Browsing by Author "Bibhuti B. Bhattacharyya, Member"

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Data Reduction and Model Selection with Wavelet Transforms
(2000-11-07) Martell, Leah A.; Jacqueline Hughes-Oliver, Co-Chair; Jye-Chyi Lu, Co-Chair; Bibhuti B. Bhattacharyya, Member; Tom Johnson, Member; Griff L. Bilbro, Member
With modern technology massive quantities of data are being collected continuously. The purpose of our research has been to develop amethod for data reduction and model selection applicable to large data setsand replicated data. We propose a novel wavelet shrinkage method byintroducing a new model selection criterion. The proposed shrinkage rule hasat least two advantages over the current shrinkage methods. First, it isadaptive to the smoothness of the signal regardless of whether it has a sparsewavelet representation, since we consider both the deterministic and thestochastic cases. The wavelet decomposition not only catches the signalcomponents for a pure signal, but de-noises and extracts these signal components for a signal contaminated by external influences. Second, theproposed method allows for fine "tuning'' based on the particular data athand. Our simulation studyshows that the methods based on the model selection criterion have better meansquare error (MSE) over the methods currently known. Two aspects make wavelet analysis the analytical tool of choice.First, thelargest in magnitude wavelet coefficients in the discrete wavelet transform (DWT) ofthe data, extract the relevant information, while discarding the resteliminates the noise component. Second, the DWT allows for a fast algorithmcalculation of computational complexity O(n). For the deterministic case we derive a bound on the approximation error of thenonlinear wavelet estimate determined by the largest in magnitude discrete wavelet coefficients. Upper bounds for the approximation error and the rateof increase of the number of wavelet coefficients in the model areobtained for the new wavelet shrinkage estimate. When the signal comes from astochastic process,a bound for the MSE is found, and for the bias of its estimate. A corrected version of the model selection criterion is introduced and some of its properties are studied. The new wavelet shrinkage is employed in the case of replicated data. An algorithm for model selection is proposed,based on which a manufacturing process can be automatically supervised for quality and efficiency. Weapply it to two real life examples.
Nonparametric Spatial analysis in spectral and space domains
(2000-08-23) Kim, Hyon-Jung; Dennis D. Boos, Chair; Montserrat Fuentes, Co-Chair; Bibhuti B. Bhattacharyya, Member; Marcia L. Gumpertz, Member; Jerry M. Davis, Member
The empirical semivariogram of residuals from a regression model withstationary errors may be used to estimate the covariance structure of the underlyingprocess.For prediction (Kriging) the bias of the semivariogram estimate induced byusing residuals instead of errors has only a minor effect because thebias is small for small lags. However, for estimating the variance of estimatedregression coefficients and of predictions,the bias due to using residuals can be quite substantial. Thus wepropose a method for reducing the bias in empirical semivariogram estimatesbased on residuals. The adjusted empirical semivariogram is then isotonizedand made positive definite and used to estimate the variance of estimatedregression coefficients in a general estimating equations setup.Simulation results for least squares and robust regression show that theproposed method works well in linear models withstationary correlated errors. Spectral Analysis with Spatial Periodogram and Data Tapers.(Under the direction of Professor Montserrat Fuentes.)The spatial periodogram is a nonparametric estimate of the spectral density, which is the Fourier Transform of the covariance function. The periodogram is a useful tool to explain the dependence structure of aspatial process.Tapering (data filtering) is an effective technique to remove the edge effects even inhigh dimensional problemsand can be applied to the spatial data in order to reduce the bias of the periodogram.However, the variance of the periodogram increases as the bias is reduced.We present a method to choose an appropriate smoothing parameter for datatapers and obtain better estimates of the spectral densityby improving the properties of the periodogram.The smoothing parameter is selected taking intoaccount the trade-off between bias and variance of the taperedperiodogram. We introduce a new asymptotic approach for spatial datacalled `shrinking asymptotics', which combines theincreasing-domain and the fixed-domain asymptotics.With this approach, the tapered spatial periodogram can be usedto determine uniquely the spectral density of the stationary process,avoiding the aliasing problem.
Statistical Analysis and Modeling of Pharmacokinetic Data from Percutaneous Absorption
(2001-03-26) Budsaba, Kamon; Charles E. Smith, Chair; Bibhuti B. Bhattacharyya, Member; Marie Davidian, Member; David A. Dickey, Member; Jim E. Riviere, Member
Statistical analysis applied to percutaneous absorption andcutaneous disposition of different types of jet fuels is presented. A slightly different question is addressed with methyl salicylate absorption, namely when one compound can be used as a simulant for another compound. A new graphical statistics method, called "Compass Plot'', is introduced for displaying the results in the design of experiments, especially for balanced factorial experiments. An example of compass plots for visualizing significant interactions in complex toxicology studies is provided. It is followed by a simulation study on an approximated F-test to determine whether a random effects model is needed for the exponential difference model. A new multivariate coefficient of variation, used as an index to determine which effects have a random component, is also introduced and investigated by simulations and two real datasets.
Unit Root Tests in Panel Data: Weighted Symmetric Estimation and Maximum Likelihood Estimation
(2001-08-23) Kim, Hyunjung; David A. Dickey, Chair; Marcia L. Gumpertz, Member; Bibhuti B. Bhattacharyya, Member; Sastry G. Pantula, Member
There has been much interest in testing nonstationarity of panel data in the econometric literature. In the last decade, several tests based on the ordinary least squares and Lagrange multiplier methodhave been developed. In contrast to a unit root test in the univariate case,test statistics in panel data have Gaussian limiting distributions.This dissertation considers weighted symmetric estimation and maximum likelihood estimation in the autoregressive model with individual effects.The asymptotic distributions have been derived as the number of individuals and time periods become large. The power study from Monte Carloexperiments shows that the proposed test statistics perform substantiallybetter than those in previous studies even for small samples.As an example, we consider the real Gross Domestic Product per Capita for 12 countries.