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Maximum Likelihood Estimation (MLE) is a statistical method for estimating the parameters of a model by maximizing the likelihood function, thereby making the observed data most probable under the assumed statistical model. It is widely used due to its desirable properties such as consistency, efficiency, and asymptotic normality, which make it a cornerstone of statistical inference and machine learning.
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Instrumental variables are used in statistical analysis to estimate causal relationships when controlled experiments are not feasible, addressing the issue of endogeneity by providing a source of variation that is correlated with the explanatory variable but uncorrelated with the error term. This method helps to isolate the causal impact of a variable by using a third variable, the instrument, which allows for consistent estimation of the parameter of interest.
The Generalized Method of Moments (GMM) is a statistical estimation technique that uses sample moments to estimate the parameters of a model, providing a flexible framework that can accommodate a wide range of economic models and data structures. GMM is particularly useful when the model is overidentified, meaning there are more moment conditions than parameters to estimate, allowing for robust inference even with potential model misspecification or heteroskedasticity in the data.
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Ordinary Least Squares (OLS) is a linear regression method that estimates the parameters of a linear relationship by minimizing the sum of the squares of the differences between observed and predicted values. It assumes linearity, independence, homoscedasticity, and normally distributed errors to produce the best linear unbiased estimator under the Gauss-Markov theorem.
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Consistency refers to the steadfast adherence to the same principles or course of action over time, which fosters reliability and trust. It is essential in various fields, from personal habits to business practices, as it creates predictability and stability, allowing for the measurement of progress and effectiveness.
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Efficiency is the ability to achieve a desired outcome with the least amount of wasted resources, such as time, energy, or materials. It is a critical factor in both economic systems and engineering processes, driving innovation and competitiveness by maximizing output while minimizing input.
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Asymptotic properties describe the behavior of statistical estimators and algorithms as the sample size approaches infinity, providing insights into their consistency, efficiency, and distribution. These properties are crucial for understanding the long-term performance and reliability of models, especially in large-sample scenarios.
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Bias reduction involves strategies and methodologies aimed at minimizing systematic errors or prejudices in data collection, analysis, and interpretation to ensure more accurate and fair outcomes. It is crucial in research and machine learning to enhance the validity and reliability of results, promoting equity and inclusivity in decision-making processes.
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The Heckman Correction is a statistical technique used to address selection bias in samples where the outcome of interest is only observed for a non-random subset of data. It involves a two-step procedure where the first step estimates the probability of selection and the second step corrects the outcome model using this selection probability to produce unbiased estimates.
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The Inverse Mills Ratio is a crucial component in correcting selection bias in regression models, particularly when dealing with censored or truncated data. It is often used in the context of the Heckman correction model to adjust for non-randomly selected samples, ensuring more accurate parameter estimation.
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The Sample Selection Model addresses bias in statistical analysis that arises when the sample is not randomly selected from the population, often due to a selection mechanism that is related to the outcome of interest. This model, often associated with the Heckman correction, helps in obtaining unbiased and consistent parameter estimates by correcting for this selection bias using a two-step estimation procedure.
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