958 resultados para Gaussian distributions
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1925/01/01.
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1928/07/01.
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1933.
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1931/01/01.
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1932.
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Ancien possesseur : Argenson, Antoine-René de Voyer (1722-1787 ; marquis de Paulmy d')
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Solid state nuclear magnetic resonance (NMR) spectroscopy is a powerful technique for studying structural and dynamical properties of disordered and partially ordered materials, such as glasses, polymers, liquid crystals, and biological materials. In particular, twodimensional( 2D) NMR methods such as ^^C-^^C correlation spectroscopy under the magicangle- spinning (MAS) conditions have been used to measure structural constraints on the secondary structure of proteins and polypeptides. Amyloid fibrils implicated in a broad class of diseases such as Alzheimer's are known to contain a particular repeating structural motif, called a /5-sheet. However, the details of such structures are poorly understood, primarily because the structural constraints extracted from the 2D NMR data in the form of the so-called Ramachandran (backbone torsion) angle distributions, g{^,'4)), are strongly model-dependent. Inverse theory methods are used to extract Ramachandran angle distributions from a set of 2D MAS and constant-time double-quantum-filtered dipolar recoupling (CTDQFD) data. This is a vastly underdetermined problem, and the stability of the inverse mapping is problematic. Tikhonov regularization is a well-known method of improving the stability of the inverse; in this work it is extended to use a new regularization functional based on the Laplacian rather than on the norm of the function itself. In this way, one makes use of the inherently two-dimensional nature of the underlying Ramachandran maps. In addition, a modification of the existing numerical procedure is performed, as appropriate for an underdetermined inverse problem. Stability of the algorithm with respect to the signal-to-noise (S/N) ratio is examined using a simulated data set. The results show excellent convergence to the true angle distribution function g{(j),ii) for the S/N ratio above 100.
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A wide range of tests for heteroskedasticity have been proposed in the econometric and statistics literature. Although a few exact homoskedasticity tests are available, the commonly employed procedures are quite generally based on asymptotic approximations which may not provide good size control in finite samples. There has been a number of recent studies that seek to improve the reliability of common heteroskedasticity tests using Edgeworth, Bartlett, jackknife and bootstrap methods. Yet the latter remain approximate. In this paper, we describe a solution to the problem of controlling the size of homoskedasticity tests in linear regression contexts. We study procedures based on the standard test statistics [e.g., the Goldfeld-Quandt, Glejser, Bartlett, Cochran, Hartley, Breusch-Pagan-Godfrey, White and Szroeter criteria] as well as tests for autoregressive conditional heteroskedasticity (ARCH-type models). We also suggest several extensions of the existing procedures (sup-type of combined test statistics) to allow for unknown breakpoints in the error variance. We exploit the technique of Monte Carlo tests to obtain provably exact p-values, for both the standard and the new tests suggested. We show that the MC test procedure conveniently solves the intractable null distribution problem, in particular those raised by the sup-type and combined test statistics as well as (when relevant) unidentified nuisance parameter problems under the null hypothesis. The method proposed works in exactly the same way with both Gaussian and non-Gaussian disturbance distributions [such as heavy-tailed or stable distributions]. The performance of the procedures is examined by simulation. The Monte Carlo experiments conducted focus on : (1) ARCH, GARCH, and ARCH-in-mean alternatives; (2) the case where the variance increases monotonically with : (i) one exogenous variable, and (ii) the mean of the dependent variable; (3) grouped heteroskedasticity; (4) breaks in variance at unknown points. We find that the proposed tests achieve perfect size control and have good power.