Statistical Analysis Stack Exchange
Statistical Analysis Stack Exchange

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1500 questions
60
votes
7 answers

Is chi-squared always a one-sided test?

A published article (pdf) contains these 2 sentences: Moreover, misreporting may be caused by the application of incorrect rules or by a lack of knowledge of the statistical test. For example, the total df in an ANOVA may be taken to be the error…
Joel W.
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2 answers

What is the variance of the weighted mixture of two gaussians?

Say I have two normal distributions A and B with means $\mu_A$ and $\mu_B$ and variances $\sigma_A$ and $\sigma_B$. I want to take a weighted mixture of these two distributions using weights $p$ and $q$ where $0\le p \le 1$ and $q = 1-p$. I know…
JoFrhwld
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60
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13 answers

Does 10 heads in a row increase the chance of the next toss being a tail?

I assume the following is true: assuming a fair coin, getting 10 heads in a row whilst tossing a coin does not increase the chance of the next coin toss being a tail, no matter what amount of probability and/or statistical jargon is tossed around…
user68492
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60
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3 answers

What is the objective function of PCA?

Principal component analysis can use matrix decomposition, but that is just a tool to get there. How would you find the principal components without the use of matrix algebra? What is the objective function (goal), and what are the constraints?
Neil McGuigan
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59
votes
5 answers

What are disadvantages of state-space models and Kalman Filter for time-series modelling?

Given all good properties of state-space models and KF, I wonder - what are disadvantages of state-space modelling and using Kalman Filter (or EKF, UKF or particle filter) for estimation? Over let's say conventional methodologies like ARIMA, VAR or…
Kochede
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59
votes
6 answers

Is random forest a boosting algorithm?

Short definition of boosting: Can a set of weak learners create a single strong learner? A weak learner is defined to be a classifier which is only slightly correlated with the true classification (it can label examples better than random…
Atilla Ozgur
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59
votes
7 answers

How do I test that two continuous variables are independent?

Suppose I have a sample $(X_n,Y_n), n=1..N$ from the joint distribution of $X$ and $Y$. How do I test the hypothesis that $X$ and $Y$ are independent? No assumption is made on the joint or marginal distribution laws of $X$ and $Y$ (least of all…
sds
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59
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2 answers

Optimal number of folds in $K$-fold cross-validation: is leave-one-out CV always the best choice?

Computing power considerations aside, are there any reasons to believe that increasing the number of folds in cross-validation leads to better model selection/validation (i.e. that the higher the number of folds the better)? Taking the argument to…
Amelio Vazquez-Reina
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59
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2 answers

What does having "constant variance" in a linear regression model mean?

What does having "constant variance" in the error term mean? As I see it, we have a data with one dependent variable and one independent variable. Constant variance is one of the assumptions of linear regression. I am wondering what homoscedasticity…
Mukul
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59
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2 answers

How can I change the title of a legend in ggplot2?

I have a plot I'm making in ggplot2 to summarize data that are from a 2 x 4 x 3 celled dataset. I have been able to make panels for the 2-leveled variable using facet_grid(. ~ Age) and to set the x and y axes using aes(x=4leveledVariable, y=DV). I…
russellpierce
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59
votes
4 answers

Confidence interval for Bernoulli sampling

I have a random sample of Bernoulli random variables $X_1 ... X_N$, where $X_i$ are i.i.d. r.v. and $P(X_i = 1) = p$, and $p$ is an unknown parameter. Obviously, one can find an estimate for $p$: $\hat{p}:=(X_1+\dots+X_N)/N$. My question is how can…
Oleg
59
votes
4 answers

Choosing between LM and GLM for a log-transformed response variable

I'm trying to understand the philosophy behind using a Generalized Linear Model (GLM) vs a Linear Model (LM). I've created an example data set below where: $$\log(y) = x + \varepsilon $$ The example does not have the error $\varepsilon$ as a…
Marc in the box
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59
votes
7 answers

Intuitive explanation of the bias-variance tradeoff?

I am looking for an intuitive explanation of the bias-variance tradeoff, both in general and specifically in the context of linear regression.
NPE
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59
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4 answers

Are all values within a 95% confidence interval equally likely?

I have found discordant information on the question: "If one constructs a 95% confidence interval (CI) of a difference in means or a difference in proportions, are all values within the CI equally likely? Or, is the point estimate the most likely,…
pmgjones
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59
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5 answers

Is it true that the percentile bootstrap should never be used?

In the MIT OpenCourseWare notes for 18.05 Introduction to Probability and Statistics, Spring 2014 (currently available here), it states: The bootstrap percentile method is appealing due to its simplicity. However it depends on the bootstrap…
Clarinetist
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