Does Gold Price Matter for Divorce Rate in Iran?

The increasing divorce rate has become a major social concern for policy makers in the Islamic government of Iran. The price of gold coin is an important factor in cost-benefit analysis for individuals in their marriage and divorce decisions in Iran. Dowries (Mehrieh) are usually in the form of gold coin and a wife has a legal right to request them from her husband upon both parties signing the marriage contract. Increasing the price of gold coin may intensify the internal stress and struggles within families, leading to a higher probability of divorce. We investigated the long-run relationship between real price of gold coin and divorce rate for the case of Iran over the period 1980–2014. Controlling for other factors such as women’s education, social globalization, economic growth rate, and the war period with Iraq, our regression results showed that there is a positive and significant long-run relationship between real price of gold coin (as well as unanticipated changes in real price of gold coin) and marital instability.     

Estimation of the parameters of Downton's bivariate exponential distribution using ranked set sampling scheme

The parameters of Downton's bivariate exponential distribution are estimated based on a ranked set sample. Parametric and nonparametric methods are considered. The suggested estimators are compared to the corresponding ones based on simple random sampling. It turns out that some of the suggested estimators are significantly more efficient than the ones based on simple random sampling.     

Testing the equality of several multivariate normal mean vectors under heteroscedasticity: A fiducial approach and an approximate test

We consider the problem of testing the equality of several multivariate normal mean vectors under heteroscedasticity. We first construct a fiducial confidence region (FCR) for the differences between normal mean vectors and we then propose a fiducial test for comparing mean vectors by inverting the FCR. We also propose a simple approximate test that is based on a modification of the χ² approximation. This simple test avoids the complications of simulation-based inference methods. We show that the proposed fiducial test has correct type one error rate asymptotically. We compare the proposed fiducial and approximate tests with the parametric bootstrap test in terms of controlling the type one error rate via an extensive simulation study. Our simulation results show that the proposed fiducial and approximate tests control the type one error rate, while there are cases that the parametric bootstrap test is out of control. We also discuss the power performance of the tests. Finally, we illustrate with a real example how our proposed methods are applicable in analyzing repeated measure designs including a single grouping variable.     

A gamma-mixture class of distributions with Bayesian application

In this article, a subjective Bayesian approach is followed to derive estimators for the parameters of the normal model by assuming a gamma-mixture class of prior distributions, which includes the gamma and the noncentral gamma as special cases. An innovative approach is proposed to find the analytical expression of the posterior density function when a complicated prior structure is ensued. The simulation studies and a real dataset illustrate the modeling advantages of this proposed prior and support some of the findings.     

Finely Resolved On‐Road PM2.5 and Estimated Premature Mortality in Central North Carolina

To quantify the on‐road PM_2.5‐related premature mortality at a national scale, previous approaches to estimate concentrations at a 12‐km × 12‐km or larger grid cell resolution may not fully characterize concentration hotspots that occur near roadways and thus the areas of highest risk. Spatially resolved concentration estimates from on‐road emissions to capture these hotspots may improve characterization of the associated risk, but are rarely used for estimating premature mortality. In this study, we compared the on‐road PM_2.5‐related premature mortality in central North Carolina with two different concentration estimation approaches—(i) using the Community Multiscale Air Quality (CMAQ) model to model concentration at a coarser resolution of a 36‐km × 36‐km grid resolution, and (ii) using a hybrid of a Gaussian dispersion model, CMAQ, and a space–time interpolation technique to provide annual average PM_2.5 concentrations at a Census‐block level (～105,000 Census blocks). The hybrid modeling approach estimated 24% more on‐road PM_2.5‐related premature mortality than CMAQ. The major difference is from the primary on‐road PM_2.5 where the hybrid approach estimated 2.5 times more primary on‐road PM_2.5‐related premature mortality than CMAQ due to predicted exposure hotspots near roadways that coincide with high population areas. The results show that 72% of primary on‐road PM_2.5 premature mortality occurs within 1,000 m from roadways where 50% of the total population resides, highlighting the importance to characterize near‐road primary PM_2.5 and suggesting that previous studies may have underestimated premature mortality due to PM_2.5 from traffic‐related emissions.     

