Central limit theorems in linear structural error-in-variables models with explanatory variables in the domain of attraction of the normal law

Linear structural error-in-variables models with univariate observations are revisited for studying modified least squares estimators of the slope and intercept. New marginal central limit theorems (CLT's) are established for these estimators, assuming the existence of four moments for the measurement errors and that the explanatory variables are in the domain of attraction of the normal law. The latter condition for the explanatory variables is used the first time, and is so far the most general in this context. It is also optimal, or nearly optimal, for our CLT's. Moreover, due to the obtained CLT's being in Studentized and self-normalized forms to begin with, they are a priori nearly, or completely, data-based, and free of unknown parameters of the joint distribution of the error and explanatory variables. Consequently, they lead to a variety of readily available, or easily derivable, large-sample approximate confidence intervals (CI's) for the slope and intercept. In contrast, in related CLT's in the literature so far, the variances of the limiting normal distributions, in general, are complicated and depend on various, typically unknown, moments of the error and explanatory variables. Thus, the corresponding CI's for the slope and intercept in the literature, unlike those of the present paper, are available only under some additional model assumptions.Comment: Published at http://dx.doi.org/10.1214/07-EJS056 in the Electronic Journal of Statistics (http://www.i-journals.org/ejs/) by the Institute of Mathematical Statistics (http://www.imstat.org

New multivariate central limit theorems in linear structural and functional error-in-variables models

This paper deals simultaneously with linear structural and functional error-in-variables models (SEIVM and FEIVM), revisiting in this context generalized and modified least squares estimators of the slope and intercept, and some methods of moments estimators of unknown variances of the measurement errors. New joint central limit theorems (CLT's) are established for these estimators in the SEIVM and FEIVM under some first time, so far the most general, respective conditions on the explanatory variables, and under the existence of four moments of the measurement errors. Moreover, due to them being in Studentized forms to begin with, the obtained CLT's are a priori nearly, or completely, data-based, and free of unknown parameters of the distribution of the errors and any parameters associated with the explanatory variables. In contrast, in related CLT's in the literature so far, the covariance matrices of the limiting normal distributions are, in general, complicated and depend on various, typically unknown parameters that are hard to estimate. In addition, the very forms of the CLT's in the present paper are universal for the SEIVM and FEIVM. This extends a previously known interplay between a SEIVM and a FEIVM. Moreover, though the particular methods and details of the proofs of the CLT's in the SEIVM and FEIVM that are established in this paper are quite different, a unified general scheme of these proofs is constructed for the two models herewith.Comment: Published at http://dx.doi.org/10.1214/07-EJS075 in the Electronic Journal of Statistics (http://www.i-journals.org/ejs/) by the Institute of Mathematical Statistics (http://www.imstat.org

Assessment of Risk Factors of Septic Complications of the Puerperium

Postpartum purulent-septic complications (PPSC) and their problems are most urgent for modern obstetrics due to their significant frequency. Maternal sepsis is one of the leading causes of maternal mortality around the world, accounting for about one-tenth of the global number of maternal deaths. Understanding the risk factors for the development of septic complications of puerperium is important for preventive strategies.Aim. To study the possibility of forming high-risk groups on the basis of analysis of anamnestic data and the course of puerperium in women with PPSC as part of the preventive measures for the development of such complications.Materials and methods. The first stage of the study involves a retrospective analysis for the allocation of risk factors for the development of PPSC in women, who underwent inpatient treatment for this pathology - main group (n=108); сontrol group (n=35) – parous with uncomplicated flow of the postpartum period. Prospective research enrolled 65 pregnant women with extragenital pathology and/or complicated pregnancy (group 1); 30 pregnant women without severe concomitant somatic pathology with physiological course of pregnancy (group 2). The following were taken into account: age, obstetrical and gynecological history, extragenital pathology, laboratory diagnostic data. Differences in mean values were considered significant with a probability level of at least 95 % (p<0.05).Results. To the risk factors for the development of PPSC, we classified as follows: gynecological diseases in history: menstrual dysfunction, chronic inflammatory diseases of the genital organs, bacterial vaginosis; complications of pregnancy and labor: preeclampsia, preterm labor, premature rupture of membranes, long anhydrous span, chorioamnionitis, weakness of labor, genital tract ruptures, placental attachment pathology, operative vaginal birth, bleeding; concomitant extragenital pathology: diabetes, obesity, diseases of the urinary system, diseases of the cardiovascular system, respiratory diseases, varicose disease, anemia.Conclusions. The connection between the presence of concomitant somatic pathology, the complicated course of pregnancy and labor and the subsequent development of septic complications in the postpartum period have been established. Prediction of the risk of their occurrence at the stage of pregraviditic preparation, with various complications of pregnancy and childbirth, especially in women with extragenital pathology, differential prevention will reduce the frequency of PPSC