Most active questions
100 questions from the last 7 days
16
votes
4
answers
993
views
Moving false positives back to the training dataset
recently I was facing the following approach: having a machine learning model (a 0-1 classifier) data scientists wanted to reduce the number of false positives detected in the validation dataset by ...
- 338
9
votes
2
answers
713
views
Preservation of mean>median for sums
Suppose $X$ and $Y$ are non-negative real random variables and that the mean is strictly greater than the median for each of the two variables. Does it follow that the mean of $X+Y$ is strictly ...
- 51k
8
votes
2
answers
345
views
Why/when will negative binomial regression flip the sign of the effect from analogous Poisson regression, after covariate adjustment
First, to be clear, the issue mentioned in the title does not happen often and, in every parametric simulation I've tried, both NB and Poisson produce similar estimates, regardless of the type of ...
- 81
5
votes
2
answers
215
views
Finding UMVUE of a Poisson parameter
Suppose $X \sim \operatorname{Poisson}(\lambda), \lambda>0$ . Let $\theta=\lambda^3e^{-2\lambda}.$
a) Show that $S=(-1)^{X-1}X(X-1)(X-2)$ is an unbiased estimator of $\theta$.
b) For a random ...
- 321
9
votes
1
answer
427
views
Derive the most powerful test
Let $F$ be a CDF on the real line with density $f$. Consider two sample problem where $X_1,\ldots,X_n$ are i.i.d with CDF $F$ and $Y_1,\ldots,Y_m$ are i.i.d from CDF $F^\delta$ for some $\delta>0$. ...
- 321
3
votes
2
answers
230
views
Hypothesis testing via overlapping CIs when one sample is very small (8) and one is large (178)
I'm taking a statistics class. The question has been graded, but I question the validity of the official answer. We are asked whether, based solely on the confidence intervals, the mean BMI differs ...
- 41
3
votes
1
answer
299
views
How is it that a time series can autocorrelate with first lag but not the second? And conequence on linear regression
When I have a time series that I want to model as an autoregressive series, I express my value at time t as a linear combination of previous values:
$$y_t=\sum_{i=1}^p\theta_iy_{t-i}+e_t$$
Right, but ...
7
votes
1
answer
192
views
Find the limiting distribution
Suppose $X_1,\ldots,X_n$ are i.i.d. random variables taking values $1,0,-1$ with probability $\frac14,\frac12,\frac14$ respectively. Define $S_n=\sum_{i=1}^nX_i$ and $U_n= \operatorname{sgn}(S_n)$ for ...
- 73
4
votes
2
answers
58
views
Coefficient of determination ($R^2$) for complex-valued models
For a model $f:\mathbb{R}\rightarrow\mathbb{R}$, the coefficient of determination is unambiguously defined by:
$$
R^2=1-\frac{\text{Unexplained variance}}{\text{Total variance}}=1-\frac{\sum_{k=1}^n\...
- 141
4
votes
1
answer
130
views
If UMP test exists then it is equivalent to UMP unbiased
A test $\phi(X)$ is said to be unbiased if the following condition holds
$E_{\theta}\phi(X)\leq \alpha$ for all $\theta \in \Omega_H$ and $E_{\theta}\phi(X)\geq \alpha$ for all $\theta \in \Omega_K$ ...
4
votes
2
answers
243
views
Why covariance instead of correlation in the definition of degrees of freedom (effective number of parameters)
The definition of degrees of freedom (effective number of parameters), sourced from here, is:
Suppose that we observe:
$$ y_i = r(x_i) + \varepsilon_i, \quad i = 1, \ldots, n, $$
where the errors $\...
- 781
2
votes
2
answers
78
views
Definition of the random-effect model
I am studying the random-effects model as a preparation for a meta-analysis. Unfortunately I am confused because there seem to be two inequivalent descriptions of the model in the literature:
In the ...
- 173
0
votes
1
answer
79
views
P-value tests small samples
I am working with small samples in each group (n=3). When checking for normal distribution and equality of variances everything is fine (p>0.05). I think these are misleading results because the ...
- 111
2
votes
1
answer
49
views
Do instrumental variables introduce problematic multicollinearity? If not, why not? If so, how is it deal with?
I've been confused about something. There are, among others, two important rules of linear regression modelling:
The independent variables should be uncorrelated with the residuals
Independent ...
- 223
2
votes
1
answer
82
views
How common (or advisable) is it to constrain factor loadings to be non-negative in CFA
I've been thinking about the practice of imposing lower bounds (e.g., setting a minimum of 0) on factor loadings $\lambda$ in confirmatory factor analysis and structural equation modeling. It seems ...
- 3,501