We derive analytic expressions for the biases, to O(n^(-1)) of the maximum likelihood estimators of the parameters of the generalized Rayleigh distribution family. Using these expressions to bias-correct the estimators is found to be extremely effective in terms of bias reduction, and generally results in a small reduction in relative mean squared error. In general, the analytic bias-corrected estimators are also found to be superior to the alternative of bias-correction via the bootstrap. / Graduate

No description available.

The present research explored the effects of Situational Attribution Training (Stewart, Latu, Kawakami, & Myers, 2010) on affective bias utilizing facial electromyography (EMG). Participants viewed a slideshow of randomly presented photographs of both and White and Black American men while rating how “friendly” each individual appeared. Simultaneously, corrugator and zygomaticus region activity, linked with positive and negative affect, respectively, was measured. Of these participants, half were randomly assigned to complete Situational Attribution Training beforehand. Results for EMG activity suggested no significant differences in EMG activity for White compared to Black photographs for either the training or control participants; thus, this study did not find evidence of affective bias by way of corrugator or zygomaticus activity. However, errors in slideshow presentation prevent clear interpretation of these results. Suggestions for future research and ways in which bias errors can be avoided are discussed.

This thesis is concerned with volatility estimation using financial panels and bias-reduction in non-linear dynamic panels in the presence of dependence. Traditional GARCH-type volatility models require large time-series for accurate estimation. This makes it impossible to analyse some interesting datasets which do not have a large enough history of observations. This study contributes to the literature by introducing the GARCH Panel model, which exploits both time-series and cross-section information, in order to make up for this lack of time-series variation. It is shown that this approach leads to gains both in- and out-of-sample, but suffers from the well-known incidental parameter issue and therefore, cannot deal with short data either. As a response, a bias-correction approach valid for a general variety of models beyond GARCH is proposed. This extends the analytical bias-reduction literature to cross-section dependence and is a theoretical contribution to the panel data literature. In the final chapter, these two contributions are combined in order to develop a new approach to volatility estimation in short panels. Simulation analysis reveals that this approach is capable of removing a substantial portion of the bias even when only 150-200 observations are available. This is in stark contrast with the standard methods which require 1,000-1,500 observations for accurate estimation. This approach is used to model monthly hedge fund volatility, which is another novel contribution, as it has hitherto been impossible to analyse hedge fund volatility, due to their typically short histories. The analysis reveals that hedge funds exhibit variation in their volatility characteristics both across and within investment strategies. Moreover, the sample distributions of fund volatilities are asymmetric, have large right tails and react to major economic events such as the recent credit crunch episode.

In the last few decades, vector autoregressive (VAR) models have gained tremendous popularity as an all-purpose tool in econometrics and other disciplines. Some of their most prominent uses are for forecasting, causality tests, tests of economic theories, hypothesis-seeking, data characterisation, innovation accounting, policy analysis, and cointegration analysis. Their popularity appears to be attributable to their flexibility relative to other models rather than to their virtues per se. In addition, analysts often use VAR models as benchmark models. VAR modeling has not gone uncriticised, though. A list of relevant arguments against VAR modelling can be found in Section 2.3 of this thesis. There is one additional problem which is rarely mentioned though, namely the often heavily biased estimates in VAR models. Although methods to reduce this bias have been available for quite some time, it has probably not been done before, at least not in any systematic way. The present thesis attempts to systematically examine the performance of bias-reduced VAR estimates, using two existing and one newly derived approximation to the bias. The thesis is orginanised as follows. After a short introductory chapter, a brief history of VAR modelling can be found in Chapter 2 together with a review of different representations and a compilation of criticisms against VAR models. Chapter 3 reports the results of very extensive Monte Carlo experiments serving dual purposes: Firstly, the simulations will reveal whether or not bias really poses a serious problem, because if it turns out that biases appear only by exception or are mainly insignificant, there would be little need to reduce the bias. Secondly, the same data as in Chapter 3 will be used in Chapter 4 to evaluate the bias approximations, allowing for direct comparison between bias-reduced and original estimates. Though Monte Carlo methods have been (rightfully) criticised for being too specific to allow for any generalisation, there seems to be no good alternative to analyse small-sample properties of complicated estimators such as these. Chapter 4 is in a sense the core of the thesis, containing evaluations of three bias approximations. The performance of the bias approximations is evaluated chiefly using single regression equations and 3D surfaces. The only truly new research result in this thesis can also be found in Chapter 4; a second-order approximation to the bias of the parameter matrix in a VAR(p) model. Its performance is compared with the performance of two existing first-order approximations, and all three are used to construct bias-reduced estimators, which are then evaluated. Chapter 5 holds an application of US money supply and inflation in order to find out whether the results in Chapter 4 can have any real impacts. Unfortunately though, bias reduction appears not to make any difference in this particular case. Chapter 6 concludes. / Diss. Stockholm : Handelshögsk.

