Independence Of Error Terms Research Articles

A robust counterpart approach for the ridge estimator to tackle outlier effect in restricted multicollinear regression models

In statistics, regression analysis is a method for predicting a target variable by establishing the optimal linear relationship between the dependent and independent variables. The ordinary least squares estimator (OLSE) is the optimal estimation method in classical regression analysis based on the Gauss–Markov theorem if the essential assumptions of normality, independence of error terms, and little or no multicollinearity in the covariates are satisfied. OLSE is profoundly affected by the collinearity between explanatory variables and outlier problems. Therefore, we require resilient strategies to resolve these challenges. Robust stochastic ridge regression is an alternative optimization problem to least squares regression when data are simultaneously contaminated by anomalies, influential observations, and multicollinearity. To combat outliers and multicollinearity problems, a robust stochastic ridge regression estimator based on the least squares trimmed method is proposed in this paper. Using simulated and real data sets, the efficacy of the proposed method with correlated and uncorrelated errors is then evaluated.

Using copulas to enable causal inference from nonexperimental data: Tutorial and simulation studies.

Causal inference in psychological research is typically hampered by unobserved confounding. A copula-based method can be used to statistically control for this problem without the need for instruments or covariates, given relatively lenient distributional assumptions on independent variables and error terms. The current study aims to: (a) provide a user-friendly introduction to the copula method for psychology researchers, and (b) examine the degree of non-normality in the independent variables required for satisfactory performance. A Monte Carlo simulation study was used to assess the behavior of the copula method under various combinations of conditions (sample size, skewness of independent variables, effect size, and magnitude of confounding). In addition, an applied example from research on the effects of parental rearing on adult personality and life satisfaction was used to illustrate the method. Simulations revealed that the copula method performed better at higher levels of skewness in the independent variables, and that the impacts of lower skewness can be offset to some extent by larger sample size. When skewness and/or sample size is too small, the copula method is biased toward the uncorrected model. In the applied example, parental rejection/punishment predicted less adaptive personality and life satisfaction, with no evidence of confounding. For parental control/overprotection, there was evidence that confounding attenuated the estimated relationship with personality/life satisfaction. Copula adjustment is a promising method for handling unobserved confounding. The discussion focuses on how to proceed when assumptions are not quite met, and outlines potential avenues for future research. (PsycInfo Database Record (c) 2021 APA, all rights reserved).

Classical Approach to Zero-Inflated Dynamic Panel Ordered Probit Model with an Application in Drug Abuse

The Zero inflated ordered categorical data with time series structure are often a characteristic of behavioral research attributed to non-participation decision and zero consumption of substance such as drugs among the participants. The existing Semi-parametric zero inflated dynamic panel probit model with selectivity have exhibited biasness and inconsistency in estimators as a result of poor treatment of initial condition and exclusion of selectivity in the unobserved individual effects respectively. The model assumed that the cut points are known to address heaping in the data and therefore cannot be used when the cut points are unknown. In this paper, a Zero inflated dynamic panel ordered probit models have been developed to address the above challenges. Average partial effects that presents the impacts on the specific probabilities per unit change in the covariates are also given. Since the solutions are not of closed form, Maximum likelihood estimation based on Newton Raphson algorithm was used to estimate the parameters of the model. A Monte Carlo study was carried out to investigate some theoretical properties of the estimators in the models. The study found that the Zero inflated dynamic panel ordered probit models with independent and correlated error terms produced consistent estimators. The Zero inflated dynamic panel ordered probit models with independent and correlated error terms had more accurate estimators than the Dynamic panel ordered probit model. The Zero inflated dynamic panel ordered probit model with correlated error terms fitted the National Longitudinal Survey of Youth 1997 better than Zero inflated dynamic panel ordered probit model with independent error terms and Dynamic panel ordered probit model. The Zero inflated dynamic panel ordered probit model with independent error terms fitted the National Longitudinal Survey of Youth 1997 better the Dynamic panel ordered probit model.

A simple test of completeness in a class of nonparametric specification

This paper provides a test for completeness in a class of nonparametric specification with an additive and independent error term. It is known that such a nonparametric location family of functions is complete if and only if the characteristic function of the error term has no zeros on the real line. Because a zero of the error characteristic function implies that of an observed marginal distribution, we propose a simple test for zeros of characteristic function of the observed distribution, in which rejection of the null hypothesis implies the completeness. This test is applicable to many popular settings, such as nonparametric regression models with instrumental variables, and nonclassical measurement error models. We describe the asymptotic behavior of the tests under the null and alternative hypotheses and investigate the finite sample properties of the proposed test through a Monte Carlo study. We illustrate our method empirically by estimating a measurement error model using the CPS/SSR 1978 exact match file.

