scholarly journals PROPERTIES OF THE INVERSE OF A NONCENTRAL WISHART MATRIX

2021 ◽  
pp. 1-25
Author(s):  
Grant Hillier ◽  
Raymond Kan
Keyword(s):  
Instrumental Variable ◽  
Wishart Matrix ◽  
Multivariate Statistical ◽  
Invariance Properties ◽  
Statistical Work ◽  
Powerful Group

The inverse of a noncentral Wishart matrix occurs in a variety of contexts in multivariate statistical work, including instrumental variable (IV) regression, but there has been very little work on its properties. In this paper, we first provide an expression for the expectation of the inverse of a noncentral Wishart matrix, and then go on to do the same for a number of scalar-valued functions of the inverse. The main result is obtained by exploiting simple but powerful group-equivariance properties of the expectation map involved. Subsequent results exploit the consequences of other invariance properties.

Long-term variations in individual particle types in the aerosol of Phoenix, Arizona, as determined using automated electron microprobe analysis and multivariate statistical techniques

1993 ◽  
Vol 51 ◽  
pp. 742-743
Author(s):  
Karen A. Katrinak ◽  
James R. Anderson ◽  
Peter R. Buseck
Keyword(s):  
Electron Microprobe ◽  
Fine Fraction ◽  
Coarse Fraction ◽  
Motor Vehicles ◽  
Multivariate Statistical Methods ◽  
Multivariate Statistical ◽  
X Ray ◽  
Mineral Particles ◽  
Anthropogenic Air Pollutants

Aerosol samples were collected in Phoenix, Arizona on eleven dates between July 1989 and April 1990. Elemental compositions were determined for approximately 1000 particles per sample using an electron microprobe with an energy-dispersive x-ray spectrometer. Fine-fraction samples (particle cut size of 1 to 2 μm) were analyzed for each date; coarse-fraction samples were also analyzed for four of the dates.The data were reduced using multivariate statistical methods. Cluster analysis was first used to define 35 particle types. 81% of all fine-fraction particles and 84% of the coarse-fraction particles were assigned to these types, which include mineral, metal-rich, sulfur-rich, and salt categories. "Zero-count" particles, consisting entirely of elements lighter than Na, constitute an additional category and dominate the fine fraction, reflecting the importance of anthropogenic air pollutants such as those emitted by motor vehicles. Si- and Ca-rich mineral particles dominate the coarse fraction and are also numerous in the fine fraction.

Angular Calibration of Ribosomal Subuntts in Factor Space

1990 ◽  
Vol 48 (1) ◽  
pp. 462-463
Author(s):  
Minakhi Pujari ◽  
Joachim Frank
Keyword(s):  
Three Dimensional ◽  
Carbon Layer ◽  
Uranyl Acetate ◽  
Particle Analysis ◽  
Factor Space ◽  
Multivariate Statistical ◽  
Ribosomal Subunits ◽  
Layer Method ◽  
Dimensional Reconstruction ◽  
Number Of Particles

In single-particle analysis of macromolecule images with the electron microscope, variations of projections are often observed that can be attributed to the changes of the particle’s orientation on the specimen grid (“rocking”). In the multivariate statistical analysis (MSA) of such projections, a single factor is often found that expresses a large portion of these variations. Successful angle calibration of this “rocking factor” would mean that correct angles can be assigned to a large number of particles, thus facilitating three-dimensional reconstruction.In a study to explore angle calibration in factor space, we used 40S ribosomal subunits, which are known to rock around an axis approximately coincident with their long axis. We analyzed micrographs of a field of these particles, taken with 20° tilt and without tilt, using the standard methods of alignment and MSA. The specimen was prepared with the double carbon-layer method, using uranyl acetate for negative staining. In the MSA analysis, the untilted-particle projections were used as active, the tilted-particle projections as inactive objects. Upon tilting, those particles whose rocking axes are parallel to the tilt axis will change their appearance in the same way as under the influence of rocking. Therefore, each vector, in factor space, joining a tilted and untilted projection of the same particle can be regarded as a local 20-degree calibration bar.

Molecular Views of Ice-Embedded Lumbricus Terrestris Erythrocruorin Obtained By Invariant Classification

1990 ◽  
Vol 48 (1) ◽  
pp. 450-451
Author(s):  
Michael schatz ◽  
Joachim Jäger ◽  
Marin van Heel
Keyword(s):  
Image Interpretation ◽  
Lumbricus Terrestris ◽  
Reference Image ◽  
Large Set ◽  
Multivariate Statistical ◽  
Data Set ◽  
Low Contrast ◽  
Negative Stain ◽  
Reference Images ◽  
Statistical Resolution

Lumbricus terrestris erythrocruorin is a giant oxygen-transporting macromolecule in the blood of the common earth worm (worm "hemoglobin"). In our current study, we use specimens (kindly provided by Drs W.E. Royer and W.A. Hendrickson) embedded in vitreous ice (1) to avoid artefacts encountered with the negative stain preparation technigue used in previous studies (2-4).Although the molecular structure is well preserved in vitreous ice, the low contrast and high noise level in the micrographs represent a serious problem in image interpretation. Moreover, the molecules can exhibit many different orientations relative to the object plane of the microscope in this type of preparation. Existing techniques of analysis requiring alignment of the molecular views relative to one or more reference images often thus yield unsatisfactory results.We use a new method in which first rotation-, translation- and mirror invariant functions (5) are derived from the large set of input images, which functions are subsequently classified automatically using multivariate statistical techniques (6). The different molecular views in the data set can therewith be found unbiasedly (5). Within each class, all images are aligned relative to that member of the class which contributes least to the classes′ internal variance (6). This reference image is thus the most typical member of the class. Finally the aligned images from each class are averaged resulting in molecular views with enhanced statistical resolution.

