Restricted Least Research Articles

The impact of trade reforms on industry wage premia in Pakistan: A sectoral perspective

Pakistan witnessed significant trade liberalization reforms between 1988 and 2005. This study investigates the impact of Pakistan's significant trade liberalization policies in 1988 on industry wage premia. We use an estimation strategy that takes into account dispersion in sector wage premiums and trade reforms over time and across sectors. We employed the wage premium approach and Restricted Least Squares to obtain sectoral wage premia. We used weighted least squares and two-stage-least-squares (2SLS) to explore the liaison between trade reforms and sector wage premia. Contrary to previous empirical studies on less developed economies, our findings reveal a significant and resilient correlation between changes in trade reforms and fluctuations in sector wage premiums during the liberalisation period of 1990-2005. Our findings are consistent with short- and medium-run trade models in which workers are immobile across industries or, on the other hand, with the presence of sector rents that are reduced when trade policy is liberalized.

Bayesian Linear Restricted Least Squares Estimators

Bayesian Linear Restricted Least Squares Estimators

Might expert knowledge improve econometric real estate mass appraisal?

The article examines whether expert knowledge improves the estimation results of real estate mass appraisal models. Six econometric models were compared: OLS, mixed, the Bayesian model, the Inequality Restricted Least Squares (IRLS) model, ridge and LASSO regression (with regularization). In three of the models (mixed, Bayesian, and IRLS) prior knowledge was applied. In mixed and Bayesian models priors took the form of intervals for model parameters. In IRLS, restrictions in the form of inequalities were applied. In the empirical example mass appraisal models were applied in the valuation of undeveloped land for residential purposes. Models with prior knowledge turned out to be the best with regard to the consistency of estimates with theory. Also, prediction accuracy was better for models with prior knowledge. In the case of low quality data expert knowledge might significantly improve estimation results of real estate mass appraisal econometric models.

Abstract TP222: The Impact Of Il-6 Level On Visit-to-visit Blood Pressure Variability And Incidence Of Stroke: A Post-hoc Analysis Of Mesa

Background: Increased blood pressure variability (BPV) has been associated with stroke risk, but no serum inflammatory markers have been identified associated with increased BPV, despite preclinical data suggesting a role. Methods: This is a post-hoc analysis of the Multi-Ethnic Study of Atherosclerosis (MESA) study. The study exposure was tertiles of serum level of interleukin-6 (IL-6) at the baseline study visit. The primary outcome was visit-to-visit BPV measured as the residual standard deviation (rSD) of at least 4 subsequent study visits (1999-2018). Two logistic regression models were fit to the top tertile (i.e. most variability) of rSD during follow-up: in Model 1, we adjusted for covariates chosen with restricted Least Absolute Shrinkage and Selection Operator (LASSO) and in Model 2, for all covariates. Results: Our analysis included 5,483 patients, of mean (SD) age 61.4 (10.0) years and with 52.9% female. Mean (SD) of IL-6 was 1.7 (1.2) (pg/mL) in the top tertile BPV rSD and 1.4 (1.1) in the bottom tertiles. The incidence of ischemic stroke and all major adverse cardiovascular event was higher in top tertile of BPV (Table 1). Elevated serum IL-6, but not other serum biomarkers of inflammation and clotting (see comment below), was associated with the highest tertile of BPV, independent of potential confounders (Table 2). Conclusion: Higher levels of serum IL-6 were associated with increased subsequent BPV in a large multiracial cohort. Further investigation is needed to better understand the relationship between chronic inflammation and BPV. Table 1. Baseline demographics, serum biomarkers, and clinical outcomes during follow-up (how long was follow-up on average?) in the full cohort, and stratified by the top versus lower tertiles of BPV. Table 2. Association of serum biomarkers at baseline with the highest tertile of blood pressure variability.*Model 1 adjusted for patient age categories (<55, 55-64, 65-69, ≥70), sex, and hypertension. **Model 2 (n=5,447) adjusted for patient age categories (<55, 55-64, 65-69, ≥70), sex, race/ethnicity, education, hypertension, diabetes, smoking, drinking, body mass index, lipid lowering medication, and mean systolic blood pressure

A Simulation Study of Some Restricted Estimators in Restricted Linear Regression Model

