Two-step robust estimator in heteroscedastic regression model in the presence of outliers

Although the ordinary least squares (OLS) estimates are unbiased in the presence of heteroscedasticity, these are no longer efficient. This problem becomes more complicated when the violation of constant error variances comes together with the existence of outliers. The weighted least squares (WLS) procedure is often used to estimate the regression parameters when heteroscedasticity occurs in the data. But there is evidence that the WLS estimators suffer a huge set back in the presence of outliers. Moreover, the use of the WLS requires a known form of the heteroscedastic errors structures. To rectify this problem, we proposed a new method that we call two step robust weighted least squares (TSRWLS) method where prior information on the structure of the heteroscedastic errors is not required. In the proposed procedure, the robust technique is used twice. Firstly, the robust weights are used for solving the heteroscedasic error and secondly, the robust weighting function is used for eliminating the effect of outliers. The performance of the newly proposed estimator is investigated extensively by real data sets and Monte Carlo simulations

Adjusting outliers in univariate circular data

Circular data analysis is a particular branch of statistics that sits somewhere between the analysis of linear data and the analysis of spherical data. Circular data are used in many scientific fields. The efficiency of the statistical methods that are applied depends on the accuracy of the data in the study. However, circular data may have outliers that cannot be deleted. If this is the case, we have two ways to avoid the effect of outliers. First, we can apply robust methods for statistical estimations. Second, we can adjust the outliers using the other clean data points in the dataset. In this paper, we focus on adjusting outliers in circular data using the circular distance between the circular data points and the circular mean direction. The proposed procedure is tested by applying it to a simulation study and to real data sets. The results show that the proposed procedure can adjust outliers according to the measures used in the paper

Dark Iron-Catalyzed Reactions in Acidic and Viscous Aerosol Systems Efficiently Form Secondary Brown Carbon

Iron-driven secondary brown carbon formation reactions from water-soluble organics in cloud droplets and aerosols create insoluble and soluble products of emerging atmospheric importance. This work shows, for the first time, results on dark iron-catalyzed polymerization of catechol forming insoluble black polycatechol particles and colored water-soluble oligomers under conditions characteristic of viscous multicomponent aerosol systems with relatively high ionic strength (I = 1–12 m) and acidic pH (∼2). These systems contain ammonium sulfate (AS)/nitrate (AN) and C3–C5 dicarboxylic acids, namely, malonic, malic, succinic, and glutaric acids. Using dynamic light scattering (DLS) and ultra high pressure liquid chromatography-mass spectrometry (UHPLC-MS), we show results on the rate of particle growth/agglomeration and identity of soluble oligomeric reaction products. We found that increasing I above 1 m and adding diacids with oxygen-to-carbon molar ratio (O:C \u3e 1) significantly reduced the rate of polycatechol formation/aggregation by a factor of 1.3 ± 0.4 in AS solution in the first 60 min of reaction time. Using AN, rates were too slow to be quantified using DLS, but particles formed after 24 h reaction time. These results were explained by the relative concentration and affinity of ligands to Fe(III). We also report detectable amounts of soluble and colored oligomers in reactions with a slow rate of polycatechol formation, including organonitrogen compounds. These results highlight that brown carbon formation from iron chemistry is efficient under a wide range of aerosol physical states and chemical composition

Oxidation of Phenolic Aldehydes by Ozone and Hydroxyl Radicals at the Air-Water Interface

Biomass burning releases highly reactive methoxyphenols into the atmosphere, which can undergo heterogeneous oxidation and act as precursors for secondary organic aerosol (SOA) formation. Understanding the reactivity of such methoxyphenols at the air–water interface is a matter of major atmospheric interest. Online electrospray ionization mass spectrometry (OESI-MS) is used here to study the oxidation of two methoxyphenols among three phenolic aldehydes, 4-hydroxybenzaldehyde, vanillin, and syringaldehyde, on the surface of water. The OESI-MS results together with cyclic voltammetry measurements at variable pH are integrated into a mechanism describing the heterogeneous oxidative processing of methoxyphenols by gaseous ozone (O3) and hydroxyl radicals (HO•). For a low molar ratio of O3 ≤ 66 ppbv, the OESI-MS spectra show that the oxidation is dominated by in situ produced HO• and results in the production of polyhydroxymethoxyphenols. When the level of O3 increases (i.e., ≥78 times), the ion count of polyhydroxymethoxyphenols increases, while new ring fragmentation products are generated, including conjugated aldehydes and double bonds as well as additional carboxylic acid groups. The interfacial reactivity of methoxyphenols with O3 and HO• is enhanced as the number of methoxy (−OCH3) groups increases (4-hydroxybenzaldehyde \u3c vanillin \u3c syringaldehyde). The experimental observations are summarized in two reaction pathways, leading to the formation of (1) hydroxylated methoxyphenols and (2) multifunctional carboxylic acids from fragmentation of the aromatic ring. The new highly oxygenated products with low volatility are excellent precursors for aqueous SOA formation

Antidiabetic Effects of Momordica Charantia (Karela) in Male Long Evans Rat

The hypoglycemic effect of Momordica charantia (Karela) has been reported from many laboratories. To our knowledge, the underlying biochemical mechanism of action of this important clinical effect has not been reported. During the course of investigation of this aspect of the herbal fruit, it was reported from our laboratory that ethanolic extract of Momordica charantia suppressed gluconeogenesis in normal and streptozotocin (STZ) induced diabetic rats by depressing the hepatic gluconeogenic enzymes fructose-1,6-bisphosphatase and glucose-6-phosphatase. The herbal extract had also enhanced the activity of glucose-6-phosphate dehydrogenase, the rate-limiting enzyme of hexose monophosphate shunt (a pathway for the oxidation of glucose)

