#### List of posts on Algebra, Statistics, Econometrics, Finance and Optimization.

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## Posts by category

**Category: Agresti & Franklin**- Conditional variance properties
- Multiple regression through the prism of dummy variables
- Testing for structural changes: a topic suitable for AP Stats
- It’s time to modernize the AP Stats curriculum
- Ditch statistical tables if you have a computer
- Nonparametric estimation for AP Stats
- Properties of correlation
- The pearls of AP Statistics 36
- Statistical measures and their geometric roots
- Properties of standard deviation
- The pearls of AP Statistics 35
- The pearls of AP Statistics 34
- Properties of variance
- The pearls of AP Statistics 33
- Properties of means
- The pearls of AP Statistics 32
- The pearls of AP Statistics 31
- The pearls of AP Statistics 30
- The pearls of AP Statistics 29
- The pearls of AP Statistics 28
- The pearls of AP Statistics 27
- The pearls of AP Statistics 26
- The pearls of AP Statistics 25
- The pearls of AP Statistics 24
- The pearls of AP Statistics 23
- The pearls of AP Statistics 22
- The pearls of AP Statistics 21
- The pearls of AP Statistics 20
- The pearls of AP Statistics 19
- The pearls of AP Statistics 18
- The pearls of AP Statistics 17
- The pearls of AP Statistics 16
- The pearls of AP Statistics 15
- The pearls of AP Statistics 14
- The pearls of AP Statistics 12
- The pearls of AP Statistics 11
- The pearls of AP Statistics 10
- The pearls of AP Statistics 9
- The pearls of AP Statistics 8
- The pearls of AP Statistics 7
- The pearls of AP Statistics 6
- The pearls of AP Statistics 5
- The pearls of AP Statistics 4
- The pearls of AP Statistics 3
- The pearls of AP Statistics 2
- The pearls of AP Statistics 1
- Properties of conditional expectation
- What is a p value?

**Category: Agresti and Franklin****Category: AP Stats and Business Stats**- Little tricks for AP Statistics
- Law of total probability - you could have invented this
- Distribution function estimation
- Intro to option greeks: delta and its determinants
- Interest rate - the puppetmaster behind option prices
- How to study mt3042 Optimisation: a guide to a guide
- Finite Horizon Dynamic Programming
- Reevaluating probabilities based on piece of evidence
- Significance level and power of test
- Violations of classical assumptions 2
- Alternatives to simple regression in Stata
- Running simple regression in Stata
- Examples of distribution functions
- Density function properties
- The pearls of AP Statistics 37
- Gauss-Markov theorem
- Regressions with stochastic regressors 2
- The law of large numbers proved
- Inductive introduction to Chebyshev inequality
- Regressions with stochastic regressors 1
- OLS estimator variance
- Properties of covariance
- All you need to know about the law of large numbers
- Proving unbiasedness of OLS estimators
- How to save on my book
- Derivation of OLS estimators: the do's and don'ts
- What is cointegration?
- What is a mean value - all means in one place
- Summation sign rules: identities for simple regression
- Simple regression - before and after estimation
- OLS estimator for multiple regression - simplified derivation
- Teaching methodology dilemma: Is lecturing good or bad?
- What is an OLS estimator - simplified derivation
- What is a Pareto chart?
- What is a binomial random variable - analogy with market demand
- What is a z score: the scientific explanation
- Scaling a distribution
- Mean plus deviation-from-mean decomposition
- Active learning - away from boredom of lectures
- Population mean versus sample mean
- Modeling a pair of random variables and scatterplot definition - Exercise 2.5
- Histogram versus time series plot - Example 2.2
- Modeling a sample from a normal distribution in Excel - Exercise 2.4
- Creating frequency table and histogram and using Excel macros - Exercise 2.3
- Simulating the binomial variable - Exercise 2.2
- Generating Bernoulli random variable (coin) in Excel - Exercise 2.1
- First message

**Category: Book reviews****Category: Dougherty Introduction to Econometrics**- Distributions derived from normal variables
- Application: Ordinary Least Squares estimator
- Violations of classical assumptions 1
- Nonlinear least squares: idea, geometry and implementation in Stata
- Introduction to Stata
- Autoregressive–moving-average (ARMA) models
- Moving average processes
- Autoregressive processes
- Stationary processes 2
- Stationary processes 1
- Nonstationary processes 2
- Error correction model
- Maximum likelihood: application to linear model
- Distribution and density functions of a linear transformation
- Maximum likelihood: idea and life of a bulb
- Binary choice models: theoretical obstacles
- Binary choice models
- Distribution function properties
- Durbin-Wu-Hausman test
- Instrumental variables estimator
- What is a stationary process?

