Women Born Preterm or with Inappropriate Weight for Gestational Age Are at Risk of Subsequent Gestational Diabetes and Pre-Eclampsia

Introduction: Low birthweight, which can be caused by inappropriate intrauterine growth or prematurity, is associated with development of gestational diabetes mellitus (GDM) as well as pre-eclampsia later in life, but the relative effects of prematurity and inappropriate intrauterine growth remain uncertain. Methods: Through nation-wide registries we identified all Danish mothers in the years 1989–2007. Two separate cohorts consisting mothers born 1974–1977 (n = 84219) and 1978–1981 (n = 32376) were studied, due to different methods o

Abstract

The Pearson diffusions is a flexible class of diffusions defined by having linear drift and quadratic squared diffusion coefficient. It is demonstrated that for this class explicit statistical inference is feasible. Explicit optimal martingale estimating functions are found, and the corresponding estimators are shown to be consistent and asymptotically normal. The discussion covers GMM, quasi-likelihood, and nonlinear weighted least squares estimation too, and it is discussed how explicit likelihood or approximate likelihood inference is possible for the Pearson diffusions. A complete model classification is presented for the ergodic Pearson diffusions. The class of stationary distributions equals the full Pearson system of distributions. Well-known instances are the Ornstein-Uhlenbeck processes and the square root (CIR) processes. Also diffusions with heavy-tailed and skew marginals are included. Special attention is given to a skew t-type distribution. Explicit formulae for the conditional moments and the polynomial eigenfunctions are derived. The analytical tractability is inherited by transformed Pearson diffusions, integrated Pearson diffusions, sums of Pearson diffusions, and stochastic volatility models with Pearson volatility process. For the non-Markov models explicit optimal prediction based estimating functions are found and shown to yield consistent and asymptotically normal estimators. Key words: eigenfunction, ergodic diffusion, integrated diffusion, martingale estimating function, likelihood inference, mixing, optimal estimating function, Pearso

Abstract

The Pearson diffusions is a flexible class of diffusions defined by having linear drift and quadratic squared diffusion coefficient. It is demonstrated that for this class explicit statistical inference is feasible. Explicit optimal martingale estimating functions are found, and the corresponding estimators are shown to be consistent and asymptotically normal. The discussion covers GMM, quasi-likelihood, and nonlinear weighted least squares estimation too, and it is discussed how explicit likelihood or approximate likelihood inference is possible for the Pearson diffusions. A complete model classification is presented for the ergodic Pearson diffusions. The class of stationary distributions equals the full Pearson system of distributions. Well-known instances are the Ornstein-Uhlenbeck processes and the square root (CIR) processes. Also diffusions with heavy-tailed and skew marginals are included. Special attention is given to a skew t-type distribution. Explicit formulae for the conditional moments and the polynomial eigenfunctions are derived. The analytical tractability is inherited by transformed Pearson diffusions, integrated Pearson diffusions, sums of Pearson diffusions, and stochastic volatility models with Pearson volatility process. For the non-Markov models explicit optimal prediction based estimating functions are found and shown to yield consistent and asymptotically normal estimators. Key words: eigenfunction, ergodic diffusion, integrated diffusion, martingale estimating function, likelihood inference, mixing, optimal estimating function, Pearso