A robust estimation method for the linear regression model parameters with correlated error terms and outliers

Independence of error terms in a linear regression model, often not established. So a linear regression model with correlated error terms appears in many applications. According to the earlier studies, this kind of error terms, basically can affect the robustness of the linear regression model analysis. It is also shown that the robustness of the parameters estimators of a linear regression model can stay using the M-estimator. But considering that, it acquires this feature as the result of establishment of its efficiency. Whereas, it has been shown that the minimum Matusita distance estimators, has both features robustness and efficiency at the same time. On the other hand, because the Cochrane and Orcutt adjusted least squares estimators are not affected by the dependence of the error terms, so they are efficient estimators. Here we are using of a non-parametric kernel density estimation method, to give a new method of obtaining the minimum Matusita distance estimators for the linear regression model with correlated error terms in the presence of outliers. Also, simulation and real data study both are done for the introduced estimation method. In each case, the proposed method represents lower biases and mean squared errors than the other two methods.

Variable selection for high-dimensional regression models with time series and heteroscedastic errors

Although existing literature on high-dimensional regression models is rich, the vast majority of studies have focused on independent and homogeneous error terms. In this article, we consider the problem of selecting high-dimensional regression models with heteroscedastic and time series errors, which have broad applications in economics, quantitative finance, environmental science, and many other fields. The error term in our model is the product of two components: one time series component, allowing for a short-memory, long-memory, or conditional heteroscedasticity effect, and a high-dimensional dispersion function accounting for exogenous heteroscedasticity. By making use of the orthogonal greedy algorithm and the high-dimensional information criterion, we propose a new model selection procedure that consistently chooses the relevant variables in both the regression and the dispersion functions. The finite sample performance of the proposed procedure is also illustrated via simulations and real data analysis.

Goodness‐of‐fit for regime‐switching copula models with application to option pricing

AbstractWe consider several time series, and for each of them, we fit an appropriate dynamic parametric model. This produces serially independent error terms for each time series. The dependence between these error terms is then modelled by a regime‐switching copula. The EM algorithm is used for estimating the parameters and a sequential goodness‐of‐fit procedure based on Cramér–von Mises statistics is proposed to select the appropriate number of regimes. Numerical experiments are performed to assess the validity of the proposed methodology. As an example of application, we evaluate a European put‐on‐max option on the returns of two assets. To facilitate the use of our methodology, we have built a R package HMMcopula available on CRAN. The Canadian Journal of Statistics 48: 79–96; 2020 © 2020 Statistical Society of Canada

Detection of Collinearity Effects on Explanatory Variables and Error Terms in Multiple Regressions

In this work we investigates the effects and consequences of multicollinearity on both standard error and explanatory variables in multiple regression, the correlation between X1 to X6 (independent variables) measure their individual effect and performance on Y (Response variable) and it is carefully observes how those explanatory variables intercorrelated with one another and to the response variable. There are many procedures available in literature for detecting presence, degree and severity of multicollinearity in multiple regression analysis here we used correlation analysis to discover it is presence; we use variance inflation factors, tolerance level, indices number, eigenvalues to access fluctuation and influence of multicollinearity present in the model. Multicollinearity was discovered in this research work with a severe proportion using arrays of correlation analysis procedure which affects the performance of the explanatory variables present in the model by making it less independent and more redundant as it should not be. Collinearity inflates variance of estimates and brings change in direction and signs of the co-efficient of the estimates leading to unrealistic erroneous inference, wrong interpretation and instability among the predictor variables. standard error is discover to be slightly height which directly affect the accuracy and precision of the final result from the analysis, it bring type 1 error during and after the hypothesis testing and finally undermined the overall inference of the entire analysis interest and is in good agreements with the finding of Complete elimination of collinearity is not possible but in this work we reduce it is degree of intensity to enhance the performance of independent variables and error term in the model.