When the multicollinearity exists in linear regression model, the result of the Restricted Least Square estimator (RLS) is unstable. So that, more researchers proposed the restricted biased estimators to improve the efficiency of RLS estimator. In this paper, Some of biased restricted estimators have been introduced to study the performance of them. The simulation study has been given to compare these estimators. According to simulation study, we found that, the shrinkage restricted ridge regression (SRRE) estimator which proposed by Baber and Mustafa [1], has good properties comparing with other restricted estimators that given in this study. A Numerical example has been considered to illustrate the performance of these estimators

Sparsely restricted penalized estimators

Parameters of a linear regression model might be estimated with Ordinary Least Squares (OLS). If there are linear restrictions on model parameters, it is possible to use Restricted Least Squares (RLS). Both OLS and RLS fail when the number of predictors is large and not suitable for model selection in a sparse model. In contrast to OLS and RLS, Least Absolute Shrinkage and Selection Operator (LASSO) and Bridge estimators perform well in sparse models and can be used for model selection and estimation, simultaneously. A Restricted LASSO (RLASSO) estimator is proposed in the literature recently but it doesn’t provide sparse solutions. In this paper, we propose new sparsely restricted penalized estimators called Sparsely Restricted LASSO (SRL) and Sparsely Restricted Bridge (SRB) based on RLASSO and Restricted Bridge (RBridge). We show that SRL and SRB produces sparse solutions while satisfying restrictions of model parameters. We compare aforementioned estimators with Monte Carlo simulations. We also use prostate cancer dataset that is widely used in the literature for a numerical application. Our comparisons show that SRL and SRB outperform the remaining estimators in terms of model selection performance and mean squared error.

Combination and Selection of Traffic Safety Expert Judgments for the Prevention of Driving Risks

In this paper, we describe a new framework to combine experts' judgments for the prevention of driving risks in a cabin truck. In addition, the methodology shows how to choose among the experts the one whose predictions fit best the environmental conditions. The methodology is applied over data sets obtained from a high immersive cabin truck simulator in natural driving conditions. A nonparametric model, based in Nearest Neighbors combined with Restricted Least Squared methods is developed. Three experts were asked to evaluate the driving risk using a Visual Analog Scale (VAS), in order to measure the driving risk in a truck simulator where the vehicle dynamics factors were stored. Numerical results show that the methodology is suitable for embedding in real time systems.

The robustness of simulation-based Markovian transition probabilities for ultra-small samples of non-performing credit

The analysis of systemic credit risk by financial regulators is largely affected by the paucity of data. Supervisors receive reports on proportions of performing and non-performing aggregate loan classes of individual banks—corporate, mortgage and consumer—often with very short history. The transition to different proportions of aggregate credit qualities can be seen as a Markov process and Christodoulakis [J. Credit Risk, 2007, 3(3), 25–39] proposed a simulation-based method for the estimation of transition probabilities under non-negativity constraints, based on the work of Kloek and van Dijk [Econometrica, 1978, 46(1), 1–19] and van Dijk and Kloek [J. Econometrics, 1980, 14, 307–328]. This paper provides Monte Carlo robustness checks for the performance of this estimator in comparison to Least Squares and Restricted Least Squares (OLS-R) in the presence of ultra-small samples. When true transition probabilities are very large or very small, the least squares estimators severely violate non-negativity restrictions, leading to a spuriously small bias as compared to Monte Carlo integration (MCI). This result is intensified for low volatility regimes and small samples. The bias of MCI diminishes in higher volatility regimes and larger samples, irrespective of the number of Bayesian replications. Regarding the accuracy statistics, we observe that the variance of every estimator increases in smaller samples and lower volatility regimes. MCI is revealed as more accurate or at least equivalent to OLS-R in all cases. Our empirical applications with real US and European data on aggregate credit portfolios revealed significant violations of non-negativity constraints by least squares methods, which contribute to favourable conclusions for MCI.

A Note on the Prediction Sum of Squares Statistic for Restricted Least Squares

There is a well-known simple formula for computing prediction sum of squares (PRESS) residuals in a regression problem without having to refit the curve for each observation. This note shows that the same basic result holds for fitting a regression function when the regression coefficients are subject to linear constraints.

A Note on the Prediction Sum of Squares Statistic for Restricted Least Squares

Abstract There is a well-known simple formula for computing prediction sum of squares (PRESS) residuals in a regression problem without having to refit the curve for each observation. This note shows that the same basic result holds for fitting a regression function when the regression coefficients are subject to linear constraints.

