Tag Archives: Statistics & Econometrics

Weekend combinatorics work problem (IV) When my daughter (who studies mathematics) and yours truly solve a combinatorics problem together it takes 12 minutes. If my daughter tries to solve the problem herself it takes her 10 minutes more than it takes when I solve it alone. How long does it take me to solve the problem?

An easy one this week: At a small economics conference, a photographer wants to line up nine participants for a photo. Two of them — Robert and Milton — insist on standing next to each other. How many different arrangements (lineups) are possible?

Chebyshev’s and Markov’s Inequality Theorems Chebyshev’s Inequality Theorem — named after Russian mathematician Pafnuty Chebyshev (1821-1894) — states that for a population (or sample) at most 1/k2 of the distribution’s values can be more than k standard deviations away from the mean. The beauty of the theorem is that although we may not know the exact distribution of the data — e.g. if it’s normally distributed  — we may still say with certitude (since the...

How to prove things .[embedded content] Great lecture series. Yours truly got Solow’s book when he was studying mathematics back in the 80s. Now in its 6th edition, it’s better than ever.

The dangers of using unproved assumptions The unpopularity of the principle of organic unities shows very clearly how great is the danger of the assumption of unproved additive formulas. The fallacy, of which ignorance of organic unity is a particular instance, may perhaps be mathematically represented thus: suppose f(x) is the goodness of x and f(y) is the goodness of y. It is then assumed that the goodness of x and y together is f(x) + f(y) when it is...

.[embedded content] Bra föreläsningsserie från Chalmers! När jag själv läste matematik i Lund på 80-talet tyckte jag bäst om kurserna i diskret matematik. Mycket logik och problem av ‘tankenötskaraktär’. Och kul hjärngympa att lägga några timmar på när man vill pausa lite från schackspel och korsord …

The Binomial and Poisson distributions (student stuff) .[embedded content]

On the validity of econometric inferences The impossibility of proper specification is true generally in regression analyses across the social sciences, whether we are looking at the factors affecting occupational status, voting behavior, etc. The problem is that as implied by the three conditions for regression analyses to yield accurate, unbiased estimates, you need to investigate a phenomenon that has underlying mathematical regularities – and, moreover,...

A different way to solve quadratic equations .[embedded content] This one is for Linnea, my youngest daughter, who has now begun studying mathematics at my university 🙂

Statistical models and the assumptions on which they build Every method of statistical inference depends on a complex web of assumptions about how data were collected and analyzed, and how the analysis results were selected for presentation. The full set of assumptions is embodied in a statistical model that underpins the method … Many problems arise however because this statistical model often incorporates unrealistic or at best unjustified assumptions …...