Goodness-of-Fit for Regime-Switching Copula Models with Application to Option Pricing

We consider several time series and for each of them, we fit an appropriate dynamic parametric model. This produces serially independent error terms for each time series. The dependence between these error terms is then modeled by a regime-switching copula. The EM algorithm is used for estimating the parameters and a sequential goodness-of- fit procedure based on Cramer-von Mises statistics is proposed to select the appropriate number of regimes. Numerical experiments are performed to assess the validity of the proposed methodology. As an example of application, we evaluate a European put-on-max option on the returns of two assets. In order to facilitate the use of our methodology, we have built a R package HMMcopula available on CRAN.

Estimation and Goodness-of-Fit for Regime-Switching Copula Models with Application

We consider several time series and for each of them, we fit an appropriate dynamic parametric model. This produces serially independent error terms for each time series. The dependence between these error terms is then modeled by a regime-switching copula. The EM algorithm is used for estimating the parameters and a sequential goodness-of-fit procedure based on Cramer-von Mises statistics is proposed to select the appropriate number of regimes. Numerical experiments are performed to assess the validity of the proposed methodology. As an example of application, we evaluate a European put-on-max option on the returns of two assets. In order to facilitate the use of our methodology, we have built a R package HMMcopula available on CRAN.

Corporate governance: evidence from Islamic banks

PurposeThis paper aims to examine the impact of Shari’ah supervisory boards (SSBs) on the performance of Islamic banks (IBs). It also tests whether SSBs’ attributes affect the performance of IBs. Based on a sample of 1,803 Islamic bank-year observations from 82 banks in 15 countries over the period 1993-2014 and controlling for factors known to affect bank performance, this study reveals a robust and significant positive relationship between SSBs and Islamic bank performance. This study also shows that the characteristics of SSBs affect the performance of IBs. This research reveals how SSBs influence the performance of IBs, as well as the processes and roles SSBs use to ensure Shari’ah compliance in business transactions.Design/methodology/approachThe purpose of this study design is to relate SSB presence, size and diversity to financial performance using three techniques. The first technique is a multivariate data analysis that analyzes data arising from more than one variable. The second technique is a clustered regression (clustering by bank), which corrects for serial correlation and produces unbiased t-statistics. Because this sample is drawn from panel data, it is expected serial autocorrelation of the independent variables and error term within banks. In cases where within-company correlation exists, t-statistics based on average regression coefficients from year-by-year regression are upwardly biased and potentially severe (Peterson, 2009). Therefore, this study uses a technique that agrees with Stock and Watson (2002), who show that the standard method of calculating heteroskedasticity-robust standard errors for the fixed-effects estimator generates inconsistent variance estimates. Thus, using the clustered regression is consistent with the fixed-effects estimator. The third technique is a two-stage least-squares regression that helps build an instrumental variable for robustness tests purposes.FindingsThe findings suggest that large corporate boards and large SSBs are more efficient in dealing with different monitoring and advisory roles than small SSBs. Consequently, this suggests that increasing the size of corporate boards and SSBs should improve monitoring and advisory functions, management behavior and organizational performance.Research limitations/implicationsIt is possible that there is an upper limit to this benefit, however; we do not explore this limit, which therefore provides opportunities for additional research. Because Shari’ah compliance relates only to a rational legal framework of negative screening relegated to interest prohibition and limiting uncertainty. The interest prohibition and limiting uncertainty have not been investigated between the two samples due to data unavailability. In addition, limited accounting-based measures of financial performance may not accurately portray IB performance; hence, an additional market measure is implemented, which is Tobin’s Q.Practical implicationsUltimately, these findings could help IBs improve their financial results by enhancing their internal and external governance mechanisms (Walsh and Seward, 1990). They provide a basis for developing larger, more diverse SSBs that are more focused on complying with Shari’ah and corporate governance. The results also have significant policy implications for improving firm-level corporate governance versus improving country-level institutional factors. Both views have their advocates. However, it is very difficult to reform the legal system in a short time. Still, this study shows that struggling IBs have a way to improve their corporate governance and simultaneously improve their financing environment.Originality/valueThis research contributes to the literature on the effects of SSBs on IBs’ organizational financial performance, processes and roles. It is the first to examine empirically the underpinnings of how SSBs affect organizational financial performance via agency theory and contingency theory.

Outcome-Driven Cluster Analysis with Application to Microarray Data.

