Sep 17

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

See My credo and How to save on my book

Jump to Matrix Algebra  or Basic statistics or Econometrics or Optimization or Quantitative Finance


Teaching methodology

When a student has problems, the culprit may be narrow internal vision. This is my most important post, and it has three videos.

Teaching methodology dilemma: Is lecturing good or bad?

Use tongue twisters in a Stats class. Auditory and visual centers explained. Improve the thought speed

Reducing memorization

A good definition follows the sequence: motivation -> definition proper -> discussion/application. Example: Pareto chart

Don't be sloppy with definitions and their sequencing: they are the foundation of theory

Team-based method. Don't check hundreds of student papers a week

You win their hearts by winning their minds, not the other way around

The student law: if you don’t require, they don’t do it. A textbook should be a staircase: each subsequent chapter should be a bit more difficult than the previous one.

Review of Agresti and Franklin "Statistics: The Art and Science of Learning from Data", 3rd edition

Review of Albert and Rossman "Workshop Statistics: Discovery with Data, A Bayesian Approach", Key College Publishing, 2001

Review of Newbold, Carlson and Thorne "Statistics for Business and Economics", Pearson, 7th edition, 2010

Review of Bock, Velleman, De Veaux "Stats: Modeling the World", Addison-Wesley, 3rd ed. 2010

Review of Hinders "5 Steps to a 5 AP Statistics, 2010-2011 Edition"

Review of Dougherty "Introduction to Econometrics"

Matrix Algebra

Matrix notation and summation

Vector and matrix multiplication

Roadmap for studying matrix multiplication

Matrix inversion: doing some housekeeping at elementary level

From invertibility to determinants: argument is more important than result

Matrix transposition: continuing learning by doing

Matrix algebra: questions for repetition

Euclidean space geometry: vector operations

Euclidean space geometry: scalar product, norm and distance

Euclidean space geometry: Cauchy-Schwarz inequality

Euclidean space geometry: questions for repetition

Basic statistics

Descriptive statistics and inferential statistics

Numerical versus categorical variable

Uniform distribution definition, with examples

Using graphs to describe data

What should you hate about AP Statistics? The TI-83+ and TI-84 graphing calculators are terrible

How to cheat with TI-83+ and TI-84

Minitab is overpriced. Use Excel instead

What is a Pareto chart and how is it different from a histogram?

The stem-and-leaf plot is an archaism - it's time to leave it behind

Histogram versus time series plot, with video

Comparing histogram, Pareto chart and times series plot

Using statistical tables for normal distribution


What is probability. Includes sample space; elementary, impossible, sure events; completeness axiom,  de Morgan’s laws, link between logic and geometry

Independence of events. Includes conditional probability, multiplication rule and visual illustration of independence

Law of total probability - you could have invented this

Significance level and power of test

Reevaluating probabilities based on piece of evidence

p value definition

Using numerical measures to describe data

What is a median, with an exercise

Using financial examples to explain properties of sample means

Properties of means

What is a mean value. All means in one place: population mean, sample mean, grouped data formula, mean of a continuous random variable

Unbiasedness definition, with intuition

All properties of variance in one place

Variance of a vector: motivation and visualization

Different faces of vector variance: again visualization helps

Inductive introduction to Chebyshev inequality

Properties of covariance

Properties of standard deviation

Correlation coefficient: the last block of statistical foundation

Statistical measures and their geometric roots

Population mean versus sample mean: summary comparison

Mean plus deviation-from-mean decomposition

Scaling a distribution

What is a z score: the scientific explanation

What is a binomial random variable - analogy with market demand

Active learning - away from boredom of lectures, with Excel file and video. How to simulate several random variables at the same time.

From independence of events to independence of random variables. Includes multiplicativity of means and additivity of variance

Normal distributions. Includes standard normal distribution, (general) normal variable, linear transformation and their properties, video and Mathematica file

Definitions of chi-square, t statistic and F statistic

Student's t distribution: one-line explanation of its origin

Confidence interval and margin of error derivation using z-score. Includes confidence and significance levels, critical value

Confidence interval using t statistic: attach probability or not attach?

