Linear algebraEigenvalues and EigenvectorsNov 18, 2020 | 20 min readTime seriesVariability of Nonstationary Time SeriesOct 9, 2020 | 13 min readLinear modelEstimationSep 30, 2019 | 16 min readMathematical statisticsBasic ConceptsSep 25, 2019 | 12 min readNonparametric methodsFundamentals of Nonparametric MethodsJan 26, 2019 | 10 min read Mathematical statisticsJan 29, 2020 | 7 min readMaximum Likelihood EstimatorUnder parametric family distributions, there's a much better way of constructing estimators - the maximum likelihood estimator.#Mathematical Statistics #Statistics #EstimationMathematical statisticsJan 28, 2020 | 3 min readThe Method of MomentsA fairly simple method of constructing estimators that's not often used now.#Mathematical Statistics #Statistics #EstimationMathematical statisticsJan 27, 2020 | 6 min readConsistencyIntroducing 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 #EstimationMathematical statisticsJan 25, 2020 | 11 min readBias and VarianceThe bias, variance and mean squared error of an estimator. The efficiency is used to compare two estimators.#Mathematical Statistics #Statistics #EstimationMathematical statisticsJan 8, 2020 | 4 min readBrief Review Before STAT 6520A brief review of probability theory and statistics we've learnt so far.#Mathematical Statistics #StatisticsMathematical statisticsDec 28, 2019 | 6 min readSampling Distribution and Limit TheoremsWe 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 VariableMathematical statisticsDec 8, 2019 | 14 min readFunctions of Random VariablesFinding 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 VariableMathematical statisticsNov 6, 2019 | 23 min readMultivariate Probability DistributionsJoint 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 VariableMathematical statisticsOct 6, 2019 | 7 min readDefinitions for Discrete Random VariablesThe probability mass function, cumulative distribution function, expectation and variance for random variables.#Mathematical Statistics #Statistics #Random VariableLinear modelSep 30, 2019 | 16 min readEstimationIn 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«««45678»»»