Linear algebra Eigenvalues and Eigenvectors Nov 18, 2020 | 20 min read Time series Variability of Nonstationary Time Series Oct 9, 2020 | 13 min read Linear model Estimation Sep 30, 2019 | 16 min read Mathematical statistics Basic Concepts Sep 25, 2019 | 12 min read Nonparametric methods Fundamentals of Nonparametric Methods Jan 26, 2019 | 10 min read Mathematical statistics Jan 29, 2020 | 7 min read Maximum Likelihood Estimator Under parametric family distributions, there's a much better way of constructing estimators - the maximum likelihood estimator. #Mathematical Statistics #Statistics #Estimation Mathematical statistics Jan 28, 2020 | 3 min read The Method of Moments A fairly simple method of constructing estimators that's not often used now. #Mathematical Statistics #Statistics #Estimation Mathematical statistics Jan 27, 2020 | 6 min read Consistency Introducing consistency, a concept about the convergence of estimators. We start from the convergence of non-random number sequences to convergence in probability, then to consistency of estimators and its properties. #Mathematical Statistics #Statistics #Estimation Mathematical statistics Jan 25, 2020 | 11 min read Bias and Variance The bias, variance and mean squared error of an estimator. The efficiency is used to compare two estimators. #Mathematical Statistics #Statistics #Estimation Mathematical statistics Jan 8, 2020 | 4 min read Brief Review Before STAT 6520 A brief review of probability theory and statistics we've learnt so far. #Mathematical Statistics #Statistics Mathematical statistics Dec 28, 2019 | 6 min read Sampling Distribution and Limit Theorems We observe a random sample from a probability distribution of interest and want to estimate its properties. The CLT also comes into place. #Mathematical Statistics #Statistics #Random Variable Mathematical statistics Dec 8, 2019 | 14 min read Functions of Random Variables Finding the distribution of a real-valued function of multiple random variables. There's the method of distribution functions, transformations and moment generating functions. #Mathematical Statistics #Statistics #Random Variable Mathematical statistics Nov 6, 2019 | 23 min read Multivariate Probability Distributions Joint probability distributions of two or more random variables defined on the same sample space. Also covers independence, conditional expectation and total expectation. #Mathematical Statistics #Statistics #Random Variable Mathematical statistics Oct 6, 2019 | 7 min read Definitions for Discrete Random Variables The probability mass function, cumulative distribution function, expectation and variance for random variables. #Mathematical Statistics #Statistics #Random Variable Linear model Sep 30, 2019 | 16 min read Estimation In this chapter we introduce the concept of linear models. We use the ordinary least squares estimator to get unbiased estimates of the unknown parameters. $R^2$ is introduced as a measure of the goodness of fit, and the different types of sum of squares in a linear model are briefly discussed. #Statistics #Regression #Estimation #Linear Algebra #Sum of Squares #Correlation «« « 4 5 6 7 8 » »»