Distribution Of Regressors Research Articles

Investigating the moderating impact of crime and corruption on the economic growth of Bangladesh: Fresh insights

This study investigates the moderating role of the corruption index with the impacts of foreign direct investment (FDI), unemployment, corruption, and crime rate on economic growth in Bangladesh from 1988 to 2019. The Augmented Dicky-Fuller (ADF) and Phillips-Peron (P-P) unit root tests were applied to check the stationary properties of the concerned variables. The auto regressor distribution lags approach is used to test the hypotheses. The results show that the corruption index as a moderator has a significant adverse impact on economic growth along with the other variables crime, and unemployment on economic growth. To put it simply, economic growth increases by decreasing corruption, unemployment, and crime rates. Similarly, FDI and trade openness appears as a catalyst for boosting economic growth, but the interaction variable of the trade and corruption index increases the trade costs that may slow down the economic growth. As among the pioneer attempts, the present study contributes to growing literature on the moderator role of the corruption index along with other determinants of economic growth by identifying the role of FDI inflows, trade, unemployment, and crime rates on economic growth in Bangladesh. These empirical findings are directed toward some critical policy implications that will help the governmental bodies and policymakers to achieve sustainable economic growth along with ensuring better employment opportunities and thereby control the crime and corruption rates in Bangladesh.

Models as Approximations I: Consequences Illustrated with Linear Regression

In the early 1980s, Halbert White inaugurated a “model-robust” form of statistical inference based on the “sandwich estimator” of standard error. This estimator is known to be “heteroskedasticity-consistent,” but it is less well known to be “nonlinearity-consistent” as well. Nonlinearity, however, raises fundamental issues because in its presence regressors are not ancillary, hence cannot be treated as fixed. The consequences are deep: (1) population slopes need to be reinterpreted as statistical functionals obtained from OLS fits to largely arbitrary joint ${x\textrm{-}y}$ distributions; (2) the meaning of slope parameters needs to be rethought; (3) the regressor distribution affects the slope parameters; (4) randomness of the regressors becomes a source of sampling variability in slope estimates of order $1/\sqrt{N}$; (5) inference needs to be based on model-robust standard errors, including sandwich estimators or the ${x\textrm{-}y}$ bootstrap. In theory, model-robust and model-trusting standard errors can deviate by arbitrary magnitudes either way. In practice, significant deviations between them can be detected with a diagnostic test.

Assumption Lean Regression

It is well known that with observational data, models used in conventional regression analyses are commonly misspecified. Yet in practice, one tends to proceed with interpretations and inferences that rely on correct specification. Even those who invoke Box’s maxim that all models are wrong proceed as if results were generally useful. Misspecification, however, has implications that affect practice. Regression models are approximations to a true response surface and should be treated as such. Accordingly, regression parameters should be interpreted as statistical functionals. Importantly, the regressor distribution affects targets of estimation and regressor randomness affects the sampling variability of estimates. As a consequence, inference should be based on sandwich estimators or the pairs (x–y) bootstrap. Traditional prediction intervals lose their pointwise coverage guarantees, but empirically calibrated intervals can be justified for future populations. We illustrate the key concepts with an empirical application.

Analysis of incremental LMS adaptive algorithm over wireless sensor networks with delayed-links

Wireless sensor networks (WSN) are used for many delay-sensitive applications, e.g. military surveillance, emergency response, city management, etc. Therefore, modeling of delay is very important. This paper presents a study of the impact of sensors' sensing delay, process delay and transmission delay in the estimation of the desired unknown parameter in the WSN. Recently proposed wireless sensor networks, in the literature, assume perfect nodes and links, in view of delay. It means that no consideration has been made about the delay in the sensing, processing and, transmission procedures. The proposed method in this paper analyzes the behavior of the distributed incremental estimation algorithm in the presence of delay in wireless sensor networks. Weighted spatio-temporal energy conservation method is used to evaluate the transient and steady state behavior of the wireless sensor networks with delay without putting any restriction on regressor's distribution. The equations that illustrate mean square deviation (MSD), excess mean square error (EMSE) and mean square error (MSE) behavior of individual nodes, are driven. Also, simulations show that overall delay could be calculated to turn off nodes in some iterations without affecting the performance of the distributed estimation algorithm or adding extra latency to the network, which can improve power management strategies by modifying sleep-wake scheduling protocols. Eventually, it is shown that simulation results have a good match with derived theoretical expressions.

Consistency of AUC Maximization as an Estimator of Binary Choice Models

This paper studies the asymptotic properties of the binary choice model estimator, based on the maximization of the Area Under receiver operating characteristic Curve (AUC). It is shown that under certain assumptions AUC maximization is a consistent method of binary choice models estimation up to normalizations. As AUC is equivalent to Mann-Whitney U statistics and Wilcoxon test of ranks, maximization of area under ROC curve is equivalent to the maximization of corresponding statistics. Comparing with the parametric methods, such as logit and probit, AUC maximization relaxes assumptions about the distribution of errors, but imposes some restrictions on the distribution of regressors, which can be easily checked, since this information is observed.

Optimality of quasi-score in the multivariate mean–variance model with an application to the zero-inflated Poisson model with measurement errors

In a multivariate mean–variance model, the class of linear score (LS) estimators based on an unbiased linear estimating function is introduced. A special member of this class is the (extended) quasi-score (QS) estimator. It is ‘extended’ in the sense that it comprises the parameters describing the distribution of the regressor variables. It is shown that QS is (asymptotically) most efficient within the class of LS estimators. An application is the multivariate measurement error model, where the parameters describing the regressor distribution are nuisance parameters. A special case is the zero-inflated Poisson model with measurement errors, which can be treated within this framework.

