# Simple hypothesis (d) Composite hypothesis MCQ 13.4

Surprisingly, our simple null hypothesis is enough to explain this track record. I don’t have any flair for picking stocks successfully, but there is a simple randomised strategy I can follow to allow me to run an investment fund which predictably gets a track record like this. My strategy to match this is to simply go to a casino, bet 90% of my cash on a 50-50 chance and then put the proceeds in a market index fund. At this point, I’ll either have 190% of my initial funds or 10% of them. Every four years, I take the money out of the index fund for a day and make a similar double-or-nothing bet on 90% of the money. How far would we expect this process to get before crashing? On average, I’d get one near-doubling before the crash – and this is all LTCM got.

## the distinction between simple hypotheses and composite ..

### Hypothesis Testing, simple against composite

N2 - In recent years several authors have recommended smooth tests for testing goodness of fit. However, the number of components in the smooth test statistic should be chosen well; otherwise, considerable loss of power may occur. Schwarz's selection rule provides one such good choice. Earlier results on simple null hypotheses are extended here to composite hypotheses, which tend to be of more practical interest. For general composite hypotheses, consistency of the data-driven smooth tests holds at essentially any alternative. Monte Carlo experiments on testing exponentiality and normality show that the data-driven version of Neyman's test compares well to other, even specialized, tests over a wide range of alternatives.

### Statistical hypothesis testing - Wikipedia

AB - In recent years several authors have recommended smooth tests for testing goodness of fit. However, the number of components in the smooth test statistic should be chosen well; otherwise, considerable loss of power may occur. Schwarz's selection rule provides one such good choice. Earlier results on simple null hypotheses are extended here to composite hypotheses, which tend to be of more practical interest. For general composite hypotheses, consistency of the data-driven smooth tests holds at essentially any alternative. Monte Carlo experiments on testing exponentiality and normality show that the data-driven version of Neyman's test compares well to other, even specialized, tests over a wide range of alternatives.