Methodology of ECG Interpretation in the AVA Program

1990 ◽  
Vol 29 (04) ◽  
pp. 337-340 ◽  
Author(s):  
H. A. Pipberger ◽  
H. V. Pipberger ◽  
C. D. McManus
Keyword(s):  
Right Atrial ◽  
Signal Recognition ◽  
Multivariate Statistical ◽  
Reference Base ◽  
T Wave ◽  
Electrolyte Disturbances ◽  
Ecg Criteria ◽  
Wall Injury ◽  
Ecg Leads ◽  
Diagnostic Module

AbstractThe AVA program combines a thirty-year history with an approach that remains innovative; namely: multivariate statistical analysis on orthogonal ECG leads. Its diagnostic reference base includes only diagnoses independently verified by non-ECG criteria. The diagnostic module assesses probabilities of nine alternative disease categories, based on QRS-T parameters; or four other categories in case of conduction defects. Probabilities of left or right atrial overload are also computed. The program also recognizes wall injury, T-wave abnormalities, electrolyte disturbances, myocardial ischemia, and makes differential diagnoses between strain and digitalis effects. An arrhythmia classification module can generate any of 40 rhythm statements. Signal recognition is based on the spatial velocity function. The program has been translated to a microcomputer version.

International Remittances and Private Healthcare in Kerala, India

2020 ◽  
Vol 17 (3) ◽  
pp. 445-460
Author(s):  
Mohd Imran Khan ◽  
Valatheeswaran C.
Keyword(s):  
Instrumental Variable ◽  
Capital Investment ◽  
Healthcare Expenditure ◽  
Healthcare Services ◽  
Private Healthcare ◽  
International Remittances ◽  
Variable Approach ◽  
Using Data ◽  
The Impact ◽  
Instrumental Variable Approach

The inflow of international remittances to Kerala has been increasing over the last three decades. It has increased the income of recipient households and enabled them to spend more on human capital investment. Using data from the Kerala Migration Survey-2010, this study analyses the impact of remittance receipts on the households’ healthcare expenditure and access to private healthcare in Kerala. This study employs an instrumental variable approach to account for the endogeneity of remittances receipts. The empirical results show that remittance income has a positive and significant impact on households’ healthcare expenditure and access to private healthcare services. After disaggregating the sample into different heterogeneous groups, this study found that remittances have a greater effect on lower-income households and Other Backward Class (OBC) households but not Scheduled Caste (SC) and Scheduled Tribe (ST) households, which remain excluded from reaping the benefit of international migration and remittances.

STATISTICAL METHODS FOR THE ASSESSMENT OF AIR POLLUTION OF JHANSI CITY, UTTAR PRADESH, INDIA

2018 ◽  
Vol 24 (1) ◽  
Author(s):  
V. S. CHAUHAN ◽  
BHANUMATI SINGH ◽  
SHREE GANESH ◽  
JAMSHED ZAIDI
Keyword(s):  
Air Pollution ◽  
Uttar Pradesh ◽  
Ambient Air ◽  
Ambient Air Pollution ◽  
Base Line ◽  
Multivariate Statistical ◽  
Large Cities ◽  
Governmental Organizations ◽  
Non Governmental Organizations ◽  
The Status

Studies on air pollution in large cities of India showed that ambient air pollution concentrations are at such levels where serious health effects are possible. This paper presents overview on the status of air quality index (AQI) of Jhansi city by using multivariate statistical techniques. This base line data can help governmental and non-governmental organizations for the management of air pollution.

Pollen morphology of some Tamarix (Tamaricaceae) species of Iran

2020 ◽  
Vol 62 (1-2) ◽  
pp. 151-161
Author(s):  
T. Shagholi ◽  
M. Keshavarzi ◽  
M. Sheidai
Keyword(s):  
North Africa ◽  
Pollen Grains ◽  
Ecological Niches ◽  
Multivariate Statistical Methods ◽  
Multivariate Statistical ◽  
Qualitative And Quantitative ◽  
Petal Length ◽  
Electron Microscopes ◽  
High Level ◽  
Scanning Electron Microscopes

Tamarix L. (Tamaricaceae) is a halophytic shrub in different parts of Asia and North Africa. Taxonomy and species limitation of Tamarix is very complex. This genus has three sections as Tamarix, Oligadenia, and Polyadenia, which are mainly separated by petal length, the number of stamens, the shape of androecial disk and attachment of filament on the androecial disk. As there was no palynological data on pollen features of Tamarix species of Iran, in the present study 12 qualitative and quantitative pollen features were evaluated to find diagnostic ones. Pollen grains of 8 Tamarix species were collected from nature. Pollen grains were studied without any treatment. Measurements were based on at least 50 pollen grains per specimen. Light and scanning electron microscopes were used. Multivariate statistical methods were applied to clarify the species relationships based on pollen data. All species studied showed monad and tricolpate (except some individuals of T. androssowii). Some Tamarix species show a high level of variability, in response to ecological niches and phenotypic plasticity, which make Tamarix species separation much more difficult. Based on the results of the present study, pollen grains features are not in agreement with previous morphological and molecular genetics about the sectional distinction.

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