# Questions tagged [slutsky-theorem]

The tag has no usage guidance.

21 questions
Filter by
Sorted by
Tagged with
51 views

### Slutsky's theorem applied to a sample mean conditional on a Bernoulli variable?

Let $(Z_{i},Y_{2i})$, $i=1,2,\ldots,N$ be iid random vectors, where $Y_{2i}$ is the outcome vector and $Z_{i}\sim\operatorname{Bernoulli}(\delta)$. Assume that $E(Y_{2i}|Z_{i})=\mu_{2}+\beta Z_{i}$ ...
• 21
210 views

### Is the limit in probablity of an inverse matrix equal to the inverse of the limit in probability of the matrix?

Suppose $X_n$ is a random matrix, which converges in probability to a matrix of constants, $Y$. It seems intuitive that therefore $X_n^{-1} \xrightarrow{p} Y^{-1}$ - so the limit in probability of an ...
• 189
81 views

• 11
4k views

### How does Slutsky's theorem extends when two random variables converge to two constants?

The Slutsky's theorem: Let $\{X_n\}$, $\{Y_n\}$ be two sequences of scalar/vector/matrix random elements. If $X_n$ converges in distribution to a random element $X$ and $Y_n$ converges in ...
• 1,020
I am confused about some details about Slutsky's theorem: Let $\{X_n\}$, $\{Y_n\}$ be two sequences of scalar/vector/matrix random elements. If $X_n$ converges in distribution to a random ...