Tests for Multiple Peaks in the Spectra of Categorical Time Series

A Fisher's-type test for the significance of peaks in the spectra of categorical time series is developed. This test extends to peaks other than the maximum. The test was based on the Walsh–Fourier periodogram, which is more suitable for data which exhibit sharp jumps rather than smooth curves. The test is applied to a data set of neonatal sleep patterns, which have previously been shown to contain at least two clinically interesting periods.     

气体压强对n型a-Si:H薄膜光学性能的影响

用射频等离子增强化学气相沉积(RF-PECVD)制备磷掺杂氢化非晶硅(a-Si:H)薄膜,研究了辉光放电气体压强(20～80Pa)对薄膜折射率、消光系数、光学带隙以及氢含量的影响;用激光拉曼光谱研究了气体压强对a-Si:H薄膜微结构的影响,并与薄膜的光学性能进行了综合讨论。结果表明,随着辉光放电气体压强的增加,a-Si:H薄膜的光学带隙和氢含量都有不同程度的增大,但折射率和消光系数却逐步减小;与此同时,薄膜内非晶网络的短程和中程有序程度逐渐恶化。     

基于线性正则变换的时频信号分离方法

时频信号分析是当今信号处理领域研究的一个热点问题,各种时频分布函数得到了广泛的研究和应用。线性正则变换是一种重要的时频分析工具。文中研究了线性正则变换与传统时频分布函数的关系;并基于这些关系,提出了一种新的时频信号分离方法,能够把在时频面上互不重叠、但在时域和频域均存在较强耦合的多分量合成信号有效地分离。仿真实例表明了该方法的正确性和实用性。     

Band Spectral Regression with Trending Data

Band spectral regression with both deterministic and stochastic trends is considered. It is shown that trend removal by regression in the time domain prior to band spectral regression can lead to biased and inconsistent estimates in models with frequency dependent coefficients. Both semiparametric and nonparametric regression formulations are considered, the latter including general systems of two‐sided distributed lags such as those arising in lead and lag regressions. The bias problem arises through omitted variables and is avoided by careful specification of the regression equation. Trend removal in the frequency domain is shown to be a convenient option in practice. An asymptotic theory is developed and the two cases of stationary data and cointegrated nonstationary data are compared. In the latter case, a levels and differences regression formulation is shown to be useful in estimating the frequency response function at nonzero as well as zero frequencies.     

Logspline Deconvolution in Besov Space

ABSTRACT. In this paper we consider logspline density estimation for random variables which are contaminated with random noise. In the logspline density estimation for data without noise, the logarithm of an unknown density function is estimated by a polynomial spline, the unknown parameters of which are given by maximum likelihood. When noise is present, B-splines and the Fourier inversion formula are used to construct the logspline density estimator of the unknown density function. Rates of convergence are established when the log-density function is assumed to be in a Besov space. It is shown that convergence rates depend on the smoothness of the density function and the decay rate of the characteristic function of the noise. Simulated data are used to show the finite-sample performance of inference based on the logspline density estimation.     

Statistical aspects of earthquake source parameter estimation in the presence of signal generated noise

Seismologists have developed models which relate observed ground motion to the physical parameters of the earthquake which caused it These models are based on an idealized model which approximates the behavior of the real earth. In this paper we will examine some of the uncertainties which cause observations to deviate from such models. These uncertainties include presence of contaminating noise and the wave scattering caused by the inhomogeneous nature of the earth. By modeling such uncertainties statistically, we are able to formulate a maximum -likelihood type procedure for model fitting and address the such issues as of the computation of standard errors and graphical diagnostics for goodness-of-fit.

The paper illustrates the procedure on observations from a small Califomian earthquake.     

Obtaining Distribution Functions by Numerical Inversion of Characteristic Functions with Applications

We review and discuss numerical inversion of the characteristic function as a tool for obtaining cumulative distribution functions. With the availability of high-speed computing and symbolic computation software, the method is ideally suited for instructional purposes, particularly in the illustration of the inversion theorems covered in graduate probability courses. The method is also available as an alternative to asymptotic approximations, Monte Carlo, or bootstrap techniques when analytic expressions for the distribution function are not available. We illustrate the method with several examples, including one which is concerned with the detection of possible clusters of disease in an epidemiologic study.     

Using the Fast Fourier Transform to Compute Multiple Comparisons With the Best and Subset Selection Critical Values

Multiple comparison methods are widely implemented in statistical packages and heavily used. To obtain the critical value of a multiple comparison method for a given confidence level, a double integral equation must be solved. Current computer implementations evaluate one double integral for each candidate critical value using Gaussian quadrature. Consequently, iterative refinement of the critical value can slow the response time enough to hamper interactive data analysis. However, for balanced designs, to obtain the critical value for multiple comparisons with the best, subset selection, and one-sided multiple comparison with a control, if one regards the inner integral as a function of the outer integration variable, then this function can be obtained by discrete convolution using the Fast Fourier Transform (FFT). Exploiting the fact that this function need not be re-evaluated during iterative refinement of the critical value, it is shown that the FFT method obtains critical values at least four times as accurate and two to five times as fast as the Gaussian quadrature method.     

Unbiasedness of fourier integral estimator under weaker assumptions

The Fourier integral estimator (FIE) of the hazard rate function have been introduced by Singpurwalla and Wong (1983) in order to improve the rate of convergence of mean square error. However, the asymptotic properties are derived under several assumptions. These assumptions are too strong to be satisfied in most applications. The situation becomes worse when some of these assumptions appear contradictory to each other. This greatly limits the usage of FIE. This paper endeavors to release or weaken some of these assumptions and therefore expand the applicable coverage of FIE.     

DFT测频的加窗插值算法与实现

分析DFT频谱中栅栏效应的形成原因,推导出DFT频谱的幅度比值校正算法,在此基础上,系统地推导不同加窗函数下的插值校正公式以提高DFT测频精度,重点探讨插值算法的工程实现方法,提出一种适于FPGA实现的基于区间搜索的频率偏差估计算法,以避免复杂的除法运算。通过对不同信噪比、不同频率偏差下的校正结果进行仿真分析,发现该算法完全满足工程实际需要。