Questions tagged [mathematical-statistics]
Mathematical theory of statistics, concerned with formal definitions and general results.
8,121 questions
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More Fantasy Football Entropy [closed]
What is the best way to set up a 12-team fantasy football league playoff … both for the 6 best teams, and the 6 worst teams?
2
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Help matching an ordered list of events (no timestamps) to a noisy timestamped time-series
I’m stuck and this is starting to feel pretty convoluted, so I’ll try to be clear.
What I have:
A timestamped stochastic time-series (e.g. market prices). It’s noisy but when an event happens the ...
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Assigning a single distribution when an experiment assigns one batch of distributions for 1 to m and another batch of distributions to n to n-m
What if there were a row of n objects divided by some 0<= m <= n, and batches of k_j elements to be collected by the n objects in sequence, alternating, from object 1 and up, and from object n ...
3
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1
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Accuracy in Machine Learning vs. Accuracy in Statistics vs. pass@1,1 in Generative Modeling: What's the Difference?
I've encountered the term "accuracy" used differently across several evaluation contexts, and I want to clearly understand their mathematical and conceptual distinctions using consistent ...
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Combining prior on effect size with new effect size estimate (Bayesian)
CONTEXT
I am a researcher planning experiments. My goal is to combine a prior on the effect size from prior literature with pilot data.
SETUP
Assume I have a prior on an effect size,
$d \sim N(d_{\...
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3
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1
answer
75
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Testing independence: $t$-test on $\{X_iY_i\}$ vs OLS $t$-test
Suppose I have i.i.d. pairs $(X_i, Y_i)$ with
$E[X_i]=E[Y_i]=0$ and $\operatorname{Var}(X_i)=\operatorname{Var}(Y_i)=1$.
I want to test
$H_0:\; X \perp Y$ (independence).
Under these moment ...
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1
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1
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Asymptotic distribution of leave-one-out jackknife replicate estimate
Say I have a sample $(X_1, \dots, X_n)$, and I calculate a sample statistic $\hat{\theta}(X_1, \dots, X_n) =: \hat{\theta}$. I'd like to construct a test which tells me how influential a single ...
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Do k-folds risk sampling bias and, if so, how do we avoid it?
In cross-validation, $k$-folds are a common way to train, compare and validate models. Often we want to find an optimal set of hyperparameters for our models. There are many ways to probe the ...
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2
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Likelihood ratio theorem for Minimal sufficient statistic when the PDF is not pointwise defined
For a background, I am a pure mathematician and am looking for a fully rigorous statement / proof for results in mathematical statistics :). It is probably better to post this in the math page but I ...
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7
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How to find confidence intervals for binary outcome probability?
I'm doing stats for medical chart review research. The binary outcomes vary in probability from less than 0.05 to greater than 0.5 depending on risk factors. For relatively more common outcomes like ...
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2
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1
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In a heteroskedastic model, can I treat the first term $ (y_{1}-\mu)^2 $ as a weighted term with weight 1?
I’m working on an MLE exercise for the following model:
$$
Y_{1} \sim \mathcal N(\mu,\sigma^2), \qquad
Y_{i} \mid Y_{i-1}=y_{i-1} \sim \mathcal N\!\big(\mu,\ \sigma^2(1+y_{i-1}^{2})\big),
\quad i\ge 2 ...
3
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0
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74
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Book recommendations for machine learning similar to "Elements of Statistical Learning" but more up-to-date [closed]
I'm an economics PhD by training but work in industry. I have been trying to get more familiar with machine learning.
A friend recommended "Elements of Statistical Learning". I'm really ...
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Asymptotic Distribution of Weighted Empirical Distribution
Suppose that we observe an i.i.d. sample $(X_1, Y_i), ..., (X_n, Y_n)$ from $(X, Y)$. We assume that $X_i$ is bounded by $B$ and $E(X) = 0$. For some $\tau \in (0, 1)$, define the $\tau$th quantile of ...
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Variance of the average treatment effect using the unit-level variances of the potential outcomes
I'm reading Chapter 19 of Imbens and Rubin (2015), which is on the estimation of variance for estimators of treatment effects. They discuss using the variance of each sample/unit's potential outcomes ...
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3
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820
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Trouble with the definition of p-value
I'm following a statistics course and our professor gave us a definition of p-value I'm having some trouble understanding. First, some preliminary notations I want to set:
$\Omega = A \cup A^\...
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