A robust modification of the Goldfeld-Quandt Test for the detection of heteroscedasticity in the presence of outliers

Problem statement: The problem of heteroscedasticity occurs in regression analysis for many practical reasons. It is now evident that the heteroscedastic problem affects both the estimation and test procedure of regression analysis, so it is really important to be able to detect this problem for possible remedy. The existence of a few extreme or unusual observations that we often call outliers is a very common feature in data analysis. In this study we have shown how the existence of outliers makes the detection of heteroscedasticity cumbersome. Often outliers occurring in a homoscedastic model make the model heteroscedastic, on the other hand, outliers may distort the diagnostic tools in such a way that we cannot correctly diagnose the heteroscedastic problem in the presence of outliers. Neither of these situations is desirable. Approach: This article introduced a robust test procedure to detect the problem of heteroscedasticity which will be unaffected in the presence of outliers. We have modified one of the most popular and commonly used tests, the Goldfeld-Quandt, by replacing its nonrobust components by robust alternatives. Results: The performance of the newly proposed test is investigated extensively by real data sets and Monte Carlo simulations. The results suggest that the robust version of this test offers substantial improvements over the existing tests. Conclusion/Recommendations: The proposed robust Goldfeld-Quandt test should be employed instead of the existing tests in order to avoid misleading conclusion

A robust rescaled moment test for normality in regression

Problem statement: Most of the statistical procedures heavily depend on normality assumption of observations. In regression, we assumed that the random disturbances were normally distributed. Since the disturbances were unobserved, normality tests were done on regression residuals. But it is now evident that normality tests on residuals suffer from superimposed normality and often possess very poor power. Approach: This study showed that normality tests suffer huge set back in the presence of outliers. We proposed a new robust omnibus test based on rescaled moments and coefficients of skewness and kurtosis of residuals that we call robust rescaled moment test. Results: Numericalexamples and Monte Carlo simulations showed that this proposed test performs better than the existingtests for normality in the presence of outliers. Conclusion/Recommendation: We recommend using ourproposed omnibus test instead of the existing tests for checking the normality of the regressionresiduals

The performance of robust weighted least squares in the presence of outliers and heteroscedastic errors

The Ordinary Least Squares (OLS) method is the most popular technique in statistics and is often use to estimate the parameters of a model because of tradition and ease of computation. The OLS provides an efficient and unbiased estimates of the parameters when the underlying assumptions, especially the assumption of contant error variances (homoscedasticity), are satisfied. Nonetheless, in real situation it is difficult to retain the error variance homogeneous for many practical reasons and thus there arises the problem of heteroscedasticity. We generally apply the Weighted Least Squares (WLS) procedure to estimate the regression parameters when heteroscedasticity occurs in the data. Nevertheless, there is evidence that the WLS estimators suffer a huge set back in the presence of a few atypical observations that we often call outliers. In this situation the analysis will become more complicated. In this paper we have proposed a robust procedure for the estimation of regression parameters in the situation where heteroscedasticity comes together with the existence of outliers. Here we have employed robust techniques twice, once in estimating the group variances and again in determining weights for the least squares. We call this method Robust Weighted Least Squares (RWLS). The performance of the newly proposed method is investigated extensively by real data sets and Monte Carlo Simulations. The results suggest that the RWLS method offers substantial improvements over the existing methods

Detection of outliers in the response and explanatory variables of the simple circular regression model

The circular regression model may contain one or more data points which appear to be peculiar or inconsistent with the main part of the model. This may be occur due to recording errors, sudden short events, sampling under abnormal conditions etc. The existence of these data points “outliers” in the data set cause lot of problems in the research results and the conclusions. Therefore, we should identify them before applying statistical analysis. In this article, we aim to propose a statistic to identify outliers in the both of the response and explanatory variables of the simple circular regression model. Our proposed statistic is robust circular distance RCDxy and it is justified by the three robust measurements such as proportion of detection outliers, masking and swamping rates

Reactivity of aminophenols in forming nitrogen-containing brown carbon from iron-catalyzed reactions

Nitrogen-containing organic carbon (NOC) in atmospheric particles is an important class of brown carbon (BrC). Redox active NOC like aminophenols received little attention in their ability to form BrC. Here we show that iron can catalyze dark oxidative oligomerization of o- and p-aminophenols under simulated aerosol and cloud conditions (pH 1–7, and ionic strength 0.01–1 M). Homogeneous aqueous phase reactions were conducted using soluble Fe(III), where particle growth/agglomeration were monitored using dynamic light scattering. Mass yield experiments of insoluble soot-like dark brown to black particles were as high as 40%. Hygroscopicity growth factors (κ) of these insoluble products under sub- and super-saturated conditions ranged from 0.4–0.6, higher than that of levoglucosan, a prominent proxy for biomass burning organic aerosol (BBOA). Soluble products analyzed using chromatography and mass spectrometry revealed the formation of ring coupling products of o- and p-aminophenols and their primary oxidation products. Heterogeneous reactions of aminophenol were also conducted using Arizona Test Dust (AZTD) under simulated aging conditions, and showed clear changes to optical properties, morphology, mixing state, and chemical composition. These results highlight the important role of iron redox chemistry in BrC formation under atmospherically relevant conditions