We disbelieve it; we deny it; we even disguise it; but racial prejudice continues to permeate the United States. As a result, researchers labor to determine variables that can reduce these attitudes and consequently, improve social behavior. Three confirmed conditions that can reduce racial attitudes include: (a) awareness to racial biases, (b) motivation for bias reduction, and (c) cognitive strategies for prejudice regulation. However, racial awareness are usually nonexistent for White Americans, and when introduced, racial awareness can cause negative outcomes, such as guilt or denial, that can decrease motivation to reduce one’s prejudice levels. The construct and practices of mindfulness may provide a solution to these limitations and help reduce racial prejudice levels for White individuals. The present dissertation explored the initial steps of this racial mindfulness program of research by first investigating the influence of White participants' degree of mindfulness on their racial prejudice levels using structural equation modeling. Because mindfulness can increase awareness to stimuli, mindfulness could meet the first prejudice reduction condition (i.e., raise awareness to racial stimuli), and therefore, reduce racial prejudice levels directly. In addition, mindfulness has been found to increase similar variables that influences motivation to reduce racial prejudice levels, such as empathy and interconnectedness. Therefore, White participants’ degree of mindfulness could decrease their racial prejudice levels indirectly as well. Results from this study indicated that mindfulness did not reduce racial prejudice levels directly or indirectly, although there were some methodology limitations that could have obscured the results. The next step investigated if White participants' degree of mindfulness can attenuate the negative affects that can arise when Whites first become aware of racial biases, as mindfulness has been found to mitigate ego defensiveness and negative emotions when one's self-esteem is threatened. Written reactions to a White privilege article from White participants identified as holding a high and low degree of general mindfulness were subject to content analysis. The results indicated that participants with a high degree of mindfulness exhibited greater awareness and acceptance to White privilege and less negative reactions. The findings support the need to create and explore a racial mindfulness intervention. / text

Stochastic programming combines ideas from deterministic optimization with probability and statistics to produce more accurate models of optimization problems involving uncertainty. However, due to their size, stochastic programming problems can be extremely difficult to solve and instead approximate solutions are used. Therefore, there is a need for methods that can accurately identify optimal or near optimal solutions. In this dissertation, we focus on improving Monte-Carlo sampling-based methods that assess the quality of potential solutions to stochastic programs by estimating optimality gaps. In particular, we aim to reduce the bias and/or variance of these estimators. We first propose a technique to reduce the bias of optimality gap estimators which is based on probability metrics and stability results in stochastic programming. This method, which requires the solution of a minimum-weight perfect matching problem, can be run in polynomial time in sample size. We establish asymptotic properties and present computational results. We then investigate the use of sampling schemes to reduce the variance of optimality gap estimators, and in particular focus on antithetic variates and Latin hypercube sampling. We also combine these methods with the bias reduction technique discussed above. Asymptotic properties of the resultant estimators are presented, and computational results on a range of test problems are discussed. Finally, we apply methods of assessing solution quality using antithetic variates and Latin hypercube sampling to a sequential sampling procedure to solve stochastic programs. In this setting, we use Latin hypercube sampling when generating a sequence of candidate solutions that is input to the procedure. We prove that these procedures produce a high-quality solution with high probability, asymptotically, and terminate in a finite number of iterations. Computational results are presented.

