Some misspecfication problems in long-memory time series models

Doctor of Philosophy in Mathematics

Novel Regression Methods For Spectral Data

Singular Value Decomposition (SVD), Principal Component Analysis (PCA) and Multiple Linear Regression (MLR) are some of the mathematical pre- liminaries that are discussed prior to explaining PLS and PCR models. Both PLS and PCR are applied to real spectral data and their di erences and similarities are discussed in this thesis. The challenge lies in establishing the optimum number of components to be included in either of the models but this has been overcome by using various diagnostic tools suggested in this thesis. Correspondence analysis (CA) and PLS were applied to ecological data. The idea of CA was to correlate the macrophytes species and lakes. The di erences between PLS model for ecological data and PLS for spectral data are noted and explained in this thesis. i

Comparing Near-infrared Conventional Diffuse Reflectance Spectroscopy And Hyperspectral Imaging For Determination Of The Bulk Properties Of Solid Samples By Multivariate Regression: Determination Of Mooney Viscosity And Plasticity Indices Of Natural Rubber.

Conventional reflectance spectroscopy (NIRS) and hyperspectral imaging (HI) in the near-infrared region (1000-2500 nm) are evaluated and compared, using, as the case study, the determination of relevant properties related to the quality of natural rubber. Mooney viscosity (MV) and plasticity indices (PI) (PI0 - original plasticity, PI30 - plasticity after accelerated aging, and PRI - the plasticity retention index after accelerated aging) of rubber were determined using multivariate regression models. Two hundred and eighty six samples of rubber were measured using conventional and hyperspectral near-infrared imaging reflectance instruments in the range of 1000-2500 nm. The sample set was split into regression (n = 191) and external validation (n = 95) sub-sets. Three instruments were employed for data acquisition: a line scanning hyperspectral camera and two conventional FT-NIR spectrometers. Sample heterogeneity was evaluated using hyperspectral images obtained with a resolution of 150 × 150 μm and principal component analysis. The probed sample area (5 cm(2); 24,000 pixels) to achieve representativeness was found to be equivalent to the average of 6 spectra for a 1 cm diameter probing circular window of one FT-NIR instrument. The other spectrophotometer can probe the whole sample in only one measurement. The results show that the rubber properties can be determined with very similar accuracy and precision by Partial Least Square (PLS) regression models regardless of whether HI-NIR or conventional FT-NIR produce the spectral datasets. The best Root Mean Square Errors of Prediction (RMSEPs) of external validation for MV, PI0, PI30, and PRI were 4.3, 1.8, 3.4, and 5.3%, respectively. Though the quantitative results provided by the three instruments can be considered equivalent, the hyperspectral imaging instrument presents a number of advantages, being about 6 times faster than conventional bulk spectrometers, producing robust spectral data by ensuring sample representativeness, and minimizing the effect of the presence of contaminants.

Effect of Disease Severity and Optic Disc Size on Diagnostic Accuracy of RTVue Spectral Domain Optical Coherence Tomograph in Glaucoma

PURPOSE. To evaluate the effect of disease severity and optic disc size on the diagnostic accuracies of optic nerve head (ONH), retinal nerve fiber layer (RNFL), and macular parameters with RTVue (Optovue, Fremont, CA) spectral domain optical coherence tomography (SDOCT) in glaucoma. METHODS. 110 eyes of 62 normal subjects and 193 eyes of 136 glaucoma patients from the Diagnostic Innovations in Glaucoma Study underwent ONH, RNFL, and macular imaging with RTVue. Severity of glaucoma was based on visual field index (VFI) values from standard automated perimetry. Optic disc size was based on disc area measurement using the Heidelberg Retina Tomograph II (Heidelberg Engineering, Dossenheim, Germany). Influence of disease severity and disc size on the diagnostic accuracy of RTVue was evaluated by receiver operating characteristic (ROC) and logistic regression models. RESULTS. Areas under ROC curve (AUC) of all scanning areas increased (P < 0.05) as disease severity increased. For a VFI value of 99%, indicating early damage, AUCs for rim area, average RNLI thickness, and ganglion cell complex-root mean square were 0.693, 0.799, and 0.779, respectively. For a VFI of 70%, indicating severe damage, corresponding AUCs were 0.828, 0.985, and 0.992, respectively. Optic disc size did not influence the AUCs of any of the SDOCT scanning protocols of RTVue (P > 0.05). Sensitivity of the rim area increased and specificity decreased in large optic discs. CONCLUSIONS. Diagnostic accuracies of RTVue scanning protocols for glaucoma were significantly influenced by disease severity. Sensitivity of the rim area increased in large optic discs at the expense of specificity. (Invest Ophthalmol Vis Sci. 2011;92:1290-1296) DOI:10.1167/iovs.10-5516