**Category: EC2020****Category: EC2020 Elements of econometrics****Category: Econometrics****Category: FN3142 Quantitative Finance**- Law of iterated expectations: geometric aspect
- Law of iterated expectations: informational aspect
- Portfolio analysis: return on portfolio
- Applications of the diagonal representation IV
- Efficient market hypothesis is subject to interpretation
- The Newey-West estimator: uncorrelated and correlated data
- Solution to Question 2 from UoL exam 2016, zone A
- Sampling from uniform distribution - example of convolution
- Density of a sum of independent variables is given by convolution
- Solution to Question 1 from UoL exam 2017, Zone B
- Solution to Question 1 from UoL exam 2016, Zone B
- Solution to Question 1 from UoL exam 2016, Zone A
- Expected shortfall is next after Value at Risk
- Conditional expectation generalized to continuous random variables
- Value at Risk and its calculation for a normal distribution
- Visualization of payoffs on calls and puts
- Intro to option greeks: theta, intrinsic value and time value
- Option chain and efficient market hypothesis
- Volatility - king among option price determinants
- Call options and probabilistic intuition - dependence on time
- Call options and probabilistic intuition - dependence on stock price
- Call options and probabilistic intuition - dependence on strike
- Old versus new tools in Quantitative Finance
- Canonical form for time series
- Conditional-mean-plus-remainder representation

**Category: Matrix algebra**- Determinant of a transpose
- Multilinearity in columns
- Determinant of a product
- Leibniz formula for determinants
- Properties of permutation matrices
- Permutation matrices
- Properties IV-VI
- Axioms 1-3 and Properties I-III
- Determinants: starting simple
- Questions for repetition
- Eigenvalues and eigenvectors of a projector
- Constructing a projector onto a given subspace
- Geometry and algebra of projectors
- Questions for repetition
- Questions for repetition
- Applications of the diagonal representation III
- Applications of the diagonal representation II
- Applications of the diagonal representation I
- Diagonalization of symmetric matrices
- General properties of symmetric matrices
- Eigenvalues and eigenvectors
- Orthogonal matrices
- Matrix similarity
- Final touches on linear independence
- Law and order in the set of matrices
- Complex numbers: time to turn on the beacon
- Summary and questions for repetition
- Rank of a matrix and the rank-nullity theorem
- Basis and dimension
- Linear dependence of vectors: definition and principal result
- Solvability of an equation with a square matrix
- Is the inverse of a linear mapping linear?
- Geometry of linear equations: questions for repetition
- Geometry of linear equations: orthogonal complement and equation solvability
- Geometry of linear equations: structure of image and null space
- Geometry of linear equations: linear spaces and subspaces
- Geometry of linear equations: matrix as a mapping
- Euclidean space geometry: questions for repetition
- Euclidean space geometry: Cauchy-Schwarz inequality
- Euclidean space geometry: scalar product, norm and distance
- Euclidean space geometry: vector operations
- Matrix algebra: questions for repetition
- Matrix transposition: continuing learning by doing
- From invertibility to determinants: argument is more important than result
- Matrix inversion: doing some housekeeping at elementary level
- Roadmap for studying matrix multiplication
- Vector and matrix multiplication
- Matrix notation and summation

**Category: MT2175 Further linear algebra****Category: MT3042 Optimisation theory**- From minimum to infimum: Math is just a logical game
- See if this definition of a function is better than others
- Logical structure of definitions
- Solution to exercise 6.1: how to use homogeneity
- The right solution to Example 6.5
- The economical way to use the Kuhn-Tucker theorem
- Cauchy-Schwarz inequality and optimization 2
- Cauchy-Schwarz inequality and optimization 1
- Consumption-Savings Problem
- Using convexity in optimization
- The Kuhn-Tucker theorem ins and outs
- The Kuhn-Tucker theorem: a first look
- The Lagrangian multiplier interpretation
- Lagrange method: case of many equality constraints
- Lagrange method: sufficient conditions
- Lagrange method: necessary condition
- Importance of implicit function theorem for optimization
- Optimization with constraints: economic and financial examples
- Unconstrained optimization on the plane 2
- Unconstrained optimization on the plane 1
- Taylor decomposition for unconstrained optimization
- The Cobb-Douglas function and level sets
- Geometry behind optimization
- Geometry related to derivatives

**Category: Optimisation theory****Category: Option properties****Category: Quantitative Finance****Category: ST104A****Category: ST104B****Category: Statistics 1****Category: Statistics 2****Category: The College Board**