One goal of cluster analysis is to sort characteristics into groups (clusters) so that those in the same group are more highly correlated to each other than they are to those in other groups. An example is the search for groups of genes whose expression of RNA is correlated in a population of patients. These genes would be of greater interest if their common level of RNA expression were additionally predictive of the clinical outcome. This issue arose in the context of a study of trauma patients on whom RNA samples were available. The question of interest was whether there were groups of genes that were behaving similarly, and whether each gene in the cluster would have a similar effect on who would recover. For this, we develop an algorithm to simultaneously assign characteristics (genes) into groups of highly correlated genes that have the same effect on the outcome (recovery). We propose a random effects model where the genes within each group (cluster) equal the sum of a random effect, specific to the observation and cluster, and an independent error term. The outcome variable is a linear combination of the random effects of each cluster. To fit the model, we implement a Markov chain Monte Carlo algorithm based on the likelihood of the observed data. We evaluate the effect of including outcome in the model through simulation studies and describe a strategy for prediction. These methods are applied to trauma data from the Inflammation and Host Response to Injury research program, revealing a clustering of the genes that are informed by the recovery outcome.

Bayesian joint modeling of correlated counts data with application to adverse birth outcomes

In disease mapping, health outcomes measured at the same spatial locations may be correlated, so one can consider joint modeling the multivariate health outcomes accounting for their dependence. The general approaches often used for joint modeling include shared component models and multivariate models. An alternative way to model the association between two health outcomes, when one outcome can naturally serve as a covariate of the other, is to use ecological regression model. For example, in our application, preterm birth (PTB) can be treated as a predictor for low birth weight (LBW) and vice versa. Therefore, we proposed to blend the ideas from joint modeling and ecological regression methods to jointly model the relative risks for LBW and PTBs over the health districts in Saskatchewan, Canada, in 2000–2010. This approach is helpful when proxy of areal-level contextual factors can be derived based on the outcomes themselves when direct information on risk factors are not readily available. Our results indicate that the proposed approach improves the model fit when compared with the conventional joint modeling methods. Further, we showed that when no strong spatial autocorrelation is present, joint outcome modeling using only independent error terms can still provide a better model fit when compared with the separate modeling.

Investigation of the marked and long-standing spatial inhomogeneity of the Hungarian suicide rate: A spatial regression approach

BackgroundIn the last century Hungary had astonishingly high suicide rates characterized by marked regional within-country inequalities, a spatial pattern which has been quite stable over time. AimsTo explain the above phenomenon at the level of micro-regions (n=175) in the period between 2005 and 2011. MethodsOur dependent variable was the age and gender standardized mortality ratio (SMR) for suicide while explanatory variables were factors which are supposed to influence suicide risk, such as measures of religious and political integration, travel time accessibility of psychiatric services, alcohol consumption, unemployment and disability pensionery. When applying the ordinary least squared regression model, the residuals were found to be spatially autocorrelated, which indicates the violation of the assumption on the independence of error terms and – accordingly – the necessity of application of a spatial autoregressive (SAR) model to handle this problem. According to our calculations the SARlag model was a better way (versus the SARerr model) of addressing the problem of spatial autocorrelation, furthermore its substantive meaning is more convenient. ResultsSMR was significantly associated with the “political integration” variable in a negative and with “lack of religious integration” and “disability pensionery” variables in a positive manner. Associations were not significant for the remaining explanatory variables. LimitationsSeveral important psychiatric variables were not available at the level of micro-regions. We conducted our analysis on aggregate data. ConclusionOur results may draw attention to the relevance and abiding validity of the classic Durkheimian suicide risk factors – such as lack of social integration – apropos of the spatial pattern of Hungarian suicides.

Bayesian modeling of autoregressive partial linear models with scale mixture of normal errors

Normality and independence of error terms are typical assumptions for partial linear models. However, these assumptions may be unrealistic in many fields, such as economics, finance and biostatistics. In this paper, a Bayesian analysis for partial linear model with first-order autoregressive errors belonging to the class of the scale mixtures of normal distributions is studied in detail. The proposed model provides a useful generalization of the symmetrical linear regression model with independent errors, since the distribution of the error term covers both correlated and thick-tailed distributions, and has a convenient hierarchical representation allowing easy implementation of a Markov chain Monte Carlo scheme. In order to examine the robustness of the model against outlying and influential observations, a Bayesian case deletion influence diagnostics based on the Kullback–Leibler (K–L) divergence is presented. The proposed method is applied to monthly and daily returns of two Chilean companies.