Distribution function

Distribution function properties

Density function properties

Examples of distribution functions

Distribution and density functions of a linear transformation

Binary choice models

Binary choice models: theoretical obstacles

Maximum likelihood

Maximum likelihood: idea and life of a bulb

Maximum likelihood: application to linear model


Properties of conditional expectation

Conditional expectation generalized to continuous random variables

Conditional variance properties

Simulation of random variables

Importance of simulation in Excel for elementary stats courses

Generating the Bernoulli random variable (coin), with Excel file

Simulating the binomial variable in Excel and deriving its distribution, with Excel file

Creating frequency table and histogram and using Excel macros, with Excel file

Modeling a sample from a normal distribution, with Excel file

Modeling a pair of random variables and scatterplot definition, with video

Sampling distributions

Demystifying sampling distributions: too much talking about nothing

Law of large numbers and central limit theorem

Law of large numbers explained

Law of large numbers illustrated

Law of large numbers: the mega delusion of AP Statistics, with Excel file

All about the law of large numbers. Includes convergence in probability, preservation of arithmetic operations and application to simple regression

Central Limit Theorem versus Law of Large Numbers. Includes convergence in distribution and Excel file

Law of large numbers proved



Simulation for simple regression, with Excel file

Simple regression - before and after estimation

Summation sign rules: identities for simple regression

What is an OLS estimator - simplified derivation

Derivation of OLS estimators: the do's and don'ts

Unbiasedness of OLS estimators - the do's and don'ts

OLS estimator variance

Gauss-Markov theorem

Coefficient of determination: an inductive introduction to R squared

Testing for structural changes: a topic suitable for AP Stats

Violations of classical assumptions 1

Violations of classical assumptions 2

Multiple regression through the prism of dummy variables

OLS estimator for multiple regression - simplified derivation

Nonparametric estimation for AP Stats

Regressions with stochastic regressors 1

Regressions with stochastic regressors 2

Instrumental variables estimator

Durbin-Wu-Hausman test

Time series models

What is a stationary process? A sum of two independent stationary processes is also stationary

Nonstationary processes 1

Nonstationary processes 2

Stationary processes 1

Stationary processes 2

Autoregressive processes

Moving average processes

Autoregressive–moving-average (ARMA) models

What is cointegration? Cointegration is similar to linear dependence of vectors

Error correction model

Using Stata for statistical problems

Introduction to Stata

Running simple regression in Stata

Alternatives to simple regression in Stata

Nonlinear least squares: idea, geometry and implementation in Stata


Logical structure of definitions

See if this definition of a function is better than others

Least upper bound and largest lower bound

How to study mt3042 Optimisation: a guide to a guide

Geometry related to derivatives

Geometry behind optimization

The Cobb-Douglas function and level sets

Taylor decomposition for unconstrained optimization

Unconstrained optimization on the plane: necessary condition

Unconstrained optimization on the plane: sufficient conditions

Optimization with constraints: economic and financial examples

Importance of implicit function theorem for optimization

Lagrange method: necessary condition

Lagrange method: sufficient conditions

Lagrange method: case of many equality constraints

The Lagrangian multiplier interpretation

The Kuhn-Tucker theorem: a first look

The Kuhn-Tucker theorem ins and outs

Finite Horizon Dynamic Programming

Using convexity in optimization

Cauchy-Schwarz inequality and optimization 1

Cauchy-Schwarz inequality and optimization 2

The economical way to use the Kuhn-Tucker theorem

The right solution to Example 6.5

Solution to exercise 6.1: how to use homogeneity

Quantitative Finance

Efficient market hypothesis is subject to interpretation

Conditional-mean-plus-remainder representation

Canonical form for time series

Old versus new tools in Quantitative Finance

Distribution function estimation

Value at Risk and its calculation for a normal distribution

Expected shortfall is next after Value at Risk

Solution to Question 1 from UoL exam 2016, Zone A

Solution to Question 1 from UoL exam 2016, Zone B

Solution to Question 1 from UoL exam 2017, Zone B

Density of a sum of independent variables is given by convolution

Sampling from uniform distribution - example of convolution

Solution to Question 2 from UoL exam 2016, zone A

The Newey-West estimator: uncorrelated and correlated data

Probabilistic intuition behind call option properties

Call options and probabilistic intuition - dependence on strike

Call options and probabilistic intuition - dependence on stock price

Call options and probabilistic intuition - dependence on time

Volatility - king among option price determinants

Interest rate - the puppetmaster behind option prices

Option chain and efficient market hypothesis

Intro to option greeks: delta and its determinants

Intro to option greeks: theta, intrinsic value and time value

Visualization of payoffs on calls and puts