Novel Spatially Adaptive Image Denoising Algorithm Based on Covariance Estimation in Wavelet Domain

A new method for image denoising is proposed. By analyzing image's statistical properties in wavelet domain, it is shown that the natural image has a strong and spatial variable covariance structure relationship in local space of sub-band. A non-direct estimation method is suggested to make an adaptive estimate of spatial variable covariance by estimating the correlation coefficient and variance of subband image separately. It can be used to estimate adaptive filtering of subband image. The experiment shows that this method can improve the image's SNR, and has strong ability to preserve edges.

Covariance estimation via fiducial inference

As a classical problem,covariance estimation has drawn much attention from the statistical com-munity for decades.Much work has been done under the frequentist and Bayesian frameworks.Aiming to quantify the uncertainty of the estimators without having to choose a prior,we have developed a fiducial approach to the estimation of covariance matrix.Built upon the Fiducial Berstein-von Mises Theorem,we show that the fiducial distribution of the covariate matrix is consistent under our framework.Consequently,the samples generated from this fiducial distri-bution are good estimators to the true covariance matrix,which enable us to define a meaningful confidence region for the covariance matrix.Lastly,we also show that the fiducial approach can be a powerful tool for identifying clique structures in covariance matrices.

An approximate point-based alternative for the estimation of variance under big BAF sampling

Background:A new variance estimator is derived and tested for big BAF(Basal Area Factor)sampling which is a forest inventory system that utilizes Bitterlich sampling(point sampling)with two BAF sizes,a small BAF for tree counts and a larger BAF on which tree measurements are made usually including DBHs and heights needed for volume estimation.Methods:The new estimator is derived using the Delta method from an existing formulation of the big BAF estimator as consisting of three sample means.The new formula is compared to existing big BAF estimators including a popular estimator based on Bruce’s formula.Results:Several computer simulation studies were conducted comparing the new variance estimator to all known variance estimators for big BAF currently in the forest inventory literature.In simulations the new estimator performed well and comparably to existing variance formulas.Conclusions:A possible advantage of the new estimator is that it does not require the assumption of negligible correlation between basal area counts on the small BAF factor and volume-basal area ratios based on the large BAF factor selection trees,an assumption required by all previous big BAF variance estimation formulas.Although this correlation was negligible on the simulation stands used in this study,it is conceivable that the correlation could be significant in some forest types,such as those in which the DBH-height relationship can be affected substantially by density perhaps through competition.We derived a formula that can be used to estimate the covariance between estimates of mean basal area and the ratio of estimates of mean volume and mean basal area.We also mathematically derived expressions for bias in the big BAF estimator that can be used to show the bias approaches zero in large samples on the order of 1n where n is the number of sample points.

Estimation of time series noise covariance using correlation technology

Covariance of clean signal and observed noise is necessary for extracting clean signal from a time series.This is transferred to calculate the covariance of observed noise and clean signal's MA process,when the clean signal is described by an autoregressive moving average (ARMA) model.Using the correlations of the innovations data from observed time series to form a least-squares problem,a concisely autocovariance least-square (CALS) method has been proposed to estimate the covariance.We also extended our work to the case of unknown MA process coefficients.Comparisons between Odelson's autocovariance least-square (ALS) estimation algorithm and the proposed CALS method show that the CALS method could get a much more exact and compact estimation of the covariance than ALS and its extended form.

High Dimensionality Effects on the Efficient Frontier: A Tri-Nation Study

Markowitz Portfolio theory under-estimates the risk associated with the return of a portfolio in case of high dimensional data. El Karoui mathematically proved this in [1] and suggested improved estimators for unbiased estimation of this risk under specific model assumptions. Norm constrained portfolios have recently been studied to keep the effective dimension low. In this paper we consider three sets of high dimensional data, the stock market prices for three countries, namely US, UK and India. We compare the Markowitz efficient frontier to those obtained by unbiasedness corrections and imposing norm-constraints in these real data scenarios. We also study the out-of-sample performance of the different procedures. We find that the 2-norm constrained portfolio has best overall performance.

