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3
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0answers
25 views

Diferrencing vs Moving Average

Moving Average and differencing a series can both be used to remove seasonality. Does the difference of these two lie in the model they are used? Moving Average used in classical decomposition and ...
0
votes
1answer
40 views

Forecast error for AR and MA process

AR(p) process is denoted by: $X_t=\mu+\alpha_1(X_{t-1}-\mu)+\alpha_2(X_{t-2}-\mu)+...\alpha_p(X_{t-p}-\mu)+Z_t$ I don't understand forecast error. Let $\epsilon_{t+l}$ be the forecast error at $l$ ...
1
vote
1answer
29 views

SARIMA model equation

Can someone please tell me in the book here how is this SARIMA equation obtained? I know that AR(1)=$Y_t=\alpha_1Y_{t-1}+e_t$ Non Seasonal AR(1)=> $Y_t(1-\alpha_1B)=e_t$. My question is what ...
5
votes
3answers
100 views

What makes constant function an estimator?

This is a theoretical one. This question is inspired by recent question and discussion on bootstrap, where a constant estimator, i.e. a constant function $$f(x) = \lambda$$ was used as an example of ...
1
vote
0answers
9 views

Recaculating control limits when an out of control situation is displayed

When plotting control charts if a point plots outside the control limits then the reason for that point to plot outside is checked and if an assignable cause is found to be the cause then after ...
1
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0answers
20 views

Changing a target value that minimize the product being outside the specifications in quality control

I was doing problems in the article here. In the question on page 16 I don't understand part b) how to find a target value that minimize the product being outside the specifications. Can someone ...
0
votes
1answer
39 views

Distribution of Minimum of RVs

I'm having trouble seeing why for RVs $X_{1}, \ldots, X_{n}$ it is true that: $$Pr(min(X_{1}, \ldots, X_{n}) > x ) = Pr(X_{1} > x, \ldots, X_{n} > x)$$ In other words: Why is the event that ...
4
votes
1answer
102 views

Justifying and choosing a proper scoring rule

Most resources on proper scoring rules mention a number of different scoring rules like log-loss, Brier score or spherical scoring. However, they often don't give much guidance on the differences ...
0
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0answers
9 views

How to determine if a U chart or a C chart to be used

This is regarding theory of attribute type control charts.In a question it is given data for the number of non confirmities per 1000 meters of wire. I have to calculate control limits for a ...
1
vote
0answers
18 views

Calculating $\bar c $ in C chart

In studying C chart I came accross this problem in Statistical Process control by Douglas .C.Montgomary. In this exercise it says: A control chart is used to control the fraction of non ...
0
votes
0answers
16 views

Area of Opportunity in C chart and U chart

In the article whether to use C chart of U chart is determined by area of opportunity.But I don't understand what is meant by area of opportunity and how it relates to C chart and U chart.Can ...
0
votes
1answer
46 views

Auto correlation function of AR(p) process

I am doing a time series course and in the theory part there are few things I don't understand.In obtaining auto correlation function for AR(p) process it is done as: AR(p)=$X_t = α_1X_{t−1} + ...
3
votes
0answers
31 views

Is there a way to visualize what “Minimal sufficiency” and “Completeness” of a statistic means?

As defined (for example, in Wikipedia): Completeness is a property of a statistic in relation to a model for a set of observed data. In essence, it is a condition which ensures that the parameters of ...
2
votes
1answer
37 views

Control limits in $\bar{x}$ and R chart

I am learning a Quality Control course and in theory part I don't understand calculating the control limits for $\bar{x}$ and R chart.I want to know, say when I calculate the R chart control limits no ...
1
vote
1answer
53 views

Definition of Scale median

Lehmann, in Theory of Point Estimation p.212 (and also on p.169), defines scale median as the solution to: $${E(X)I(X\le c)} = {E(X)I(X\ge c)}$$ given $X$ is a positive random variable, and ...
0
votes
0answers
23 views

Regression using a priori knowledge

I am sorry if the title (and probably the question) is not very clear but I have a regression problem which might be a bit over my head if I want to do it well. I am only interested in getting some ...
3
votes
2answers
74 views

Why are econometric analyses valid when the subject of study is inherently different?