A Comparison of Spatial Designs for Field Variety Trials

Summary Experimental designs can be constructed to be efficient in the presence of spatial correlation. Available construction methods include those based on autoregressive and linear variance models. This paper investigates spatial designs across a range of assumed autoregressive structures. Results show that when the spatial component is low relative to the independent error term, efficient spatial designs can be constructed without having to specify parameters for the spatial structure.

Application of Spatial Regression Models to Income Poverty Ratios in Middle Delta Contiguous Counties in Egypt

Regression analysis depends on several assumptions that have to be satisfied. A major assumption that is never satisfied when variables are from contiguous observations is the independence of error terms. Spatial analysis treated the violation of that assumption by two derived models that put contiguity of observations into consideration. Data used are from Egypts 2006 latest census, for 93 counties in middle delta seven adjacent Governorates. The dependent variable used is the percent of individuals classified as poor (those who make less than 1$ daily). Predictors are some demographic indicators. Explanatory Spatial Data Analysis (ESDA) is performed to examine the existence of spatial clustering and spatial autocorrelation between neighboring counties. The ESDA revealed spatial clusters and spatial correlation between locations. Three statistical models are applied to the data, the Ordinary Least Square regression model (OLS), the Spatial Error Model (SEM) and the Spatial Lag Model (SLM).The Likelihood Ratio test and some information criterions are used to compare SLM and SEM to OLS. The SEM model proved to be better than the SLM model. Recommendations are drawn regarding the two spatial models used.

Methodological Advances in Strategic Management Research

Despite the increased attention that has been directed at methodological issues in business strategy during the past 15 years, a number of challenges still exist. One challenge is how to correctly test for mediated effects, given that many of the models in the strategy area violate assumptions regarding the independence of error terms in regression equations. Violating these assumptions leads to biased parameter estimates, and impedes the ability of researchers to make correct inferences about the mechanisms that explain substantive relationships. Another related challenge is the issue of endogeneity. Endogeneity occurs when an independent variable is correlated with the error term in an OLS regression model. Although this issue has been a topic of discussion for a number of decades in other fields, it has only recently begun to attract attention among strategy researchers. A third challenge relates to the appropriate way to test non-linear relationships using polynomial variables. Despite the fact that s...

A variance-covariance structure to take into account repeated measurements and heteroscedasticity in growth modeling

This study proposes a within-subject variance-covariance (VC) structure to take into account repeated measurements and heteroscedasticity in a context of growth modeling. The VC structure integrates a variance function and a continuous autoregressive covariance structure. It was tested on a nonlinear growth model parameterized with data from permanent sample plots. Using a stand-level approach, basal area growth was independently modeled for red spruce (Picea rubens Sarg.) and balsam fir [Abies balsamea (L.) Mill.] in mixed stands. For both species, the implementation of the VC structure significantly improved the maximum likelihood of the model. In both cases, it efficiently accounted for heteroscedasticity and autocorrelation, since the normalized residuals no longer exhibited departures from the assumptions of independent error terms with homogeneous variances. Moreover, compared with traditional nonlinear least squares (NLS) models, models parameterized with this VC structure may generate more accurate predictions when prior information is available. This case study demonstrates that the implementation of a VC structure may provide parameter estimates that are consistent with asymptotically unbiased variances in a context of nonlinear growth modeling using a stand-level approach. Since the variances are no longer biased, the hypothesis tests performed on the estimates are valid when the number of observations is large.

Empirical Kriging models and their applications to QSAR

AbstractA general Kriging model consists of two additive components: a parametric term and a stochastic error process. It is known that Kriging is an interpolating predictor and allows for a better fit to the data, but suffers from a decreasing ability to generalize to unseen data. By incorporating a disturbing or an independent random error term into Kriging model, the resulting model, which is called empirical Kriging model in the literature, may provide more accurate prediction for the highly noisy data than the Kriging model. This paper presents an extensive survey of the empirical Kriging model for quantitative structure‐activity relationship (QSAR) research and extends the parameters estimation technique with highly efficiency. In addiction, QSAR models are established by combining Kriging model or empirical Kriging model with principal components regression (PCR) and partial least squares regression (PLSR). We demonstrate for the real data set that the suggested empirical Kriging model can significantly improve the prediction ability of some commonly used models, including the Kriging model. Copyright © 2007 John Wiley & Sons, Ltd.