Comparing the efficiency of structural and functional methods in measurement error models

The paper is a survey of recent investigations by the authors and others into the relative efficiencies of structural and functional estimators of the regression parameters in a measurement error model. While structural methods, in particular the quasi-score (QS) method, take advantage of the knowledge of the regressor distribution (if available), functional methods, in particular the corrected score (CS) method, discards such knowledge and works even if such knowledge is not available. Among other results, it has been shown that QS is more efficient than CS as long as the regressor distribution is completely known. However, if nuisance parameters in the regressor distribution have to be estimated, this is no more true in general. But by modifying the QS method, the adverse effect of the nuisance parameters can be overcome. For small measurement errors, the efficiencies of QS and CS become almost indistinguishable, whether nuisance parameters are present or not. QS is (asymptotically) biased if the regressor distribution has been misspecified, while CS is always consistent and thus more robust than QS.

Dimension reduction based on weighted variance estimate

In this paper, we propose a new estimate for dimension reduction, called the weighted variance estimate (WVE), which includes Sliced Average Variance Estimate (SAVE) as a special case. Bootstrap method is used to select the best estimate from the WVE and to estimate the structure dimension. And this selected best estimate usually performs better than the existing methods such as Sliced Inverse Regression (SIR), SAVE, etc. Many methods such as SIR, SAVE, etc. usually put the same weight on each observation to estimate central subspace (CS). By introducing a weight function, WVE puts different weights on different observations according to distance of observations from CS. The weight function makes WVE have very good performance in general and complicated situations, for example, the distribution of regressor deviating severely from elliptical distribution which is the base of many methods, such as SIR, etc. And compared with many existing methods, WVE is insensitive to the distribution of the regressor. The consistency of the WVE is established. Simulations to compare the performances of WVE with other existing methods confirm the advantage of WVE.

Bias of the structural quasi-score estimator of a measurement error model under misspecification of the regressor distribution

In a structural measurement error model the structural quasi-score (SQS) estimator is based on the distribution of the latent regressor variable. If this distribution is misspecified, the SQS estimator is (asymptotically) biased. Two types of misspecification are considered. Both assume that the statistician erroneously adopts a normal distribution as his model for the regressor distribution. In the first type of misspecification, the true model consists of a mixture of normal distributions which cluster around a single normal distribution, in the second type, the true distribution is a normal distribution admixed with a second normal distribution of low weight. In both cases of misspecification, the bias, of course, tends to zero when the size of misspecification tends to zero. However, in the first case the bias goes to zero in a flat way so that small deviations from the true model lead to a negligible bias, whereas in the second case the bias is noticeable even for small deviations from the true model.

Extending Sliced Inverse Regression

Sliced inverse regression (SIR) and an associated chi-squared test for dimension have been introduced as a method for reducing the dimension of regression problems whose predictor variables are normal. In this article the assumptions on the predictor distribution, under which the chi-squared test was proved to apply, are relaxed, and the result is extended. A general weighted chi-squared test that does not require normal regressors for the dimension of a regression is given. Simulations show that the weighted chi-squared test is more reliable than the chi-squared test when the regressor distribution digresses from normality significantly, and that it compares well with the chi-squared test when the regressors are normal.

Series Estimation of Regression Functionals

Two-step estimators, where the first step is the predicted value from a nonparametric regression, are useful in many contexts. Examples include a non-parametric residual variance, probit with nonparametric generated regressors, efficient GMM estimation with randomly missing data, heteroskedasticity corrected least squares, semiparametric regression, and efficient nonlinear instrumental variables estimators. The purpose of this paper is the development of consistency and asymptotic normality results when the first step is a series estimator. The paper presents the form of a correction term for the first step on the second-step asymptotic variance and gives a consistent variance estimator. Data-dependent numbers of terms are allowed for, and the regressor distribution can be discrete, continuous, or a mixture of the two. Results for several new estimators are given.

Unconditional Asymptotic Results for Simple Linear Regression

A fundamental specification issue in linear regression is the joint distribution of the regressors and the disturbance. The standard linear model posits regressors that are fixed in repeated samples and, perforce, independent of any random variable, including the disturbance. When regressors are random, the key assumption of fixity in repeated sampling is replaced with either an assumption of zero correlation between regressor and disturbance or, more strongly, independence between the two. It is widely recognized that a violation of uncorrelatedness is a serious misspecification of the linear regression. It appears not to be widely recognized that lack of independence has serious implications for inference even if regressors and disturbance are uncorrelated. The inferential errors that arise in this case are due to inconsistent estimates of the variances of regression coefficients. The purpose of this article is to explore the asymptotic consequences of stochastic regressors. The context of the discussion is a simple (one X) regression with iid regressor and disturbance. This simple structure serves to focus on the joint distribution of regressor and disturbance and to simplify the arguments notationally and conceptually. In particular, the iid assumption allows the use of easily grasped theorems in asymptotic distribution theory. Although the context of the discussion is limited, results are illuminated that carry over into more general settings. The generalizations to multiple regression are straightforward. Generalizations to non-iid circumstances can be found in White (1984) and Gallant and White (1988).