This article introduces a dual problem of widely used calibration ratio-type estimators for estimating population mean of the study variable considering auxiliary information under dual constraints using stratified systematic sampling design. Under large sample approximations, the expression for bias and variance of the proposed estimator are derived. In addition, the optimality condition for the proposed estimator and hence optimum variance expression is also obtained for the same. Moreover, a study based on real-life data is carried out to judge the performance of the proposed calibration estimator in terms of minimum relative bias and relative root mean squared error criterion. The study reveals that the calibration ratio-type estimator under dual constraints may be preferred in practice as it provides consistent and more precise parameter estimates.

In this article, a Stein-type weighted limited information maximum likelihood (LIML) estimator is proposed. It is based on a weighted average of the ordinary least squares (OLS) and LIML estimators, with weights inversely proportional to the Hausman test statistic. The asymptotic distribution of the proposed estimator is derived by means of local-to-exogenous asymptotic theory. In addition, the asymptotic risk of the Stein-type LIML estimator is calculated, and it is shown that the risk is strictly smaller than the risk of the LIML under certain conditions. A Monte Carlo simulation and an empirical application of a green patent dataset from Nordic countries are used to demonstrate the superiority of the Stein-type LIML estimator to the OLS, two-stage least squares, LIML and combined estimators when the number of instruments is large.

Valid instrumental variables (IVs) must not directly impact the outcome variable and must also be uncorrelated with nonmeasured variables. However, in practice, IVs are likely to be invalid. The existing methods can lead to large bias relative to standard errors in situations with many weak and invalid instruments. In this paper, we derive a LASSO procedure for the k-class IV estimation methods in the linear IV model. In addition, we propose the jackknife IV method by using LASSO to address the problem of many weak invalid instruments in the case of heteroscedastic data. The proposed methods are robust for estimating causal effects in the presence of many invalid and valid instruments, with theoretical assurances of their execution. In addition, two-step numerical algorithms are developed for the estimation of causal effects. The performance of the proposed estimators is demonstrated via Monte Carlo simulations as well as an empirical application. We use Mendelian randomization as an application, wherein we estimate the causal effect of body mass index on the health-related quality of life index using single nucleotide polymorphisms as instruments for body mass index.

This doctoral dissertation comprises four papers. The aims of this dissertation are twofold: first, it introduces model averaging methods that use weights inversely proportional to the Hausman test statistic; second, it explores variable selection methods for estimating causal effects by identifying both valid and invalid instruments. Each paper assesses the performance of these novel methods by developing theoretical asymptotic properties, conducting Monte Carlo simulations, and applying them empirically.

The first paper focuses on the use of instrumental variable estimation methods regression with many instruments in the linear model. A weighted average approach is introduced by combining least squares and limited information maximum likelihood estimators.

The second paper addresses the issue of endogeneity in the instrumental variable probit model by developing a Stein weighted average control function maximum likelihood estimator. The asymptotic distribution and asymptotic risk of the proposed estimator are derived.

The third paper focuses on the use of Lasso instrumental variables estimation methods. In addition, the jackknife instrumental variable approach is introduced using the Lasso procedure. The proposed methods are robust for estimating causal effects in the presence of both invalid and valid instruments. Additionally, for convenience, we created an R package for implementing the proposed methods.

The fourth paper introduces the best subset instrumental estimator via mixed integer optimization to estimate causal effects and select invalid instruments. It is shown that the best subset instrumental variable estimator outperforms the two-stage least squares, Lasso-type instrumental variables methods, and two-sample analysis methods.

Denna doktorsavhandling består av fyra artiklar. Avhandlingens syften är tvåfaldiga: för det första introduceras metoder som tar ett genomsnitt baserat på vikter som är proportionella till inversen av ett Hausman-test; för det andra undersöks metoder för val av variabler för att skatta kausala effekter genom att identifiera både giltiga och ogiltiga instrumentvariabler. Varje artikel utvärderar prestationsförmågan hos de nya metoderna genom att härleda teoretiska asymptotiska egenskaper, genom Monte Carlo-simuleringar samt genom empiriska tillämpningar.

Den första artikeln fokuserar på skattningsmetoder för linjära regressionsmodeller med instrumentvariabler som inkluderar många instrument. En metod baserat på ett viktat genomsnitt introduceras genom att kombinera minsta kvadratmetoden och s.k. limited information maximum likelihood-skattning.

Den andra artikeln adresserar problemet med endogenitet i probitmodeller med instrumentvariabler genom att utveckla en viktad Stein-estimator som inkluderar en kontrollfunktionsskattning genom maximum likelihood. Den asymptotiska fördelningen och asymptotiska risken för den föreslagna skattningsmetoden härleds.

