Category Archives: Statistics

Some notes on Kalman Filtering

State Space form Measurement Equation Transition Equation Future form

Posted in Statistics, Time Series | Tagged , , , | Leave a comment

Big Data for Volatility vs.Trend

So different aspects of Big Data — in this case dense vs. tall — are of different value for different things. ┬áDense data promote accurate volatility estimation, and tall data promote accurate trend estimation. More (No Hesitations blog)

Posted in Statistics | Tagged , , | Leave a comment

The limitations of randomised controlled trials

In recent years, the use of randomised controlled trials has spread from labour market and welfare programme evaluation to other areas of economics (and to other social sciences), perhaps most prominently in development and health economics. This column argues that … Continue reading

Posted in Statistics, Uncategorized | Tagged , , | Leave a comment

Rio’s Inequality

Let and be two integrable real-valued random variables and let be the quantile function of . Then if is integrable over we have where is the a-mixing coefficient. Proof: Set and then since and note also that which implies that

Posted in Inequalities, Statistics | Tagged , , | Leave a comment

Kolmogorov’s Maximal Inequality

Let be independent random variables with . Set . Then Proof: Let Notice that and

Posted in Inequalities, Statistics | Tagged , , | Leave a comment

An inequality of the expectation

Let be i.i.d. r.vs with and . Then Proof: So

Posted in Inequalities, Statistics | Tagged , , | Leave a comment

LAN for Linear Processes

Consider a m-vector linear process where are i.i.d. m-vector random variables with p.d.f. on , are matrices depending on a parameter vector . Set Assume the following conditions are satisfied A1 i) For some where denotes the sum of the … Continue reading

Posted in Statistics | Tagged , , | Leave a comment