Difference based Ridge and Liu type Estimators in Semiparametric Regression Models

We consider a difference based ridge regression estimator and a Liu type estimator of the regression parameters in the partial linear semiparametric regression model, y = Xβ + f + ε. Both estimators are analysed and compared in the sense of mean-squared error. We consider the case of independent errors with equal variance and give conditions under which the proposed estimators are superior to the unbiased difference based estimation technique. We extend the results to account for heteroscedasticity and autocovariance in the error terms. Finally, we illustrate the performance of these estimators with an application to the determinants of electricity consumption in Germany.Difference based estimator; Differencing estimator, Differencing matrix, Liu estimator, Liu type estimator, Multicollinearity, Ridge regression estimator, Semiparametric model

Difference based ridge and Liu type estimators in semiparametric regression models

AbstractWe consider a difference based ridge regression estimator and a Liu type estimator of the regression parameters in the partial linear semiparametric regression model, y=Xβ+f+ε. Both estimators are analyzed and compared in the sense of mean-squared error. We consider the case of independent errors with equal variance and give conditions under which the proposed estimators are superior to the unbiased difference based estimation technique. We extend the results to account for heteroscedasticity and autocovariance in the error terms. Finally, we illustrate the performance of these estimators with an application to the determinants of electricity consumption in Germany

Multıcollınearıty ın regressıon analysıs: Parametrıc and semıparametrıc estımatıon

Çoklu bağlantı çoklu regresyon modellerinde iki veya daha fazla açıklayıcı değisken arasında doğrusal bir iliskiye yakın bir iliski olması durumudur. Doğrusal ve semiparametrik regresyon modellerinde açıklayıcı değiskenler arasında çoklu bağlantı olması durumunda en küçük kareler yöntemi ile elde edilen parametre tahminlerinin olumsuz etkilendiği bilinmektedir. Bu duruma çözüm olarak birçok yöntem önerilmistir. Bu yöntemlerden bir tanesi en küçük kareler tahmin edicisi yerine yanlı tahmin edicileri kullanmaktır. Yanlı tahmin edicilerin çoklu bağlantı durumunda daha etkin sonuçlar verdiği bilinmektedir. Bu çalısmada parametrik ve semiparametrik regresyon modellerinde çoklu bağlantı durumunda kullanılabilecek yeni tahmin ediciler önerilmistir. Bu tahmin edicilerin üstün olma kosulları verilmistir. Teorik bulgular uygulamalarla ve simülasyon çalısmaları ile desteklenmistir.Multicollinearity is a statistical phenomenon in which two or more predictor variables in a multiple regression model have a nearly linear relation. In this situation the coefficient estimates may change erratically in response to small changes in the data. Multicollinearity seriously affects calculations regarding individual predictors. That is, a multiple regression model with correlated predictors may give invalid results about any individual predictor; therefore it is a phenomenon that should be considered carefully. There have been many attempts in literature as a remedy to multicollinearity problem. The main stream approach is using biased estimators in place of ordinary least squares (OLS) estimators. It is well known that biased estimators are more efficient than OLS estimators in case of multicollinearity. In this study, new biased estimators are proposed for parametric or semiparametric regression models that are exposed to multicollinearity problem. The mean squared error matrix (MSEM) superiority conditions are given for each estimator. Theoretical findings are supported with applications and simulation studies

A Confidence Corridor for Expectile Functions

Let (X1; Y1), …, (Xn; Yn) be i.i.d. rvs and let v(x) be the unknown τ - expectile regression curve of Y conditional on X. An expectile-smoother vn(x) is a localized, nonlinear estimator of v(x). The strong uniform consistency rate is established under general conditions. In many applications it is necessary to know the stochastic fluctuation of the process {vn(x) – v(x)}. Using strong approximations of the empirical process and extreme value theory, we consider the asymptotic maximal deviation sup0≤x≤1 |vn(x) – v(x)|. The derived result helps in the construction of a uniform confidence band for the expectile curve v(x). This paper considers fitting a simultaneous confidence corridor (SCC) around the estimated expectile function of the conditional distribution of Y given x based on the observational data generated according to a nonparametric regression model. Moreover, we construct the simultaneous confidence corridors around the expectiles of the residuals from the temperature models to investigate the temperature risk drivers

The effects of antibiotics and melatonin on hepato-intestinal inflammation and gut microbial dysbiosis induced by a short-term high-fat diet consumption in rats

High-fat diet (HFD) consumption leads to metabolic disorders, gastrointestinal dysfunction and intestinal dysbiosis. Antibiotics also disrupt the composition of intestinal microbiota. The aim of the present study was to investigate the impact of a short-term feeding with HFD on oxidative status, enteric microbiota, intestinal motility and the effects of antibiotics and/or melatonin treatments on diet-induced hepato-intestinal dysfunction and inflammation. Male Sprague-Dawley rats were pair-fed with either standard chow or HFD (45 % fat) and were given tap water or melatonin (4 mg/kg per d) or melatonin plus antibiotics (ABX; neomycin, ampicillin, metronidazole; each 1 g/l) in drinking water for 2 weeks. On the 14th day, colonic motility was measured and the next day intestinal transit was assessed using charcoal propagation. Trunk blood, liver and intestine samples were removed for biochemical and histopathological evaluations, and faeces were collected for microbiota analysis. A 2-week HFD feeding increased blood glucose level and perirenal fat weight, induced low-level hepatic and intestinal inflammation, delayed intestinal transit, led to deterioration of epithelial tight junctions and overgrowth of colonic bacteria. Melatonin intake in HFD-fed rats reduced ileal inflammation, colonic motility and perirenal fat accumulation. ABX abolished increases in fat accumulation and blood glucose, reduced ileal oxidative damage, suppressed HFD-induced overgrowth in colonic bacteria, and reversed HFD-induced delay in intestinal transit; however, hepatic neutrophil accumulation, hepatic injury and dysfunction were further enhanced. In conclusion, the results demonstrate that even a short-term HFD ingestion results in hepato-intestinal inflammatory state and alterations in bacterial populations, which may be worsened with antibiotic intake, but alleviated by melatonin