Deriving Restricted Least Squares without a Lagrangean

Deriving Restricted Least Squares without a Lagrangean

Nonnegativity restricted least squares combinations

In combining reasonably efficient forecasts of a time series, nonnegative weights are intuitively meaningful and their constrained least squares estimators are known to have desirable theoretical properties. It is analytically shown that whether such inequality (or equality) constraints will result in gains in efficiency depends on the number of observations in the fit sample and the mean level of the fit set. Next, the performances of the combination forecasts of a macroeconomic time series obtained using Nonnegativity Restricted Least Squares (NRLS) and other combination methods are exhaustively compared. It is shown that NRLS combination models are more efficient, more robust, and less sensitive to sample size than Ordinary Least Squares, Equality Restricted Least Squares, minimum-variance, and outperformance models. They are more efficient than historical weighting and equal weighting methods only for large samples. Two heuristic NRLS algorithms are shown to yield equally accurate and robust combined forecasts.

An empirical analysis of the accuracy of SA, OLS, ERLS and NRLS combination forecasts

Theoretically, the efficiency of OLS combination forecasts can be improved by imposing linear equality or nonnegativity restrictions on the combination weights. In Equality Restricted Least Squares (ERLS) combinations, the weights are restricted to sum to unity, whereas in Nonnegativity Restricted Least Squares (NRLS) combinations, the weights are constrained to be nonnegative. There is little empirical evidence on the relative peformance of OLS, ERLS and NRLS combination forecasts. In this study, we provide empirical results on the relative accuracy of OLS, ERLS, NRLS and Simple Average (SA) ex ante combined forecasts using three macroeconomic and thirty-seven firm specific series. The empirical results reveal that combined forecasts are not always more accurate. NRLS and SA combinations almost always outperform OLS and ERLS combinations, while NRLS combinations are at least as robust and accurate as SA combinations. On average, ERLS combination models without a constant term produce more accurate forecasts than OLS combination models.

Using Restricted Least Squares to Delineate the Effects of Misspecification in Linear Models

Using Restricted Least Squares to Delineate the Effects of Misspecification in Linear Models

Estimation of the voter transition matrix

This paper is concerned with an estimation of the voter transition matrix using programming methods. Thus, applying the Minimum Absolute Deviations (MAD) and the Restricted Least Squares (RLS) principles, the corresponding estimator has been determined, where the first one seems to be more efficient than the second.

Quadratic risk domination of restricted least squares estimators via Stein-ruled auxiliary constraints

Abstract This paper develops an estimator that under the standard assumption of the General Linear Model, including normality of disturbances, can be designed to dominate the Restricted Least Squares estimator in quadratic risk under very general conditions. The domination is achieved for any choice of symmetric positive definite weighting matrix used in defining the quadratic risk function, regardless of the correctness of the constraints used to define the restricted least squares estimator. The general problem conditions under which the estimator exists, and the risk behavior of the estimator over the parameter space are identified.

An Algorithm for Restricted Least Squares Regression

Abstract A commonly occurring problem in statistics is that of minimizing a least squares expression subject to side constraints. Here a simple iterative algorithm is presented and shown to converge to the desired solution. Several examples are presented, including finding the closest concave (convex) function to a set of points and other general quadratic programming problems. The dual problem to the basic problem is also discussed and a solution for it is given in terms of the algorithm. Finally, extensions to expressions other than least squares are given.

Restricted Least Squares Estimation of the Spectra and Concentration of Two Unknown Constituents Available in Mixtures

The problem considered is the identification of two unknown chemical compounds and the estimation of their proportions in a set of unknown mixtures of the two compounds, given data that are vectors of measurements on their mixtures. It is assumed that the expected value of a mixture vector is an unknown convex linear combination of two unknown component vectors and least squares estimation is used to obtain a set of possible solutions of the mixing proportions and the component vectors. Obtaining a unique solution requires additional constraints or information. The solution set is interpreted geometrically and examples involving amino acids and light absorbance data are given.

Comment on “Splines and Restricted Least Squares”

Abstract The flexibility of the restricted least squares (RLS) method described by Buse and Lim (1977) for cubic spline regression models is used to consider other polynomial splines. Some of the conclusions of the analysis of a sample data set in the Buse and Lim article are criticized for failing to consider less restrictive models. The data are reanalyzed, the end result being a simpler quadratic spline regression model.

Comment on "Splines and Restricted Least Squares"

Comment on "Splines and Restricted Least Squares"