Effectiveness of a random compound noise strategy for robust parameter design

Robust parameter design has been widely used to improve the quality of products and processes. Although a product array, in which an orthogonal array for control factors is crossed with an orthogonal array for noise factors, is commonly used for parameter design experiments, this may lead to an unacceptably large number of experimental runs. The compound noise strategy proposed by Taguchi [30 G. Taguchi, System of Experimental Design: Engineering Methods to Optimize Quality and Minimize Costs, UNIPUB/Kraus International, White Plains, New York, 1987. [Google Scholar]] can be used to reduce the number of experimental runs. In this strategy, a compound noise factor is formed based on the directionality of the effects of noise factors. However, the directionality is usually unknown in practice. Recently, Singh et al. [28 J. Singh, D.D. Frey, N. Soderborg, and R. Jugulum, Compound noise: Evaluation as a robust parameter design method, Qual. Reliab. Eng. Int. 23 (2007), 387–398. doi: 10.1002/qre.812[Crossref], [Web of Science ®] , [Google Scholar]] proposed a random compound noise strategy, in which a compound noise factor is formed by randomly selecting a setting of the levels of noise factors. The present paper evaluates the random compound noise strategy in terms of the precision of the estimators of the response mean and the response variance. In addition, the variances of the estimators in the random compound noise strategy are compared with those in the n-replication design. The random compound noise strategy is shown to have smaller variances of the estimators than the 2-replication design, especially when the control-by-noise-interactions are strong.     

Least squares parameter estimation in multiplicative noise models

A simple multiplicative noise model with a constant signal has become a basic mathematical model in processing synthetic aperture radar images. The purpose of this paper is to examine a general multiplicative noise model with linear signals represented by a number of unknown parameters. The ordinary least squares (LS) and weighted LS methods are used to estimate the model parameters. The biases of the weighted LS estimates of the parameters are derived. The biases are then corrected to obtain a second-order unbiased estimator, which is shown to be exactly equivalent to the maximum log quasi-likelihood estimation, though the quasi-likelihood function is founded on a completely different theoretical consideration and is known, at the present time, to be a uniquely acceptable theory for multiplicative noise models. Synthetic simulations are carried out to confirm theoretical results and to illustrate problems in processing data contaminated by multiplicative noises. The sensitivity of the LS and weighted LS methods to extremely noisy data is analysed through the simulated examples.     

Adaptive Kalman Filtering with Multivariate Generalized Laplace System Noise

An adaptive Kalman filter is proposed to estimate the states of a system where the system noise is assumed to be a multivariate generalized Laplace random vector. In the presence of outliers in the system noise, it is shown that improved state estimates can be obtained by using an adaptive factor to estimate the dispersion matrix of the system noise term. For the implementation of the filter, an algorithm which includes both single and multiple adaptive factors is proposed. A Monte-Carlo investigation is also carried out to access the performance of the proposed filters in comparison with other robust filters. The results show that, in the sense of minimum mean squared state error, the proposed filter is superior to other filters when the magnitude of a system change is moderate or large.     

Faster Convergence to the Estimation of Quadratic Variation with Microstructure Noise

The continuous quadratic variation of asset return plays a critical role for high-frequency trading. However, the microstructure noise could bias the estimation of the continuous quadratic variation. Zhang et al. (2005 Zhang, L., Mykland, P., Ait-Sahalia, Y. (2005). A tale of two time scales: determining integrated volatility with noisy high-frequency data. J. Amer. Statist. Assoc. 100(472):1394–1411.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) proposed a batch estimator for the continuous quadratic variation of high-frequency data in the presence of microstructure noise. It gives the estimates after all the data arrive. This article proposes a recursive version of their estimator that outputs variation estimates as the data arrive. Our estimator gives excellent estimates well before all the data arrive. Both real high-frequency futures data and simulation data confirm the performance of the recursive estimator.     

Semiparametric Inference in Correlated Long Memory Signal Plus Noise Models

This article proposes an extension of the log periodogram regression in perturbed long memory series that accounts for the added noise, while also allowing for correlation between signal and noise, a common situation in many economic and financial series. Consistency (for d < 1) and asymptotic normality (for d < 3/4) are shown with the same bandwidth restriction as required for the original log periodogram regression in a fully observable series, with the corresponding gain in asymptotic efficiency and faster convergence over competitors. Local Wald, Lagrange Multiplier, and Hausman type tests of the hypothesis of no correlation between the latent signal and noise are also proposed.     

On maximum likelihood estimation of the long-memory parameter in fractional Gaussian noise

Approximate normality and unbiasedness of the maximum likelihood estimate (MLE) of the long-memory parameter H of a fractional Brownian motion hold reasonably well for sample sizes as small as 20 if the mean and scale parameter are known. We show in a Monte Carlo study that if the latter two parameters are unknown the bias and variance of the MLE of H both increase substantially. We also show that the bias can be reduced by using a parametric bootstrap procedure. In very large samples, maximum likelihood estimation becomes problematic because of the large dimension of the covariance matrix that must be inverted. To overcome this difficulty, we propose a maximum likelihood method based upon first differences of the data. These first differences form a short-memory process. We split the data into a number of contiguous blocks consisting of a relatively small number of observations. Computation of the likelihood function in a block then presents no computational problem. We form a pseudo-likelihood function consisting of the product of the likelihood functions in each of the blocks and provide a formula for the standard error of the resulting estimator of H. This formula is shown in a Monte Carlo study to provide a good approximation to the true standard error. The computation time required to obtain the estimate and its standard error from large data sets is an order of magnitude less than that required to obtain the widely used Whittle estimator. Application of the methodology is illustrated on two data sets.     

Simulations and computations of nonparametric density estimates for the deconvolution problem

The nonparametric density function estimation using sample observations which are contaminated with random noise is studied. The particular form of contamination under consideration is Y = X + Z, where Y is an observable random variableZ is a random noise variable with known distribution, and X is an absolutely continuous random variable which cannot be observed directly. The finite sample size performance of a strongly consistent estimator for the density function of the random variable X is illustrated for different distributions. The estimator uses Fourier and kernel function estimation techniques and allows the user to choose constants which relate to bandwidth windows and limits on integration and which greatly affect the appearance and properties of the estimates. Numerical techniques for computation of the estimated densities and for optimal selection of the constant are given.     

Information analysis of local suppression scheme based on a spatial-temporal model

In a wireless sensor network, data collection is relatively cheap whereas data transmission is relatively expensive. Thus, preserving battery life is critical. If the process of interest is sufficiently predictable, the suppression in transmission can be adopted to improve efficiency of sensor networks because the loss of information is not great. The prime interest lies in finding an inference-efficient way to support suppressed data collection application. In this paper, we present a suppression scheme for a multiple nodes setting with spatio-temporal processes, especially when process knowledge is insufficient. We also explore the impact of suppression schemes on the inference of the regional processes under various suppression levels. Finally, we formalize the hierarchical Bayesian model for these schemes.