Effect of Disease Severity on the Performance of Cirrus Spectral-Domain OCT for Glaucoma Diagnosis

PURPOSE. To evaluate the effect of disease severity on the diagnostic accuracy of the Cirrus Optical Coherence Tomograph (Cirrus HD-OCT; Carl Zeiss Meditec, Inc., Dublin, CA) for glaucoma detection. METHODS. One hundred thirty-five glaucomatous eyes of 99 patients and 79 normal eyes of 47 control subjects were recruited from the longitudinal Diagnostic Innovations in Glaucoma Study (DIGS). The severity of the disease was graded based on the visual field index (VFI) from standard automated perimetry. Imaging of the retinal nerve fiber layer (RNFL) was obtained using the optic disc cube protocol available on the Cirrus HD-OCT. Pooled receiver operating characteristic (ROC) curves were initially obtained for each parameter of the Cirrus HD-OCT. The effect of disease severity on diagnostic performance was evaluated by fitting an ROC regression model, with VFI used as a covariate, and calculating the area under the ROC curve (AUCs) for different levels of disease severity. RESULTS. The largest pooled AUCs were for average thickness (0.892), inferior quadrant thickness (0.881), and superior quadrant thickness (0.874). Disease severity had a significant influence on the detection of glaucoma. For the average RNFL thickness parameter, AUCs were 0.962, 0.932, 0.886, and 0.822 for VFIs of 70%, 80%, 90%, and 100%, respectively. CONCLUSIONS. Disease severity had a significant effect on the diagnostic performance of the Cirrus HD-OCT and thus should be considered when interpreting results from this device and when considering the potential applications of this instrument for diagnosing glaucoma in the various clinical settings. (Invest Ophthalmol Vis Sci. 2010;51:4104-4109) DOI:10.1167/iovs.094716

Comparison of central macular thickness (CMT) measurement between time domain and spectral domain (SD) optical coherence tomography (OCT) and reproducibility of SD OCT in active neovascular AMD

Purpose: To evaluate the reproducibility of Cirrus-SD OCT measurements and to compare central macular thickness (CMT) measurements between TD-Stratus and SD-Cirrus OCT in patients with active exudative AMD. Methods: Consecutive case series of patients with active exudative AMD seen in the Medical Retina Department. Patients underwent 1 scan with Stratus (macular thickness map protocol) and 5 scans with Cirrus (Macular Cube protocol) at the same visit by the same experienced examiner. To be included, patients best-corrected visual acuity (BCVA) had to be >20/200 while all scans had to be of sufficient quality, well-centered and at least one Cirrus scan with CMT >300 microns. The repeatability of the SD Cirrus was estimated by using all 5 CMT measurements and the mean of the Cirrus measurements was compared with the CMT obtained by TD Stratus. Results: Cirrus OCT demonstrated high intraobserver repeatability at the central foveal region (ICC 96%). The mean of the CMT measurements was 321microns for Stratus and 387 microns for Cirrus. The average difference was 65m (SD=30). The coefficient of concordance between Stratus and Cirrus CMT measurements was rho=0,749 with a high precision and a moderate accuracy. The equation of the line of regression between Stratus and meanCirrus is given by the following: M_stratus = 0,848 x m_cirrus - 4,496 (1).Conclusions: The Cirrus macular cube protocol allows reproducible CMT measurements in patients with active exudative AMD. In cases of upgrading from TD to SD use and vice versa, there is the possibility to predict the measurements by using the equation (1). These real life data and conclusions can help in improving our clinical management of patients with neovascular AMD.

An infrared spectral signature of human lymphocyte subpopulations from peripheral blood.

Metastatic melanomas are frequently refractory to most adjuvant therapies such as chemotherapies and radiotherapies. Recently, immunotherapies have shown good results in the treatment of some metastatic melanomas. Immune cell infiltration in the tumor has been associated with successful immunotherapy. More generally, tumor infiltrating lymphocytes (TILs) in the primary tumor and in metastases of melanoma patients have been demonstrated to correlate positively with favorable clinical outcomes. Altogether, these findings suggest the importance of being able to identify, quantify and characterize immune infiltration at the tumor site for a better diagnostic and treatment choice. In this paper, we used Fourier Transform Infrared (FTIR) imaging to identify and quantify different subpopulations of T cells: the cytotoxic T cells (CD8+), the helper T cells (CD4+) and the regulatory T cells (T reg). As a proof of concept, we investigated pure populations isolated from human peripheral blood from 6 healthy donors. These subpopulations were isolated from blood samples by magnetic labeling and purities were assessed by Fluorescence Activated Cell Sorting (FACS). The results presented here show that Fourier Transform Infrared (FTIR) imaging followed by supervised Partial Least Square Discriminant Analysis (PLS-DA) allows an accurate identification of CD4+ T cells and CD8+ T cells (>86%). We then developed a PLS regression allowing the quantification of T reg in a different mix of immune cells (e.g. Peripheral Blood Mononuclear Cells (PBMCs)). Altogether, these results demonstrate the sensitivity of infrared imaging to detect the low biological variability observed in T cell subpopulations.