On Two-stage Estimate Based on Independent Estimate of Covariance Matrix

When an independent estimate of covariance matrix is available, we often prefer two-stage estimate （TSE）. Expressions of exact covarianee matrix of the TSE obtained by using all and some covariables in eovariance adjustment approach are given, and a necessary and sufficient condition for the TSE to be superior to the least square estimate and related large sample test is also established. Furthermore the TSE, by using some covariables, is expressed as weighted least square estimate. Basing on this fact, a necessary and sufficient condition for the TSE by using some covariables to be superior to the TSE by using all eovariables is obtained. These results give us some insight into the selection of covariables in the TSE and its application.

A two-step method for estimating high-dimensional Gaussian graphical models

The problem of estimating high-dimensional Gaussian graphical models has gained much attention in recent years. Most existing methods can be considered as one-step approaches, being either regression-based or likelihood-based. In this paper, we propose a two-step method for estimating the high-dimensional Gaussian graphical model. Specifically, the first step serves as a screening step, in which many entries of the concentration matrix are identified as zeros and thus removed from further consideration. Then in the second step, we focus on the remaining entries of the concentration matrix and perform selection and estimation for nonzero entries of the concentration matrix. Since the dimension of the parameter space is effectively reduced by the screening step,the estimation accuracy of the estimated concentration matrix can be potentially improved. We show that the proposed method enjoys desirable asymptotic properties. Numerical comparisons of the proposed method with several existing methods indicate that the proposed method works well. We also apply the proposed method to a breast cancer microarray data set and obtain some biologically meaningful results.

Ozone concentrations, flux and potential effect on yield during wheat growth in the NorthwestShandong Plain of China

Ozone（O3） concentration and flux（Fo） were measured using the eddy covariance technique over a wheat field in the Northwest-Shandong Plain of China. The O3-induced wheat yield loss was estimated by utilizing O3exposure-response models. The results showed that：（1） During the growing season（7 March to 7 June, 2012）, the minimum（16.1 ppb V） and maximum（53.3 ppb V）mean O3 concentrations occurred at approximately 6：30 and 16：00, respectively. The mean and maximum of all measured O3 concentrations were 31.3 and 128.4 ppb V, respectively. The variation of O3 concentration was mainly affected by solar radiation and temperature.（2） The mean diurnal variation of deposition velocity（V d） can be divided into four phases, and the maximum occurred at noon（12：00）. Averaged V d during daytime（6：00–18：00） and nighttime（18：00–6：00） were 0.42 and 0.14 cm/sec, respectively. The maximum of measured V d was about1.5 cm/sec. The magnitude of V d was influenced by the wheat growing stage, and its variation was significantly correlated with both global radiation and friction velocity.（3） The maximum mean F o appeared at 14：00, and the maximum measured F o was-33.5 nmol/（m^2·sec）. Averaged F o during daytime and nighttime were-6.9 and-1.5 nmol/（m^2·sec）, respectively.（4） Using O3 exposure-response functions obtained from the USA, Europe, and China, the O3-induced wheat yield reduction in the district was estimated as 12.9% on average（5.5%–23.3%）. Large uncertainties were related to the statistical methods and environmental conditions involved in deriving the exposure-response functions.

Outlier Detection via a Block Diagonal Product Estimator

Outlier detection is a fundamental topic in robust statistics.Traditional outlier detection methods try to find a clean subset of given size,which is used to estimate the location vector and scatter matrix,and the outliers can be flagged by the Mahalanobis distance.However,methods such as the minimum covariance determinant approach cannot be applied directly to high-dimensional data,especially when the dimension of the sample is greater than the sample size.A novel fast detection procedure based on a block diagonal partition is proposed,and the asymptotic distribution of the modified Mahalanobis distance is obtained.The authors verify the specificity and sensitivity of this procedure by simulation and real data analysis in high-dimensional settings.