Deconvolution for an atomic distribution

Let $X_1,...,X_n$ be i.i.d. observations, where $X_i=Y_i+\sigma Z_i$ and $Y_i$ and $Z_i$ are independent. Assume that unobservable $Y$'s are distributed as a random variable $UV,$ where $U$ and $V$ are independent, $U$ has a Bernoulli distribution with probability of zero equal to $p$ and $V$ has a distribution function $F$ with density $f.$ Furthermore, let the random variables $Z_i$ have the standard normal distribution and let $\sigma>0.$ Based on a sample $X_1,..., X_n,$ we consider the problem of estimation of the density $f$ and the probability $p.$ We propose a kernel type deconvolution estimator for $f$ and derive its asymptotic normality at a fixed point. A consistent estimator for $p$ is given as well. Our results demonstrate that our estimator behaves very much like the kernel type deconvolution estimator in the classical deconvolution problem.Comment: Published in at http://dx.doi.org/10.1214/07-EJS121 the Electronic Journal of Statistics (http://www.i-journals.org/ejs/) by the Institute of Mathematical Statistics (http://www.imstat.org

Nonparametric volatility density estimation for discrete time models

We consider discrete time models for asset prices with a stationary volatility process. We aim at estimating the multivariate density of this process at a set of consecutive time instants. A Fourier type deconvolution kernel density estimator based on the logarithm of the squared process is proposed to estimate the volatility density. Expansions of the bias and bounds on the variance are derived

Nonparametric methods for volatility density estimation

Stochastic volatility modelling of financial processes has become increasingly popular. The proposed models usually contain a stationary volatility process. We will motivate and review several nonparametric methods for estimation of the density of the volatility process. Both models based on discretely sampled continuous time processes and discrete time models will be discussed. The key insight for the analysis is a transformation of the volatility density estimation problem to a deconvolution model for which standard methods exist. Three type of nonparametric density estimators are reviewed: the Fourier-type deconvolution kernel density estimator, a wavelet deconvolution density estimator and a penalized projection estimator. The performance of these estimators will be compared. Key words: stochastic volatility models, deconvolution, density estimation, kernel estimator, wavelets, minimum contrast estimation, mixin

A method for delineation of bone surfaces in photoacoustic computed tomography of the finger

Photoacoustic imaging of interphalangeal peripheral joints is of interest in the context of using the synovial membrane as a surrogate marker of rheumatoid arthritis. Previous work has shown that ultrasound produced by absorption of light at the epidermis reflects on the bone surfaces within the finger. When the reflected signals are backprojected in the region of interest, artifacts are produced, confounding interpretation of the images. In this work, we present an approach where the photoacoustic signals known to originate from the epidermis, are treated as virtual ultrasound transmitters, and a separate reconstruction is performed as in ultrasound reflection imaging. This allows us to identify the bone surfaces. Further, the identification of the joint space is important as this provides a landmark to localize a region-of-interest in seeking the inflamed synovial membrane. The ability to delineate bone surfaces allows us not only to identify the artifacts, but also to identify the interphalangeal joint space without recourse to new US hardware or a new measurement. We test the approach on phantoms and on a healthy human finger

Deconvolution for an atomic distribution: rates of convergence

Let $X_1,..., X_n$ be i.i.d.\ copies of a random variable $X=Y+Z,$ where $X_i=Y_i+Z_i,$ and $Y_i$ and $Z_i$ are independent and have the same distribution as $Y$ and $Z,$ respectively. Assume that the random variables $Y_i$'s are unobservable and that $Y=AV,$ where $A$ and $V$ are independent, $A$ has a Bernoulli distribution with probability of success equal to $1-p$ and $V$ has a distribution function $F$ with density $f.$ Let the random variable $Z$ have a known distribution with density $k.$ Based on a sample $X_1,...,X_n,$ we consider the problem of nonparametric estimation of the density $f$ and the probability $p.$ Our estimators of $f$ and $p$ are constructed via Fourier inversion and kernel smoothing. We derive their convergence rates over suitable functional classes. By establishing in a number of cases the lower bounds for estimation of $f$ and $p$ we show that our estimators are rate-optimal in these cases.Comment: 27 page

Initial results of finger imaging using Photoacoustic Computed Tomography

We present a photoacoustic computed tomography investigation on a healthy human finger, to image blood vessels with a focus on vascularity across the interphalangeal joints. The cross-sectional images were acquired using an imager specifically developed for this purpose. The images show rich detail of the digital blood vessels with diameters between 100 $\mu$m and 1.5 mm in various orientations and at various depths. Different vascular layers in the skin including the subpapillary plexus could also be visualized. Acoustic reflections on the finger bone of photoacoustic signals from skin were visible in sequential slice images along the finger except at the location of the joint gaps. Not unexpectedly, the healthy synovial membrane at the joint gaps was not detected due to its small size and normal vascularization. Future research will concentrate on studying digits afflicted with rheumatoid arthritis to detect the inflamed synovium with its heightened vascularization, whose characteristics are potential markers for disease activity.Comment: 2 figure