Spatial and Spectral Separability of Grasslands in the inner Turku Archipelago using Landsat Thematic Mapper Satellite Imagery

The present study investigates the spatial and spectral discrimination potential for grassland patches in the inner Turku Archipelago using Landsat Thematic Mapper satellite imagery. The spatial discrimination potential was computed through overlay analysis using official grassland parcel data and a hypothetical 30 m resolution satellite image capturing the site. It found that Landsat TM imagery’s ability to retrieve pure or near-pure pixels (90% purity or more) from grassland patches smaller than 1 hectare was limited to 13% success, compared to 52% success when upscaling the resolution to 10 x 10 m pixel size. Additionally, the perimeter/area patch metric is proposed as a predictor for the suitability of the spatial resolution of input imagery. Regression analysis showed that there is a strong negative correlation between a patch’s perimeter/area ratio and its pure pixel potential. The study goes on to characterise the spectral response and discrimination potential for the five main grassland types occurring in the study area: recreational grassland, traditional pasture, modern pasture, fodder production grassland and overgrown grassland. This was done through the construction of spectral response curves, a coincident spectral plot and a contingency matrix as well as by calculating the transformed divergence for the spectral signatures, all based on training samples from the TM imagery. Substantial differences in spectral discrimination potential between imagery from the beginning of the growing season and the middle of summer were found. This is because the spectral responses for these five grassland types converge as the peak of the growing season draws nearer. Recreational grassland shows a consistent discrimination advantage over other grassland types, whereas modern pasture is most easily confused. Traditional pasture land, perhaps the most biologically valuable grassland type, can be spectrally discriminated from other grassland types with satisfactory success rates provided early growing season imagery is used.

An Autoregressive Spectral Density Estimator at Frequency Zero for Nonstationarity Tests.

Many unit root and cointegration tests require an estimate of the spectral density function at frequency zero at some process. Kernel estimators based on weighted sums of autocovariances constructed using estimated residuals from an AR(1) regression are commonly used. However, it is known that with substantially correlated errors, the OLS estimate of the AR(1) parameter is severely biased. in this paper, we first show that this least squares bias induces a significant increase in the bias and mean-squared error of kernel-based estimators.

The relationship between diffuse spectral reflectance of the soil and its cation exchange capacity is scale-dependent

Diffuse reflectance spectroscopy (DRS) is increasingly being used to predict numerous soil physical, chemical and biochemical properties. However, soil properties and processes vary at different scales and, as a result, relationships between soil properties often depend on scale. In this paper we report on how the relationship between one such property, cation exchange capacity (CEC), and the DRS of the soil depends on spatial scale. We show this by means of a nested analysis of covariance of soils sampled on a balanced nested design in a 16 km × 16 km area in eastern England. We used principal components analysis on the DRS to obtain a reduced number of variables while retaining key variation. The first principal component accounted for 99.8% of the total variance, the second for 0.14%. Nested analysis of the variation in the CEC and the two principal components showed that the substantial variance components are at the > 2000-m scale. This is probably the result of differences in soil composition due to parent material. We then developed a model to predict CEC from the DRS and used partial least squares (PLS) regression do to so. Leave-one-out cross-validation results suggested a reasonable predictive capability (R2 = 0.71 and RMSE = 0.048 molc kg− 1). However, the results from the independent validation were not as good, with R2 = 0.27, RMSE = 0.056 molc kg− 1 and an overall correlation of 0.52. This would indicate that DRS may not be useful for predictions of CEC. When we applied the analysis of covariance between predicted and observed we found significant scale-dependent correlations at scales of 50 and 500 m (0.82 and 0.73 respectively). DRS measurements can therefore be useful to predict CEC if predictions are required, for example, at the field scale (50 m). This study illustrates that the relationship between DRS and soil properties is scale-dependent and that this scale dependency has important consequences for prediction of soil properties from DRS data

Physical interpretation of the correlation between multi-angle spectral data and canopy height

Recent empirical studies have shown that multi-angle spectral data can be useful for predicting canopy height, but the physical reason for this correlation was not understood. We follow the concept of canopy spectral invariants, specifically escape probability, to gain insight into the observed correlation. Airborne Multi-Angle Imaging Spectrometer (AirMISR) and airborne Laser Vegetation Imaging Sensor (LVIS) data acquired during a NASA Terrestrial Ecology Program aircraft campaign underlie our analysis. Two multivariate linear regression models were developed to estimate LVIS height measures from 28 AirMISR multi-angle spectral reflectances and from the spectrally invariant escape probability at 7 AirMISR view angles. Both models achieved nearly the same accuracy, suggesting that canopy spectral invariant theory can explain the observed correlation. We hypothesize that the escape probability is sensitive to the aspect ratio (crown diameter to crown height). The multi-angle spectral data alone therefore may not provide enough information to retrieve canopy height globally.

