We establish in this work sufficient conditions for the existence of periodic solutions for the Liénard equation .     

The solid state structure of [b(10)h(11)](-) and its dynamic NMR spectra in solution

The structure of [PPh(3)(benzyl)][B(10)H(11)] was determined at -123 degrees C and 24 degrees C by single-crystal X-ray analyses. The B(10) core of [B(10)H(11)](-) is similar in shape to that of [B(10)H(10)](2)(-). The 11th H atom asymmetrically caps a polar face of the cluster and shows no tendency for disorder in the solid state. Variable temperature multinuclear NMR studies shed light on the dynamic nature of [B(10)H(11)](-) in solution. In addition to the fluxionality of the cluster H atoms, the boron cage is fluxional at moderate temperatures, in contrast to [B(10)H(10)](2)(-). Multiple exchange processes are believed to take place as a function of temperature. Results of ab initio calculations are presented. Crystal data: [PPh(3)(benzyl)][B(10)H(11)] at -123 degrees C, P2(1)/c, a = 9.988(2) A, b = 18.860(2) A, c = 15.072(2) A, beta = 107.916(8) degrees, V = 2701.5(7) A(3), Z = 4; [PPh(3)(benzyl)][B(10)H(11)] at 24 degrees C, P2(1)/c, a = 10.067(5) A, b = 19.009(9) A, c = 15.247(7) A, beta = 107.952(9) degrees, V = 2775(2) A(3), Z = 4.     

Avidin self-associates with boric acid gel suspensions: an affinity boron carrier that might be developed for boron neutron-capture therapy

It has been shown in preliminary studies that the antibacterial protein avidin self-associates with the boric acid gel polymer, and avidin-coated gel particles in the micrometer and submicrometer size ranges are of interest for boron neutron-capture therapy (BNCT), which is neutron-induced fission of boron-10 to produce intense alpha radiation for tumor destruction. The gel particles carry large amounts of boron-10 and are theoretically able effect a meaningful tissue dosing through BNCT. A gross precipitation of gel particles occurs within 46 min of mixing when the avidin/colloid ratio is about 0.34 g avidin/g colloid. This is a minimum time if gel and avidin concentrations are in the low microgram/milliliter range, but at higher proportions of avidin the time delay to precipitation increases significantly; i.e., the colloid surface becomes blocked, inhibiting lattice formation. The avidin-coated gel particles eventually cross-link, forming a solid matrix and precipitating on a timescale measured on the order of an hour. At shorter exposure times rapid agglutination-like reactions were observed with biotinylated bovine albumin, suggesting that two-stage pretargeting of specific tissues should be possible with biotinylated antitumor antibodies. However, for BNCT to be practical, avidin's interaction with the gel needs to be strengthened, and all aryl-B(OH)(2) groups on the particle surfaces must be blocked, or else the particles will interact strongly and nonspecifically with each other and with the carbohydrate groups present on most cell surfaces. Glyceric acid delays the precipitation of the particle suspensions while most simple and complex carbohydrates accelerate it.