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Questions tagged [st.statistics]

Applied and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments.

Applied and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments.

The statistics question asked on MO is usually expected to be more mathematical and theoretically oriented than those asked on http://stats.stackexchange.com . They are mostly methodology-related or with a specific concern on a certain topic of statistics.

1847 questions
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Calculating the "Most Helpful" review

How would you calculate the order of a list of reviews sorted by "Most Helpful" to "Least Helpful"? Here's an example inspired by product reviews on Amazon: Say a product has 8 total reviews and they are sorted by "Most Helpful" to "Least Helpful"…
user1901
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16
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Correlation and Causation. When can we believe correlation (reasonably, at least) imply causation

We always hear, when reading on correlation, that "correlation does not imply causation." Still, I have never seen any source that tries to answer the question of when can we reasonably conclude a causal relation between variables X, Y from a…
Herb
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2 answers

How can these statistical arguments be made logically rigorous?

Suppose an urn contains unknown but non-random numbers of red and green marbles, and I take a random sample of a known and non-random size. Observing the numbers of red and green marbles in the sample, I need to hazard my best guess as to the…
Michael Hardy
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Generate Bernoulli vector with given covariance matrix

I am from different background, so please forgive me if the answer is so well known. Let $C=(c_{ij})$ be a given $n\times n$ matrix. Do we have a way to generate samples of random Bernoulli vectors with covariance matrix equal to $C$? More…
Yi Huang
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9
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6 answers

Data Mining-- how do you know whether the pattern you extract is valid?

I've been asking myself this question all the time. Let's say you are given a large set of time series data. Your task is to find out patterns that are meaningful or that you can use for future trend prediction. The issue now is, how do you know for…
Graviton
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uneven spaced time series

Let $(t_k), k \in \mathbb{N}$, be an increasing sequence of real numbers ($t_{k-1} < t_k$) and $(X_{t_k}$) be a sequence of real numbers indexed by $(t_k)$. Such a sequence is sometimes called a time series. The idea is that this series represents a…
Tim van Beek
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8
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1 answer

Estimate population size based on repeated observation

I take the bus to work every day. Every bus has a serial number, but unlike in the German Tank Problem, I don't know if they are numbered uniformly $1...n$. Suppose the first $k$ buses are all different, but on day $k+1$ I take one I've been on…
Grandpa
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1 answer

How to estimate a time distribution

This likely isn't a research-level question, but it is at least a question of interest to this researcher. I'm happy with an answer that sends me somewhere (preferably online) to read about a well-known (to somebody) solution, if there is such a…
Kevin O'Bryant
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2 answers

Gaps between descending order statistics

Let $\{X_{1},X_{2},\cdots,X_{n}\}$ be a random sample of size $n$. Denote $(X_{(1)},X_{(2)},\cdots,X_{(n)})$ to be its descending order statistics. Define gap $g_{i}(n)$ to be $g_{i}(n)=X_{(i)}-X_{(i-1)},1\leq i\leq n$. My question is what is the…
Youzhou Zhou
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7
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4 answers

discrete stochastic process: exponentially correlated Bernoulli?

There is a question that was asked on stackoverflow that at first sounds simple but I think it's a lot harder than it sounds. Suppose we have a stationary random process that generates a sequence of random variables x[i] where each individual random…
Jason S
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7
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0 answers

Convergence of Maximum Likelihood Estimator

I apologize for the basic question. If $\{p_\theta(x): \theta\in K\subseteq\mathbb{R}\}$ is a smooth family of distributions, then the MLE $\hat{\theta}_n,$ under suitable regularity conditions satisfies…
Hedonist
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6
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2 answers

Confidence intervals when the number of samples is random

I am interested in computing confidence intervals for the mean of a random variable $X$ given $\require{cancel}\xcancel{N \text{ i.i.d. samples}}$ an i.i.d. sample of $N$ copies of $X$, where $N$ is $\operatorname{Binomial}(n, p)$. Any time I read…
George
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2 answers

Is a function of complete statistics again complete?

suppose $T$ is a complete stats for a parameter $\theta$. Is any function $f(T)$ again complete? It sounds weird but the definition seems to confirm that $f(T)$ is indeed complete..
user135939
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5
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2 answers

Population Spearman Rank Correlation Coefficient

I am doing some research on the Spearman Rank Correlation Coefficient; all the references I can find refer essentially to a sample statistic. That is, given a sample of the jointly distributed $(x_i,y_i)$, one can compute the Spearman Coefficient…
Steven Pav
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0 answers

Has anyone used reflection in bootstrapping methods for one parameter hypothesis tests?

Here's my idea for a bootstrapping method for testing hypotheses about one parameter. Please tell me if you have seen this somewhere before. If not, I'd appreciate pointers for direction of further research. Suppose I want to do a two-tailed…
Anna Varvak
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