Sampling designs for regression coefficient estimation with correlated errors

The problem of estimating regression coefficients from observations at a finite number of properly designed sampling points is considered when the error process has correlated values and no quadratic mean derivative. Sacks and Ylvisaker (1966,Ann. Math. Statist.,39, 66–89) found an asymptotically optimal design for the best linear unbiased estimator (BLUE). Here, the goal is to find an asymptotically optimal design for a simpler estimator. This is achieved by properly adjusting the median sampling design and the simpler estimator introduced by Schoenfelder (1978, Institute of Statistics Mimeo Series No. 1201, University of North Carolina, Chapel Hill). Examples with stationary (Gauss-Markov) and nonstationary (Wiener) error processes and with linear and nonlinear regression functions are considered both analytically and numerically.Research supported by the Air Force Office of Scientific Research Contract No. 91-0030.     

On Ruijsenaars' asymptotic expansion of the logarithm of the double gamma function

We study the remainder RN(x) in an asymptotic expansion due to S.N.M. Ruijsenaars, for the logarithm of the double gamma function. We show that for any even number N the function is completely monotonic on (0,∞). This proves a recent conjecture of H.L. Pedersen. In addition, we give an estimate for the remainder RN(x) for N even.     

Remarks on a sine polynomial

Let n ≥ 0 be an integer. Then we have for ${x\in(0,\pi)}Let n ≥ 0 be an integer. Then we have for x ? (0,p){x\in(0,\pi)} :

?k=0n (( 2n+1) || (n-k ))\fracsin((2k+1)x)2k+1 ￡ \frac8n  n!(2n+1)!!.\sum_{k=0}^n { 2n+1 \choose n-k }\frac{\sin((2k+1)x)}{2k+1}\leq\frac{8^n \, n!}{(2n+1)!!}.      65. A tripeptide-like prolinamide-thiourea as an aldol reaction catalyst      Fotaras S  Kokotos CG  Kokotos G 《Organic & biomolecular chemistry》2012,10(29):5613-5619 A tripeptide-like prolinamide-thiourea catalyst with (S)-proline, (1S,2S)-diphenylethylenediamine and (S)-di-tert-butyl aspartate as building blocks provides the products of the reaction between ketones and aromatic aldehydes in high to quantitative yields and high stereoselectivities (up to 99:1 dr and 99% ee). Both the chiral centers of the diamine unit are essential, while the thiourea hydrogen originating from the amine and the amide hydrogen play a predominant role for the catalyst efficiency.      66. A Bernstein function related to Ramanujan’s approximations of exp(n)      Stamatis Koumandos 《The Ramanujan Journal》2013,30(3):447-459 Ramanujan’s sequence θ(n),n=0,1,2,…?, is defined by $\frac{e^{n}}{2}=\sum_{j=0}^{n-1}\frac{n^{j}}{j!}+\frac{n^{n}}{n!} \theta(n)$ . It is possible to define, in a simple manner, the function θ(x) for all nonnegative real numbers x. We show that the function $\lambda(x):=x (\theta(x)-\frac{1}{3} )$ is a Bernstein function on [0,∞), that is, λ(x) is nonnegative with completely monotonic derivative on [0,∞). This implies some earlier results concerning complete monotonicity of the function θ(x) on [0,∞).      67. Prediction of stable processes: Spectral and moving average representations      Stamatis Cambanis  A. Reza Soltani 《Probability Theory and Related Fields》1984,66(4):593-612 Summary For stable processes which are Fourier transforms of processes with independent increments, we obtain a Wold decomposition, we characterize their regularity and singularity, and, in the discrete-parameter case, we derive their linear predictors. In sharp contrast with the Gaussian case, regular stable processes which are Fourier transforms of processes with independent increments are not moving averages of stable motion.This research was supported by the Air Force Office of Scientific Research Grant No. F 49620 82C0009      68. Homodiboriranides: The Simplest Negatively Charged Homoaromatic Compounds      Peter Wiliershausen  Claudia Kybart  Nicolaos Stamatis  Werner Massa  Michael Bühl  Paul von Ragu Schleyer  Armin Berndt 《Angewandte Chemie (International ed. in English)》1992,31(9):1238-1240       69. On α-symmetric multivariate distributions      Stamatis Cambanis  Robert Keener  Gordon Simons 《Journal of multivariate analysis》1983,13(2):213-233 A random vector is said to have a 1-symmetric distribution if its characteristic function is of the form φ(|t1| + … + |tn|). 1-Symmetric distributions are characterized through representations of the admissible functions φ and through stochastic representations of the radom vectors, and some of their properties are studied.      70. On the theory of elliptically contoured distributions      Stamatis Cambanis  Steel Huang  Gordon Simons 《Journal of multivariate analysis》1981,11(3):368-385 The theory of elliptically contoured distributions is presented in an unrestricted setting, with no moment restrictions or assumptions of absolute continuity. These distributions are defined parametrically through their characteristic functions and then studied primarily through the use of stochastic representations which naturally follow from the work of Schoenberg [5] on spherically symmetric distributions. It is shown that the conditional distributions of elliptically contoured distributions are elliptically contoured, and the conditional distributions are precisely identified. In addition, a number of the properties of normal distributions (which constitute a type of elliptically contoured distributions) are shown, in fact, to characterize normality.      [首页] « 上一页 [1] [2] [3] [4] [5] [6] 7 [8] 下一页 » 末  页»

