On OLS Estimation of Stochastic Linear Regression Model

This paper mainly discusses the formulation of stochastic linear statistical model and its assumptions and finally explores an important aspect namely the Ordinary Least Squares (OLS) estimation of stochastic linear regression model. In addition to these inference in stochastic linear regression model is also presented here. Nimitozbay et.al [1], in their paper proposed the weighted mixed regression estimation of the coefficient vector in a linear regression model with stochastic linear restrictions binding the regression coefficients. In 1980, P.A.V.B. Swamy et.al proposed a linear regression model where the coefficient vector is a weekly stationary multivariate stochastic process and that model provides a convenient representation of a general class of non-stationary processes. They proposed prediction and estimation methods which are linear and easy to compute. Daojiang et.al [2] in 2014, in their paper depicted an innovative estimation technique to the multicollinearity in statistical model which is linear in the case of existence of stochastic linear constraints on the parameters and a very different estimation technique was presented by mixing the OME and PCR estimator also known as SRPC regression estimator. In 2014, Shuling Wang et.al [3] in their paper proposed some diagnostic methods in restricted stochastic statistical models which are linear. Gil Gonjalez et.al [4], in 2007, in their paper, derived the LSEs for the simple linear statistical model and examined them from a theoretical perspective.

Correlation between expressiveness and syntactic independence of Russian onomatopoeic verbal interjections

This article considers Russian onomatopoeic verbal interjections due to the fact that these linguistic units possess a unique grammatical feature of being either completely syntactically independent or act as members of sentence, depending on the context and speaker’s communicative intention. Moreover, there is ambiguity concerning their expressiveness. In some cases they are prosodically foregrounded and have reduplicated morphemes, in others no pauses in speech separate them from the host construction and no expressive morphology is demonstrated. This research aims at establishing correlation between prosodic/morphological expressiveness and syntactic independence of Russian onomatopoeic verbal interjections with the help of a statistical model. Firstly, corpus analysis of data from the Russian Corpus of Spoken Language is applied examine expressiveness of these linguistic units, as well as to investigate their syntactic independence. Finally, a Log-Linear Statistical Model is applied to establish dependencies between absence/presence of these three features and to determine which ones of them have significant correlations.

Moist Process Biases in Simulations of the Madden–Julian Oscillation Episodes Observed during the AMIE/DYNAMO Field Campaign

Two Madden–Julian oscillation (MJO) episodes observed during the 2011 Atmospheric Radiation Measurement Program MJO Investigation Experiment (AMIE)/DYNAMO field campaign are simulated using a regional model with various cumulus parameterizations, a regional cloud-permitting model, and a global variable-resolution model with a high-resolution region centered over the tropical Indian Ocean. Model biases in relationships relevant to existing instability theories of MJO are examined and their relative contributions to the overall model errors are quantified using a linear statistical model. The model simulations capture the observed approximately log-linear relationship between moisture saturation fraction and precipitation, but precipitation associated with the given saturation fraction is overestimated especially at low saturation fraction values. This bias is a major contributor to the excessive precipitation during the suppressed phase of MJO. After accounting for this bias using a linear statistical model, the spatial and temporal structures of the model-simulated MJO episodes are much improved, and what remains of the biases is strongly correlated with biases in saturation fraction. The excess precipitation bias during the suppressed phase of the MJO episodes is accompanied by excessive column-integrated radiative forcing and surface evaporation. A large portion of the bias in evaporation is related to biases in wind speed, which are correlated with those of precipitation. These findings suggest that the precipitation bias sustains itself at least partly by cloud radiative feedbacks and convection–surface wind interactions.