Den tredje artikeln fokuserar på användningen av Lasso-metoder för att skatta instrumentvariabelmodeller. Dessutom introduceras en jackknife-baserad metod för att skatta instrumentvariabelmodeller med hjälp av Lasso. De föreslagna metoderna är robusta när man ska skatta kausala effekter genom modeller som innehåller många ogiltiga och giltiga instrumentvariabler.

Den fjärde artikeln introducerar val av instrumentvariabler genom modellvalssmetoden best subset via mixed integer-optimering för att skatta kausala effekter samt för att välja ogiltiga instrumentvariabler. Resultaten visar att den nya metoden är överlägsen flera tidigare utvecklade metoder.

Comparisons among some new types of weighted mixed regression estimators for the linear regression model under the stochastic linear restrictions have been made in this paper. The mean squared error criterion is used to examine the superiority of different weighted mixed regression estimators. A Monte Carlo simulation study and real-life application are carried out to compare the performance of these estimators for different cases. Finally, we suggest the best weighted mixed regression estimator with collinear regressors.

A Stein-type control function maximum likelihood (CFML) estimator is suggested for the probit model in the presence of endogeneity. This novel estimator combines the probit maximum likelihood and CFML estimators. The asymptotic distribution and risk function for the new estimator is derived. It is demonstrated that, subject to certain conditions of the shrinkage parameter, the asymptotic risk of the new estimator is strictly smaller than the risk of the CFML. Monte Carlo simulations illustrate the method's superiority in finite samples. The method is also applied to analyze the impact of managerial incentives on the use of foreign-exchange derivatives.

The Gamma Regression Model (GRM) has a variety of applications in medical sciences and other disciplines. The results of the GRM may be misleading in the presence of multicollinearity. In this article, a new biased estimator called James-Stein estimator is proposed to reduce the impact of correlated regressors for the GRM. The mean squared error (MSE) properties of the proposed estimator are derived and compared with the existing estimators. We conducted a simulation study and employed the MSE and bias evaluation criterion to judge the proposed estimator’s performance. Finally, two medical dataset are considered to show the benefit of the proposed estimator over existing estimators.

In this article, we propose generalized two-parameter (GTP) estimators and an algorithm for the estimation of shrinkage parameters to combat multicollinearity in the multinomial logit regression model. In addition, the mean squared error properties of the estimators are derived. A simulation study is conducted to investigate the performance of proposed estimators for different sample sizes, degrees of multicollinearity, and the number of explanatory variables. Swedish football league dataset is analyzed to show the benefits of the GTP estimators over the traditional maximum likelihood estimator (MLE). The empirical results of this article revealed that GTP estimators have a smaller mean squared error than the MLE and can be recommended for practitioners.

This article investigates the performance of several residuals for the Cox proportional hazards regression model to diagnose the influential observations. The standardized and adjusted forms of residuals are proposed for Cox proportional hazards regression model. In addition, Cook's distance is proposed for both standardized and adjusted residuals. The assessment of different residuals for the identification of influential observations is made through the Monte Carlo simulation. A real dataset of bone marrow transplant Leukaemia is analyzed to show the benefit of the proposed methods. Simulation and application results show that the standardized and adjusted residuals based on the Cox-Snell method perform best for the detection of influential points. Furthermore, the standardized, and adjusted Martingale and deviance residuals work better when the sample size is large.

The COVID-19 pandemic has significantly altered employment and income distribution, impacting women and men differently. This study investigates the negative effects of COVID-19 on the labour market, focusing on the gender gap in five countries in the Middle East and North Africa (MENA) region. The study indicates whether women are more susceptible to losing their jobs, either temporarily or permanently, switching their primary occupation, and experiencing decreased working hours and income compared to men during the COVID-19 outbreak. The study utilizes a multivariate Probit model to estimate the relationship between gender and adverse labour outcomes controlling for correlations among outcomes. Data are obtained from the Combined COVID-19 MENA Monitor Household Survey, covering Egypt, Tunisia, Morocco, Jordan, and Sudan. The findings of this study offer empirical evidence of the gender gap in labour market outcomes during the pandemic. Women are more likely than men to experience negative work outcomes, such as permanent job loss and change in their main job. The increased childcare and housework responsibilities have significantly impacted women's labour market outcomes during the pandemic. However, the availability of telework has reduced the likelihood of job loss among women. The study's results contribute to a better understanding of the impact of COVID-19 on gender inequality in understudied MENA countries. Mitigation policies should focus on supporting vulnerable women who have experienced disproportionate negative effects of COVID-19.