A tripeptide-like prolinamide-thiourea as an aldol reaction catalyst

A tripeptide-like prolinamide-thiourea catalyst with (S)-proline, (1S,2S)-diphenylethylenediamine and (S)-di-tert-butyl aspartate as building blocks provides the products of the reaction between ketones and aromatic aldehydes in high to quantitative yields and high stereoselectivities (up to 99:1 dr and 99% ee). Both the chiral centers of the diamine unit are essential, while the thiourea hydrogen originating from the amine and the amide hydrogen play a predominant role for the catalyst efficiency.     

A Bernstein function related to Ramanujan’s approximations of exp(n)

Ramanujan’s sequence θ(n),n=0,1,2,…?, is defined by $\frac{e^{n}}{2}=\sum_{j=0}^{n-1}\frac{n^{j}}{j!}+\frac{n^{n}}{n!} \theta(n)$ . It is possible to define, in a simple manner, the function θ(x) for all nonnegative real numbers x. We show that the function $\lambda(x):=x (\theta(x)-\frac{1}{3} )$ is a Bernstein function on [0,∞), that is, λ(x) is nonnegative with completely monotonic derivative on [0,∞). This implies some earlier results concerning complete monotonicity of the function θ(x) on [0,∞).     

Prediction of stable processes: Spectral and moving average representations

Summary For stable processes which are Fourier transforms of processes with independent increments, we obtain a Wold decomposition, we characterize their regularity and singularity, and, in the discrete-parameter case, we derive their linear predictors. In sharp contrast with the Gaussian case, regular stable processes which are Fourier transforms of processes with independent increments are not moving averages of stable motion.This research was supported by the Air Force Office of Scientific Research Grant No. F 49620 82C0009     

On α-symmetric multivariate distributions

A random vector is said to have a 1-symmetric distribution if its characteristic function is of the form φ(|t₁| + … + |t_n|). 1-Symmetric distributions are characterized through representations of the admissible functions φ and through stochastic representations of the radom vectors, and some of their properties are studied.     

On the theory of elliptically contoured distributions

The theory of elliptically contoured distributions is presented in an unrestricted setting, with no moment restrictions or assumptions of absolute continuity. These distributions are defined parametrically through their characteristic functions and then studied primarily through the use of stochastic representations which naturally follow from the work of Schoenberg [5] on spherically symmetric distributions. It is shown that the conditional distributions of elliptically contoured distributions are elliptically contoured, and the conditional distributions are precisely identified. In addition, a number of the properties of normal distributions (which constitute a type of elliptically contoured distributions) are shown, in fact, to characterize normality.