I would like to know what topics are considered 'core knowledge' for a statistician. Please keep in mind I know very little about statistics.
At my university, I hear statistics students discuss topics such as: Time series analysis, Descriptive statistics, Non-parametric statistics, ANOVA, Regression Analysis, Statistical learning, etc. Assuming these are distinct courses, I am curious what topics like these are considered 'core' for a general statistician?
Before anyone marks this as a duplicate, I have read through a good few similar threads. For instance:
However I find none of these really answer my question specifically. I don't want references. I'm interested in a specific list of topics (if one exists) that every statistician would be expected to know, with a brief description of what that topic actually is.
Perhaps to give an example: I am a maths and theoretical physics student. It seems to me that, no matter what field of expertise a maths/physics student may eventually choose, there are a number of central topics they would be expected to know. For instance, one can list the following topics that are standard for most maths degrees:
- Set Theory
- Category Theory
- Point Set Topology
- Real analysis (Calculus, Measure Theory, Functional Analysis)
- Complex Analysis
- Abstract Algebra (Group, Ring and Field Theory)
- Number Theory
- Differential Geometry
- Algebraic Topology
- Algebraic Geometry
Whether a student has taken a full course in this area or not, most maths students would be expected to know at least the basics in these 'core' areas. For physics, one can come up with a similar list.
My question is:
Can one come up with a similar list summarising the basic topics a statistician should know? If so, please give a basic description of each topic in the list (even just one or two sentences).
I understand such lists are never a perfect (or even good) way of summing up the core knowledge for a field. Nevertheless, I am interested in getting a rough idea of what topics a statistician has studied.