Measuring the positive psychological well-being of people with rheumatoid arthritis: a cross-sectional validation of the subjective vitality scale

Introduction: People with rheumatoid arthritis (RA) frequently suffer from compromised physical and psychological health, however, little is known about positive indicators of health, due to a lack of validated outcome measures. This study aims to validate a clinically relevant outcome measure of positive psychological well-being for people with RA. The first study examined the reliability and factorial validity of the Subjective Vitality Scale (SVS), whilst study 2 tested the instruments convergent validity. Methods: In study 1, National Rheumatoid Arthritis Society members (N = 333; M age = 59.82 years SD = 11.00) completed a postal questionnaire. For study 2, participants (N = 106; M age = 56 years, SD = 12 years) were those recruited to a randomized control trial comparing two physical activity interventions who completed a range of health-related questionnaires. Results: The SVS had a high level of internal consistency (α = .93, Rho = .92). Confirmatory factor analysis supported the uni-dimensional factor structure of the questionnaire among RA patients [χ = 1327 (10), CFI = 1.0, SRMSR = .01 and RMSEA = .00 (.00 - .08)]. Support for the scales convergent validity was revealed by significant (p < .05) relationships, in expected directions, with health related quality of life (r = .59), physical function (r = .58), feelings of fatigue (r = −.70), anxiety (r = −.57) and depression (r = −.73). Conclusions: Results from two studies have provided support for the internal consistency, factorial structure and convergent validity of the Subjective Vitality Scale. Researchers and healthcare providers may employ this clinically relevant, freely available and brief assessment with the confidence that it is a valid and reliable measure of positive psychological well-being for RA patients

On uniform laws of large numbers for ergodic diffusions and consistency of estimators

Consider a regular diffusion process X with finite speed measure m. Denote the normalized speed measure by µ. We prove that the uniform law of large numbers holds if the class has an envelope function that is µ-integrable, or if is bounded in L p(µ) for some p&gt;1. In contrast with uniform laws of large numbers for i.i.d. random variables, we do not need conditions on the ‘size’ of the class in terms of bracketing or covering numbers. The result is a consequence of a number of asymptotic properties of diffusion local time that we derive. We apply our abstract results to improve consistency results for the local time estimator (LTE) and to prove consistency for a class of simple M-estimators

On the rate of convergence of the maximum likelihood estimator in Brownian semimartingale models

In this paper we present a unified approach to obtaining rates of convergence for the maximum likelihood estimator (MLE) in Brownian semimartingale models of the form \d X_t = \beta^{n,\theta}_t\,\d t + \sigma^n_t\,\d W_t, \qquad t \le T_n. We show that the rate of the MLE is determined by (an appropriate version of) the entropy of the parameter space with respect to the random metric hn, defined by h^2_n(\theta, \psi) = \int_0^{T_n}\left(\frac{\beta^{n,\theta}_s-\beta^{n,\psi}_s}{\sigma^n_s}\right)^2 \,\d s. Several known results for the rates in certain popular sub-models of the Brownian semimartingale model are shown to be special cases in our general framework

A multivariate central limit theorem for continuous local martingales

A theorem on the weak convergence of a properly normalized multivariate continuous local martingale is proved. The time-change theorem used for this purpose allows for short and transparent arguments

Reproducing kernel Hilbert spaces of Gaussian priors

We review definitions and properties of reproducing kernel Hilbert spaces attached to Gaussian variables and processes, with a view to applications in nonparametric Bayesian statistics using Gaussian priors. The rate of contraction of posterior distributions based on Gaussian priors can be described through a concentration function that is expressed in the reproducing Hilbert space. Absolute continuity of Gaussian measures and concentration inequalities play an important role in understanding and deriving this result. Series expansions of Gaussian variables and transformations of their reproducing kernel Hilbert spaces under linear maps are useful tools to compute the concentration function

Nonparametric methods for volatility density estimation

Stochastic volatility modeling 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 types 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

Nonparametric volatility density estimation

We consider a continuous-time stochastic volatility model. The model contains a stationary volatility process, the density of which, at a fixed instant in time, we aim to estimate. We assume that we observe the process at discrete instants in time. The sampling times will be equidistant with vanishing distance. A Fourier-type deconvolution kernel density estimator based on the logarithm of the squared processes is proposed to estimate the volatility density. An expansion of the bias and a bound on the variance are derived

Conditional full support of Gaussian processes with stationary increments

We investigate the conditional full support (CFS) property, introduced by Guasoni et al. (2008a), for Gaussian processes with stationary increments. We give integrability conditions on the spectral measure of such a process that ensure that the process has CFS or not. In particular, the general results imply that for a process with spectral density f such that (formula follows)