Seemingly Unrelated Ridge Regression in Semiparametric Models

This article is concerned with the problem of multicollinearity in the linear part of a seemingly unrelated semiparametric (SUS) model. It is also suspected that some additional non stochastic linear constraints hold on the whole parameter space. In the sequel, we propose semiparametric ridge and non ridge type estimators combining the restricted least squares methods in the model under study. For practical aspects, it is assumed that the covariance matrix of error terms is unknown and thus feasible estimators are proposed and their asymptotic distributional properties are derived. Also, necessary and sufficient conditions for the superiority of the ridge-type estimator over the non ridge type estimator for selecting the ridge parameter K are derived. Lastly, a Monte Carlo simulation study is conducted to estimate the parametric and nonparametric parts. In this regard, kernel smoothing and cross validation methods for estimating the nonparametric function are used.     

Percentile-t Bootstrap Confidence Intervals for Period Using Periodogram

The magnitude of light intensity of many stars varies over time in a periodic way. Therefore, estimation of period and making inference about this parameter are of great interest in astronomy. The periodogram can be used to estimate period, properly. Bootstrap confidence intervals for period suggested here, are based on using the periodogram and constructed by percentile-t methods. We prove that the equal-tailed percentile-t bootstrap confidence intervals for period have an error of order n ^?1. We also show that the symmetric percentile-t bootstrap confidence intervals reduce the error to order n ^?2, and hence have a better performance. Finally, we assess the theoretical results by conducting a simulation study, compare the results with the coverages of percentile bootstrap confidence intervals for period and then analyze a real data set related to the eclipsing system R Canis Majoris collected by Shiraz Biruni Observatory.     

Singular Ridge Regression With Stochastic Constraints

This article considers the estimation of the restricted ridge regression parameter in singular models. The problem is commenced with considering elliptically contoured equality constrained and then followed by proposing the preliminary test estimator. Along with proposing some important properties of this estimator, a real example satisfying the elliptical assumption is also given to bring the problem into a noticeable issue.     

Shrinkage ridge regression in partial linear models

ABSTRACT

In this paper, shrinkage ridge estimator and its positive part are defined for the regression coefficient vector in a partial linear model. The differencing approach is used to enjoy the ease of parameter estimation after removing the non parametric part of the model. The exact risk expressions in addition to biases are derived for the estimators under study and the region of optimality of each estimator is exactly determined. The performance of the estimators is evaluated by simulated as well as real data sets.     

Inequalities for Expected Current Record Statistics

In this article, we obtain sharp distribution-free bounds for the expected value of the gap between the current records and record values as well as upper sharp bounds for the spacings between any two upper current records. We also present two-sided bounds on the errors in approximating the means of current records by inverse hazard functions.     

Some results on the mean residual waiting time of records

Often, in reliability theory, risk analysis, renewal processes and actuarial studies, mean residual life function or life expectancy plays an important role in studying the conditional tail measure of lifetime data. In this paper, we introduce the notion of the mean residual waiting time of records and present some monotonic and aging properties. Sharp bounds for the mean residual waiting time of records are also investigated.     

On the efficiency of monte carlo methods using steady state ranked simulated samples

Samawi (1999) showed that the efficiency of Monte Carlo methods of integrals estimation can be substantially improved by using ranked simulated samples (RSIS) in place of uniform simulated samples (USIS). However, in this paper it is shown that substantial improvement of efficiency can be achieved further by using the steady state ranked simulated sample (SRSIS). It appears that the modified Monte Carlo methods using SRSIS provide unbiased and more efficient estimators for the integrals. Some theoretical properties of SRSIS are given. A simulation study is conducted to compare the performance of the methods using SRSIS with respect to USIS, for some examples.     

Regression model with elliptically contoured errors

For the regression model y=X β+ε where the errors follow the elliptically contoured distribution, we consider the least squares, restricted least squares, preliminary test, Stein-type shrinkage and positive-rule shrinkage estimators for the regression parameters, β.

We compare the quadratic risks of the estimators to determine the relative dominance properties of the five estimators.     

Revisiting Fiat Regime’s Attainability of Shari’ah Objectives and Possible Futuristic Alternatives

Maqasid of Shari'ah is a millennium old theory on the higher objectives of Islamic divine law. As the discipline of Islamic economics and finance grew in politico-economic importance in the past three decades, a cathartic trend has emerged among Muslim experts to realign economic and financial practices with not merely the minimum legal requirements of religion but also the wisdom and crucial objectives of Shari'ah. An expositive example of this is the monetary economics debate of a Shari'ah consonant currency. Though vast majority of religious clerics have approbated fiat and paper currencies in strict legal terms since the 1980s, a revisionist movement since the mid-1990s seeks to counter it—some going as far as indorsing reversion to gold and silver coinage of medieval Islamic epoch of affluence. Unlike orthodox fiqhi (strict jurisprudentialism) approach that involves legalese with little leeway, Maqasid approach concerns itself with the spirit of the law. This paper operates in the exciting laboratory of Maqasidic framework to appraise the multitudinous role of fiat currency in protecting economic, political, and social public interests, prevention of harm, promotion of egalitarianism, and attainment of ultimate utopic vision of theological and spiritual demands in Shari'ah. The paper contributes, theoretically, by introducing several moral-philosophical arguments against fiat’s compatibility with Shari'ah, and, practically, by prognosticating the future course of discourse in light of advancements in technological innovations—including nascent crypto-currencies.     

Analysis of covariance under inverse Gaussian model

This paper considers the problem of analysis of covariance (ANCOVA) under the assumption of inverse Gaussian distribution for response variable. We develop the essential methodology for estimating the model parameters via maximum likelihood method. The general form of the maximum likelihood estimator is obtained in color closed form. Adjusted treatment effects and adjusted covariate effects are given, too. We also provide the asymptotic distribution of the proposed estimators. A simulation study and a real world application are also performed to illustrate and evaluate the proposed methodology.