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In statistics, ordinary least squares (OLS) is a type of linear least squares method for choosing the unknown parameters in a linear regression model (with fixed level-one [clarification needed] effects of a linear function of a set of explanatory variables) by the principle of least squares: minimizing the sum of the squares of the differences between the observed dependent variable (values ...
A Newey–West estimator is used in statistics and econometrics to provide an estimate of the covariance matrix of the parameters of a regression-type model where the standard assumptions of regression analysis do not apply. [1] It was devised by Whitney K. Newey and Kenneth D. West in 1987, although there are a number of later variants.
RATS: robusterrors option is available in many of the regression and optimization commands (linreg, nlls, etc.). Stata: robust option applicable in many pseudo-likelihood based procedures. [19] Gretl: the option --robust to several estimation commands (such as ols) in the context of a cross-sectional dataset produces robust standard errors. [20]
Optimal instruments regression is an extension of classical IV regression to the situation where E[ε i | z i] = 0. Total least squares (TLS) [6] is an approach to least squares estimation of the linear regression model that treats the covariates and response variable in a more geometrically symmetric manner than OLS. It is one approach to ...
The first term is the objective function from ordinary least squares (OLS) regression, corresponding to the residual sum of squares. The second term is a regularization term, not present in OLS, which penalizes large values. As a smooth finite dimensional problem is considered and it is possible to apply standard calculus tools.
The connection of maximum likelihood estimation to OLS arises when this distribution is modeled as a multivariate normal. Specifically, assume that the errors ε have multivariate normal distribution with mean 0 and variance matrix σ 2 I .
Pandas (styled as pandas) is a software library written for the Python programming language for data manipulation and analysis. In particular, it offers data structures and operations for manipulating numerical tables and time series. It is free software released under the three-clause BSD license. [2]
Python has the statsmodelsS package which includes many models and functions for time series analysis, including ARMA. Formerly part of the scikit-learn library, it is now stand-alone and integrates well with Pandas. PyFlux has a Python-based implementation of ARIMAX models, including Bayesian ARIMAX models.