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\section{Intro \& CLR}
nonexperimental\\
cross section data, time series data, panel/longitudinal data\\
dependent variable/regressand, independed variables/regressors/explanatory variables\\
random sampling\\
CLR 1.1 - Linearity: error term\\
CLR 1.2 - Strict Exogeneity: orthogonal\\
CLR 1.3 - Spherical Errors: conditional homoskedasticity\\
CLR 1.4 - Full Rank: no perfect collinearity\\
Nonlinearities: interaction terms, semilog model, loglinear model, translog model\\
Non-constancy of parameters: indicator/dummy variables, interaction terms\\
Fixed Regressors (non-experimental)
\section{OLS Basics}
OLS estimator of $\beta$\\
Fitted value, residual, projection matrix $P$, annihilator matrix $M$\\
Residuals orthogonal to data: $X'\hat{\varepsilon}=0$\\
Simple (2 var) CLR: formulas for slope and intercept, $R$, and $r$\\
Goodness of fit, centered/uncentered $R$ squared, coefficient of determination, multiple correlation coefficient, adjusted $R^2$, $R$ bar squared
SSR (Sum of Squared Residuals), TSS/SST (Total sum of squares, or total variation of the dependent variable), SSE (explained sum of squares)\\
perfect fit, no fit\\
partitioned form CLR, residual regression, double residual regression, Frisch-Waugh-Lovell theorem\\
demeaning, detrending, deseasonalizing
\section{OLS Estimator Properties}
$\hat{\beta}$ is: random variable, linear in $Y$, unbiased for $\beta$ conditional on $X$ (and also unconditionall), BLUE (Gauss-Markov Thm)\\
$\hat{\sigma^2}$ is: unbiased conditionally and unconditionally\\
Prediction error, Mean Square Error (MSE), Conditional Expectation Function (CEF)/Population Regression Function (PRF), Sample error
\section{CNLR}
CNLR 1.5 - Joint Normality: independence between errors and regressors\\
Standardized p-variate RV: $Z$\\
Spectral/Eigenvalue decomposition, Jordan decomposition\\
Interval Estimation, coverage probability, confidence level, confidence intervals, critical value\\
Confidence intervals/regions for $\Gamma\beta$ at $(1-\alpha)100\%$ confidence level for: $\Gamma$ is $1\times K$ or $N\times K$, and $\sigma^2$ known or unknown\\
Testing linear hypotheses: null, alternative, critical region, Type I/II Error, significance level, power function, test statistics: formulas for $Z,t,W,F$\\
Other formulas for $F$: $SSR_u$ and $SSR_r$, restricted OLS, $R_U^2$ and $R_R^2$, test of significance of the regression\\
Power functions of tests, non-central $t$ and $F$, inapplicability of $W_0$ and $F_0$ to one-sided tests\\
Chow Test (aka Test of Structural Change)\\
\section{Implications of Normality in CNLR}
MLE's of $\beta$ and $\sigma^2$\\
Fisher Information Matrix, Cramer-Rao lower bound (aka Information Inequality), $\hat{\beta_{OLS}}, \hat{\sigma^2_{OLS}}$ are BUE in CNLR\\
Asymptotic normality and efficiency of $\hat{\beta}_ML$ and $\hat{\sigma^2}_ML$.\\
Asymptotic Tests of Nonlinear Hypotheses under CNLR: Wald, LR, Lagrange Multiplier (Score) Tests (akak Trinity); Trinity for linear hypotheses; critical region sizes $W \ge LR \ge LM$
\section{Relaxing CLR/CNLR Assumptions}
Perfect collinearity, multicollinearity, condition number\\
Misspecification of Regression: short model, long model\\
Non-spherical errors, GLR, GLS, Aitken's Thm\\
Joint normality, generalized $t$ and $F$ (aka robust), WLS\\
\section{Asymptotic OLS, WLS/FWLS}
Weakly consistency, asymptotic normality of OLS, approximate inference\\
Asymptotic distribution of OLS under conditional homoskedasticity\\
Heteroskedasticity-robust/White/Eicker-White covariance matrix estimator\\
Testing linear and non-linear restrictions, testing conditional homoskedasticity\\
WLS, FWLS with Conditional heteroskedasticity\\
Best linear prediction/projection (BLP) conditional on X\\
Convergence: in distribution, almost sure, in probability, in $n^{th}$ moment\\
Limit Theorems: Mann-Wald/Continuity, Slutsky, Delta-Method, Cramer-Wold Device\\
LLNs: for iid data, for inid data, for did data, for dnid data, for asymptotically uncorrellated data, for covariance stationary sequences, for martingale difference sequences\\
CLTs: for iid, for inid, for did, for dnid, for Cov. stationary, for Martingale difference
\section{Extremum Estimators}
sample objective function, parameter space, NLS, ML, GMM, CMD\\
consistency, uniform convergence in probability, identification condition, compact parameter spaces\\
ULLN, asmptotitic normality of $M-$ estimators for iid data\\
Nonlinear Regression Model (NRM): Assumptions 1-12, NLS, WNLS\\
log-likelihood, MLE, Kullback Leibler Information Criterion, Consistency of MLE with and without compactness of parameter space\\
likelihood equations, asymptotic normality and efficiency of consistent roots (aka local MLEs)\\
MLE difficulties: non-unique likelihood functions, nonexistence of roots, multiple solutions; sufficient conditions for uniqueness; invariance under reparameterization\\
Asymptotic equivalency of trinity for MLEs; Trinity for generic extremum estimators; proof of asymptotic distributions (appendix)\\
Optimization Algorithms: Newton-Raphson, quadratic hill climbing, BHHH, method of scoring, quasi-Newton, DFP, Gauss Newton, downhill simplex, simulated anneality\\
Asymptotic equivalence of generic LM and LR
\section{QR Models}
QR/Discrete choice/quantal/categorical model; binary response/threshold crossing, multinomial response\\
Models: Linear Probability, Probit, Logit, Log-Weibull, Type-I Extreme Value
Unobservable (latent) variable, indicator function, identifical, observationally equivalent\\
Random utility interpretation\\
Estimation via NLS and WNLS, ML, Properties of MLE, odds ratio (OR)\\
Ordered and unordered models, MNL, IIA, Nested Logit Model (NML), Gumbel's Type B bivariate extreme-valued distribution, MNP
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