In a preregistered study, we investigated whether two different procedures increased people’s recognition and motivation to self-regulate personal bias and also recognition and motivation to combat systemic bias. Non-Black undergraduates (N = 467) were randomly assigned to either a IAT procedure (i.e., took a racial IAT, received fixed feedback indicating racial bias, and received an explanation for why people may hold implicit biases), a discrimination experiences procedure (i.e., read about Black people’s discrimination experiences across various institutional contexts), or a control procedure (i.e., rated their preferences for common consumer products). Then, participants completed measures assessing recognition of and motivation to combat personal and systemic bias. Among average IMS participants, results indicated that the IAT procedure significantly increased recognition of personal racial bias, compared to the control procedure. The discrimination experiences procedure significantly increased motivation to combat systemic bias, support for policies aimed at addressing inequality, and motivation to self-regulate personal bias, compared to both the control and IAT procedures. We also found that the IAT heightened negative self-directed affect especially among higher IMS participants, which in turn was associated with increased acknowledgement of and motivation to combat not only personal but also systemic bias. Finally, among all participants, the discrimination experiences procedure heightened negative other-directed affect, which in turn was associated with increased recognition of and motivation to combat systemic bias. Although additional research is needed, these initial results may suggest that personal bias interventions influence personal bias outcomes but do not similarly influence systemic bias outcomes. In contrast, systemic bias interventions may be more likely to influence awareness of and motivation to combat both personal and systemic bias. These results pave the way for future investigation into the nature of crossover effects between personal and systemic bias procedures.

This dissertation consists of three projects in matched case-control studies. In the first project, we employ a general bias preventive approach developed by Firth (1993) to handle the bias of an estimator of the log-odds ratio parameter in conditional logistic regression by solving a modified score equation. The resultant estimator not only reduces bias but also can prevent producing infinite value. Furthermore, we propose a method to calculate the standard error of the resultant estimator. A closed form expression for the estimator of the log-odds ratio parameter is derived in the case of a dichotomous exposure variable. Finite sample properties of the estimator are investigated via a simulation study. Finally, we apply the method to analyze a matched case-control data from a low-birth-weight study. In the second project of this dissertation, we propose a score typed test for checking adequacy of a functional form of a covariate of interest in matched case-control studies by using penalized regression splines to approximate an unknown function. The asymptotic distribution of the test statistics under the null model is a linear combination of several chi-square random variables. We also derive the asymptotic distribution of the test statistic when the alternative model holds. Through a simulation study we assess and compare the finite sample properties of the proposed test with that of Arbogast and Lin (2004). To illustrate the usefulness of the method, we apply the proposed test to a matched case-control data constructed from the breast cancer data of the SEER study. Usually a logistic model is needed to associate the risk of the disease with the covariates of interests. However, this logistic model may not be appropriate in some instances. In the last project , we adopt idea to matched case-control studies and derive an information matrix based test for testing overall model adequacy and investigate the properties against the cumulative residual based test in Arbogast and Lin (2004) via a simulation study. The proposed method is less time consuming and has comparative power for small parameters. It is suitable to explore the overall model fitting.

Maximum likelihood is an ubiquitous method used in the estimation of generalized linear mixed model (GLMM). However, the method entails computational difficulties and relies on the normality assumption for random effects. We propose a second-order least squares (SLS) estimator based on the first two marginal moments of the response variables. The proposed estimator is computationally feasible and requires less distributional assumptions than the maximum likelihood estimator. To overcome the numerical difficulties of minimizing an objective function that involves multiple integrals, a simulation-based SLS estimator is proposed. We show that the SLS estimators are consistent and asymptotically normally distributed under fairly general conditions in the framework of GLMM. Missing data is almost inevitable in longitudinal studies. Problems arise if the missing data mechanism is related to the response process. This thesis develops the proposed estimators to deal with response data missing at random by either adapting the inverse probability weight method or applying the multiple imputation approach. In practice, some of the covariates are not directly observed but are measured with error. It is well-known that simply substituting a proxy variable for the unobserved covariate in the model will generally lead to biased and inconsistent estimates. We propose the instrumental variable method for the consistent estimation of GLMM with covariate measurement error. The proposed approach does not need any parametric assumption on the distribution of the unknown covariates. This makes the method less restrictive than other methods that rely on either a parametric distribution of the covariates, or to estimate the distribution using some extra information. In the presence of data outliers, it is a concern that the SLS estimators may be vulnerable due to the second-order moments. We investigated the robustness property of the SLS estimators using their influence functions. We showed that the proposed estimators have a bounded influence function and a redescending property so they are robust to outliers. The finite sample performance and property of the SLS estimators are studied and compared with other popular estimators in the literature through simulation studies and real world data examples.