Basic Questions Flashcards
Define an experiment
Any process of measurement or observation
Define a random variable
A variable that takes on values according to the outcome of an experiment. Can either be continuous or discrete.
Define covariance and correlation
The measure of dependence between two random variables. Correlation is a standardized measure of this dependence.
Define a random sample
A collection of observations from a population that are independent and identically distributed.
Define an unbiased estimator
An estimator whose theoretical expectation is the true value
Define a consistent estimator and any implications
An estimator which converges in probability to the true value. As n increases the distribution of the estimator will collapse around the true value. If an estimator is unbiased, the distribution of the estimator is centered at the true value for any fixed n.
Types of least squares estimators and properties of LSE
1) Ordinary least squares: assumes errors are iid with same variance and expectation of zero
2) Weighted least squares: allows unequal variances but still assumes iid
3) Generalized least squares: allows unequal variances and correlated errors
Properties: unbiased, minimum variance among all linear functions, do not need to know distribution, do need to know the model (eg Y=XB+e)
Define maximum likelihood in words and the overall properties
It is the value which maximizes the likelihood function of our parameter space, ie the MLE is the value that makes our sample most likely
Properties: Usually consistent, asymptotically most efficient, invariant to transformations. Often biased, do need to know distribution, may not exist
Define a pivot
A pivot is a function of the data and the unknown parameter whose distribution is known and does not depend on the parameter of interest.
Steps to find a confidence interval, correct interpretation
1) Find a pivot for the parameter
2) Write a probability statement involving the pivot
3) Rearrange to get CI for parameter
Interpretation: The probability that the interval includes the parameter is 1-alpha. In other words, if we were to draw many samples we would obtain many CI’s and 1-alpha% of those CI’s would include the true parameter.
Explain the difference between statistical significance and practical importance.
Statistical significance deals with the question: how sure are we that our null hypothesis is wrong? This will deal with p-values.
Practical importance deals with the question: How wrong is our null hypothesis? This is measured by something independent of sample size (usually effect size).
When to use a nonparametric test?
It is similar to t-test, use when data is not normal. The sample is considered to be iid from a symmetric, continuous distribution
Define a categorical variable
A variable whose support is a set of categories, eg hair color
In probability, what is an event?
A subset of the sample space
Difference between ANOVA and regression?
ANOVA can be applied to any regression model (no matter if the model contains only continuous, only categorical, or both kinds of predictors). ANOVA assesses the impact of a predictor or a whole set of predictors on the residuals: how much of the variation in the data can be explained by these predictors? The regression analysis, on the other hand, is a complementary tool to asses the quantitative relation between a predictor and the response.
