# Questions tagged [definition]

This tag indicates questions about definitions of statistical terms. Use a more general tag [terminology] for questions on statistical parlance that are not specifically about definitions.

552 questions
Filter by
Sorted by
Tagged with
10 views

### Can manual feature extraction be considered a part of a learning algorithm?

We can view a learning algorithm as a tuple $(\mathcal{H}, \mathcal{O}, \mathcal{L})$ where $\mathcal{H}$, $\mathcal{O}$ and $\mathcal{L}$ are the hypothesis class, optimizer and loss function ...
• 477
1 vote
45 views

### Can you arbitrarily define your sample space?

Let's say you flip a fair coin. A sample space is a set of possible outcomes of an experiment. So, intuitively, the sample space will be {Head, Tail}. However, I have seen that it is also possible to ...
1 vote
107 views

### Formal definition of sufficient statistic

Let $(\Omega_X,\mathcal{F}_X)$ and $(\Omega _T,\mathcal{F}_T)$ be measurable spaces. Let $\mathfrak{M}$ be a family of probability measures on $(\Omega_X,\mathcal{F}_X)$. Let $X:\Omega\to \Omega _X$ ...
• 133
2k views

### When is it important for a practitioner to understand CIs?

I have a physician friend who asks me questions about stats. He gets confused about stuff, e.g., the definition of a confidence interval (CI) and its intricacies. For example, he finds the following ...
• 2,634
94 views

### Fixed vs random: how can a fixed effect be constant across individuals?

For years, I have been trying to find a definition for fixed and random effects. I often see statements like this: Fixed effects are constant across individuals. - almost universal We define effects (...
• 23
1 vote
51 views

### Motivation behind definition of PMF of function of $2$ variables

I am really curious to understand what motivates the definition $$p_{g(X,Y)} (g(X,Y)=z) = \sum_{(x,y)\in g^{-1}(\{z\})} p_{X,Y} (x,y)$$ where $g$ is a two variable function, and $X,Y$ are random ...
• 189
365 views

• 599
1k views

### Rationale behind defining distribution function with strict inequality

A friend from Italy pointed me to a nice Probability Theory book written in Italian by G. Dall'Aglio, a well-known Italian probabilist; Original title: Calcolo delle Probabilità, terza edizione, ...
• 12k
135 views

### Are random variables mathematical functions when dealing with continuous sample spaces?

I'm struggling with some basic concepts regarding the definitions of random variables. If I'm not mistaken, random variables are functions which aim to "translate" outcomes of a sample space ...
• 107
70 views

### Definition of Hypothesis Testing in All of Statistics

In the book All of Statistics by Larry Wesserman, the author says "Let $X$ be a random variable and let $\mathcal{X}$ be the range of $X$. We test a hypothesis by finding an appropriate subset of ...
2k views

### Regression vs. Classification: Is there a clear, generally accepted definition?

As a mathematician/economist, I am not trained to think in classification and regression tasks. This is why I wonder: is there a clear, widely accepted definition of regression and classification ...
• 3,603
1 vote
38 views

### Provide an example of a dataset where maximum likelihood is inapplicable as third moments and fourth moments "assumptions" do not apply

An additional complication arises with estimation, since maximum likelihood estimation may not be feasible without making unrealistically strong ?????"assumptions"????? about third‐ and ...
5k views

### What is the difference between something being "true" and 'true with probability 1"?

In the beginning of chapter 2 of Information Theory, Inference and Algorithms, the author says that he will refrain from being unnecessarily rigorous and provides the example of saying that something ...
• 1,617
1 vote
334 views

### What is the definition of a non-linear estimator? I heard that ratio of estimators is non-linear

Why don't we consider nonlinear estimators for the parameters of linear regression models? says that LASSO is a non-linear estimator. I think LASSO has a solution via matrix multiplication. I don'...
2k views

• 205