Efficiency of the QR class estimator in semiparametric regression models to combat multicollinearity

There are some classes of biased estimators for solving the multicollinearity among the predictor variables in statistical literature. In this research, we propose a modified estimator based on the QR decomposition in the semiparametric regression models, to combat the multicollinearity problem of design matrix which makes the data to be less distorted than the other methods. We derive the properties of the proposed estimator, and then, the necessary and sufficient condition for the superiority of the partially generalized QR-based estimator over partially generalized least-squares estimator is obtained. In the biased estimators, selection of shrinkage parameters plays an important role in data analysing. We use generalized cross-validation criterion for selecting the optimal shrinkage parameter and the bandwidth of the kernel smoother. Finally, the Monté-Carlo simulation studies and a real application related to bridge construction data are conducted to support our theoretical discussion.     

Performance of extrapolation based on Pitman's measure of closeness in spatial regression models with extended skew t innovations

Pitman's measure of closeness and mean square error of prediction are two well-known criteria for comparison between estimators and also between predictors. In a stationary first order multiplicative spatial autoregressive model, interpolation and extrapolation are compared based on these two criteria. A wide class of different innovation types are also studied containing Gaussian, exponential, asymmetric Laplace and extended skew t distributions.     

Phase I risk-adjusted control charts for surgical data with ordinal outcomes

In recent years, risk-adjusted control charts that account for the preoperative risk of patients have been widely used for monitoring of surgical outcomes. Generally, risk-adjusted control charts have been developed on the basis of a binary classification of surgical outcomes. However, for a patient who survives an operation, it is reasonable to consider different grades of recovery in an ordinal manner. On the other hand, Phase I monitoring of risk-adjusted control charts has been neglected. Hence, in this paper, a general Phase I risk-adjusted control chart is proposed to monitor ordinal outcomes of surgical outcomes. The proposed risk-adjusted model is developed on the basis of proportional odds logistic regression models. The application of the proposed model is illustrated by analyzing the data in a case study and its performance is evaluated using a Monte Carlo simulation study.     

A 6.55 factor primal-dual approximation algorithm for the connected facility location problem

In the connected facility location (ConFL) problem, we are given a graph G=(V,E) with nonnegative edge cost c _e on the edges, a set of facilities ??V, a set of demands (i.e., clients) $\mathcal{D}\subseteq VIn the connected facility location (ConFL) problem, we are given a graph G=(V,E) with nonnegative edge cost c _e on the edges, a set of facilities ℱ⊆V, a set of demands (i.e., clients) D í V\mathcal{D}\subseteq V , and a parameter M≥1. Each facility i has a nonnegative opening cost f _i and each client j has d _j units of demand. Our objective is to open some facilities, say F⊆ℱ, assign each demand j to some open facility i(j)∈F and connect all open facilities using a Steiner tree T such that the total cost, which is ?_{i ? F}f_i+?_{j ? D}d_jc_i(j)j+M?_{e ? T}c_e\sum_{i\in F}f_{i}+\sum_{j\in \mathcal{D}}d_{j}c_{i(j)j}+M\sum_{e\in T}c_{e} , is minimized. We present a primal-dual 6.55-approximation algorithm for the ConFL problem which improves the previous primal-dual 8.55-approximation algorithm given by Swamy and Kumar (Algorithmica 40:245–269, 2004).     

Diagnosis Aids in Multivariate Multiple Linear Regression Profiles Monitoring

Diagnosis aids in addition to detecting the out-of-control state is an important issue in multivariate multiple linear regression profiles monitoring; because a large number of parameters and profiles in this structure are involved. In this paper, we specifically concentrate on identification of profile(s) and parameter(s) which have changed during the process in multivariate multiple linear regression profiles structure in Phase II. We demonstrate the effectiveness of our proposed approaches through Monte Carlo simulations and a real case study in terms of accuracy percent.