Predicting spectral features in galaxy spectra from broad-band photometry

We explore the prospects of predicting emission-line features present in galaxy spectra given broad-band photometry alone. There is a general consent that colours, and spectral features, most notably the 4000 angstrom break, can predict many properties of galaxies, including star formation rates and hence they could infer some of the line properties. We argue that these techniques have great prospects in helping us understand line emission in extragalactic objects and might speed up future galaxy redshift surveys if they are to target emission-line objects only. We use two independent methods, Artificial Neural Networks (based on the ANNz code) and Locally Weighted Regression (LWR), to retrieve correlations present in the colour N-dimensional space and to predict the equivalent widths present in the corresponding spectra. We also investigate how well it is possible to separate galaxies with and without lines from broad-band photometry only. We find, unsurprisingly, that recombination lines can be well predicted by galaxy colours. However, among collisional lines some can and some cannot be predicted well from galaxy colours alone, without any further redshift information. We also use our techniques to estimate how much information contained in spectral diagnostic diagrams can be recovered from broad-band photometry alone. We find that it is possible to classify active galactic nuclei and star formation objects relatively well using colours only. We suggest that this technique could be used to considerably improve redshift surveys such as the upcoming Fibre Multi Object Spectrograph (FMOS) survey and the planned Wide Field Multi Object Spectrograph (WFMOS) survey.

Alteration of soil properties through a weathering sequence as evaluated by spectral reflectance

In the study of physical, chemical, and mineralogical data related to the weathering of soils and the quantification of their properties, remote sensing constitutes an important technique that, in addition to conventional analyses, can contribute to soil survey. The objectives of this research were to characterize and differentiate soils developed from basaltic rocks that occur in the Parana state, Brazil and to quantify soil properties based on their spectral reflectance. These observations were used to verify the relationship between the soils and reflectance with regard to weathering, organic matter (OM), and forms of Fe. From the least to the most weathered soil, we used a Typic Argiudoll (Reddish Brunizem), Rhodudalf (Terra Roxa Estruturada), and Rhodic Hapludox (Very Dark Red Latosol). The spectral reflectances between 400 and 2500 nm were obtained in the laboratory from soil samples collected at two depth increments, 0- to 20- and 40- to 60-cm, using an Infra Red Intelligent Spectroradiometer (IRIS). Correlation, regression, and discriminant estimates were used in analyzing the soil and spectral data. Results of this study indicated that soils could be separated at the soil-type level based on reflectance intensity in various absorption bands. Soil collected in the 40- to 60-cm depth appeared to have higher reflectance intensities than those from the 0- to 20-cm depth. Removal of OM from soil samples promoted higher reflectance intensity in the entire spectrum. Amorphous and crystalline Fe influenced reflectance differently. Weathering of basaltic soils was correlated with alterations in the reflectance intensities and absorption features of the spectral curves. Multivariate analysis demonstrated that this technique was efficient in the estimation of clay, silt, kaolinite, crystalline Fe, amorphous Fe, and Mg through the use of reflected energy of the soils.

Precision of yule-walker methods for the arma spectral model

In this work a new method is proposed of separated estimation for the ARMA spectral model based on the modified Yule-Walker equations and on the least squares method. The proposal of the new method consists of performing an AR filtering in the random process generated obtaining a new random estimate, which will reestimate the ARMA model parameters, given a better spectrum estimate. Some numerical examples will be presented in order to ilustrate the performance of the method proposed, which is evaluated by the relative error and the average variation coefficient.

The role of clouds in improving the regression model for hourly values of diffuse solar radiation

The study introduces a new regression model developed to estimate the hourly values of diffuse solar radiation at the surface. The model is based on the clearness index and diffuse fraction relationship, and includes the effects of cloud (cloudiness and cloud type), traditional meteorological variables (air temperature, relative humidity and atmospheric pressure observed at the surface) and air pollution (concentration of particulate matter observed at the surface). The new model is capable of predicting hourly values of diffuse solar radiation better than the previously developed ones (R-2 = 0.93 and RMSE = 0.085). A simple version with a large applicability is proposed that takes into consideration cloud effects only (cloudiness and cloud height) and shows a R-2 = 0.92. (C) 2011 Elsevier Ltd. All rights reserved.