# Tagged Questions

Mathematical statistics is the study of statistics from a mathematical standpoint, using probability theory as well as other branches of mathematics such as linear algebra and analysis.

24 views

### Estimating a random variable from repeated trials

I have an $n$ sided die and suspect that it is biased. I'm interested in the probability of rolling a $1$, so I roll the die $m$ times and count up the number of times I roll $1$, then divide the ...
20 views

### How can we use the Lindley's method to approximate the following expression?

The Lindley's(1980) approximation is one of the most popular methods that is used to obtain Bayes estimates. In this method we need to maximum likelihood estimators(MLEs) of the unknown parameters. ...
39 views

### Showing Residual Sum of Squares for Multiple Linear Regression is 0

Problem: I have the linear regression model: $y_i=\beta_0+\sum_{k=1}^p \beta_kx_{ik}+\epsilon_i$ where $\epsilon_i\sim N(0,\sigma^2)$, for $i = 1,2,\ldots ,n$. I want to prove that the residual sum ...
17 views

14 views

### Proof that SSR = SST when they have the same degree of freedom? [closed]

Intuitively, this makes sense, but is there any way to prove it?
24 views

26 views

### Consistent Estimator and Convergence Variance

I was practicing an exam, and came along this question: A consistent estimator converges in probability to the true parameter value. Therefore, the variance of such an estimator converges to zero ...
31 views

### Proof by contradidction that the mean of a set cannot be greater than the greatest value in that set.

I want to prove that given a set of values $x_1, x_2, ..., x_n$, the mean of those values cannot be greater than the greatest of those values. Let the mean $\frac{x_1 + x_2 +... + x_n}{n} = a$ ...
25 views

### Notation for minimum

I'm reading Huber's Robust Statistics right now, and at the beginning of Chapter 3, he writes the following notation: $\sum \rho(x_i;T_n) = \min!$ Similarly, a few lines down, he writes: \$\sum \rho(...