Comparison of usefulness of computer assisted continuous 48-h 3-lead with 12-lead ECG ischaemia monitoring for detection and quantitation of ischaemia in patients with unstable angina

AIMS: The selection of ECG leads used for ST monitoring may influence detection and quantitation of ischaemia. METHODS: We compared on-line continuous 48-h 12-lead against 3-lead ST monitoring in 130 unstable angina patients (Mortara. ELI-100). Onset and offset of ST episodes were defined by the lead with the first > or = 100 microV ST change relative to baseline and the lead with the latest return to baseline ST level, respectively. ST episodes were calculated for 12 leads and 3 leads (V2, V5, III) separately. RESULTS: ST episodes were detected in 88 patients (77%) by 12-lead and in 71 patients (62%) by 3-lead ST monitoring (P < 0.02). The median number (25.75%) of episodes/patient was 1 (0.3) for 3-lead and 2 (1.6) for 12-lead (P < 0.0001). The total duration of ischaemia detected during 12-lead far exceeded 3-lead monitoring: 12.3 (1, 58.2) and 1.7 (0, 23.3) min respectively (P < 0.0001). The probability of recurrent ischaemia declined most during the first 24 h of monitoring. After a period without ST changes of 1, 12, 24 and 36 h, the probabilities of recurrent ischaemia were 63, 31, 14 and 9%, respectively. CONCLUSIONS: Continuous 12-lead ST monitoring increases detection rate and duration of ST episodes compared to 3-lead ST monitoring. The use of continuous 12-lead ECG monitoring devices on emergency wards and coronary care units is recommended

Recommendations for dealing with waste contaminated with Ebola virus: a Hazard Analysis of Critical Control Points approach

Objective To assess, within communities experiencing Ebola virus outbreaks, the risks associated with the disposal of human waste and to generate recommendations for mitigating such risks. Methods A team with expertise in the Hazard Analysis of Critical Control Points framework identified waste products from the care of individuals with Ebola virus disease and constructed, tested and confirmed flow diagrams showing the creation of such products. After listing potential hazards associated with each step in each flow diagram, the team conducted a hazard analysis, determined critical control points and made recommendations to mitigate the transmission risks at each control point. Findings The collection, transportation, cleaning and shared use of blood-soiled fomites and the shared use of latrines contaminated with blood or bloodied faeces appeared to be associated with particularly high levels of risk of Ebola virus transmission. More moderate levels of risk were associated with the collection and transportation of material contaminated with bodily fluids other than blood, shared use of latrines soiled with such fluids, the cleaning and shared use of fomites soiled with such fluids, and the contamination of the environment during the collection and transportation of blood-contaminated waste. Conclusion The risk of the waste-related transmission of Ebola virus could be reduced by the use of full personal protective equipment, appropriate hand hygiene and an appropriate disinfectant after careful cleaning. Use of the Hazard Analysis of Critical Control Points framework could facilitate rapid responses to outbreaks of emerging infectious disease

Skin Cancers Among Albinos at a University Teaching Hospital in Northwestern Tanzania: A Retrospective Review of 64 Cases.

Skin cancers are a major risk associated with albinism and are thought to be a major cause of death in African albinos. The challenges associated with the care of these patients are numerous and need to be addressed. The aim of this study was to outline the pattern and treatment outcome of skin cancers among albinos treated at our centre and to highlight challenges associated with the care of these patients and proffer solutions for improved outcome. This was a retrospective study of all albinos with a histopathological diagnosis of skin cancer seen at Bugando Medical Centre from March 2001 to February 2010. Data collected were analyzed using descriptive statistics. A total of 64 patients were studied. The male to female ratio was 1.5:1. The median age of patients was 30 years. The median duration of illness at presentation was 24 months. The commonest reason for late presentation was financial problem. Head and the neck was the most frequent site afflicted in 46(71.8%) patients. Squamous cell carcinoma was the most common histopathological type in 75% of cases. Surgical operation was the commonest modality of treatment in 60 (93.8%) patients. Radiotherapy was given in 24(37.5%) patients. Twenty-seven (42.2%) of the patients did not complete their treatment due to lack of funds. Local recurrence following surgical treatment was recorded in 6 (30.0%) patients. Only thirty-seven (61.7%) patients were available for follow-up at 6-12 months and the remaining patients were lost to follow-up. Skin cancers are the most common cancers among albinos in our environment. Albinism and exposure to ultraviolet light appears to be the most important risk factor in the development of these cancers. Late presentation and failure to complete treatment due to financial difficulties and lack of radiotherapy services at our centre are major challenges in the care of these patients. Early institution of preventive measures, early presentation and treatment, and follow-up should be encouraged in this population for better outcome