I am reading numerous articles pertaining to unemployment as references for my own work. Yet I've encountered many where they use long time series in countries which have had some sort of pertinent ...
0
votes
1answer
26 views

Ensemble in stochastic process

I am learning a time series and forecasting course.In the book "The Analysis of Time Series by Chris Chatfield" it says that We only have single outcome of the process and a single observation on ...
0
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0answers
30 views

Statistical learning theory

I am looking for some good books for statistical learning theory. For an introduction I went through "An elementary introduction statistical learning theory Kulakrani" It was a good read with less ...
0
votes
1answer
32 views

Requirements for a valid neural network activation function?

What rules define a valid neural network activation function, excluding biological plausibility? What set of principles do softmax, rectified linear units, hyperbolic tangent, sigmoid, etc. follow? ...
4
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0answers
25 views

Polling vs averaging in Random Forest models

Why is it that for Random Forest we take the average vote from each classifier in the ensemble rather than the average probability from each classifier in the ensemble? Is there theory behind why ...
0
votes
0answers
14 views

Linear-time approximation to kernel SVM?

Scaling kernel support vector machines to large datasets is a very challenging problem. For linear SVMs, PEGASOS is able to learn efficiently online, so training time scales linearly with the size of ...
0
votes
0answers
9 views

Intuition for uniform integrability as asymptotic light tails

I am trying to get an intuition to the concept of uniform integrability: $$ \lim_m \sup\lim_n \mathbb{E}[|X_n| I_{\{X_n \geq m \}}] \to 0 $$ Can this be seen as a form of "asymptotic light tails"? ...
2
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1answer
81 views

Logistic regression & categorical explanatory variables

I'd like to perform logistic regression with some categorical explanatory variables with more categories than just binary 0/1. Is this possible and why? I am inclined to think that this would give ...
3
votes
0answers
44 views

Formalizing pdf using both discrete and continuous densities

I'm trying to formalize the probability density function for a rather simple process, but I'm having difficulty writing it precisely. Specifically, consider simulating a 1-D Gaussian random walk ...
0
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0answers
39 views

Most Important Stat Theory Concepts — Interview [duplicate]

I have an interview with a top company for a data scientist position. I was made aware that they will be testing probability/statistical theory concepts. So the question: If you had 1 hour tops ...
1
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2answers
46 views

Mixed variable, joint distribution, How do we know which one is continuous distribution, which one is discrete

If we have one continuous r.v. $x$ and a discrete r.v. $y$ which takes one of the two values $y_1$ and $y_2$. Let's say we know the prior probabilities $P(y_1)$ and $P(y_2)$. From Bayes theorem we ...
8
votes
1answer
125 views

Why is variability measured relative to a point?

Why are measures of dispersion calculated relative to some central point? Why wouldn't, for instance, all possible non-repeated, pairwise differences in the dataset be a valid measure of spread?
3
votes
2answers
77 views

Combining models for prediction based on residual performance

I have never read or seen someone do this before, so I wanted to pose the question here. Suppose I fit a basic linear model, $\text{price of house} = \beta_0 + \beta_1*\text{taxes} + ...
1
vote
2answers
60 views

Can a nuisance multi-class classifier do better than binary classifier?

This is rather a theoretical question in order to save the trouble in trying to do empirical testing and is part of a bet, so I hope I am right... Say there are M classes in the data BUT you want to ...
2
votes
1answer
80 views

How can you derive the sample size to obtain a particular type II error rate?

I often see that the sample size for a $z$-test to achieve a particular type II error rate $\beta$ (at a given significance level, $\alpha$) is: $$n = ...
0
votes
0answers
28 views

Mixed model weight matrix

Consider Henderson’s classic mixed model equations: What is the nature of the weight matrix, S-1? I believe that this is composed of the covariance matrix, but at the same time it is diagonal. ...
1
vote
1answer
91 views

Is it valid to apply large scale statistics to a single case?

I have a small black box that displays a 0 or a 1 every time I press its button. I can tell you, truthfully, that over the past 20,000,000,000 times it has been pressed, 19,999,999,990 times it has ...
0
votes
1answer
90 views

When Monte Carlo simulation can't be used to simulate a statistical system?

My question is simple. Which are the general conditions for which a Monte Carlo simulation can be used to represent a statistical system? Or conversely, which are the statistical system that cannot be ...
0
votes
0answers
53 views

Approximating a binomial distribution with a mixture normal

This is purely a theoretical question (I legitimately can't think of a real application), but if you wanted to approximate a binomial distributed variable with a two-component mixture normal, is there ...
0
votes
1answer
103 views

Non significant Pearson correlations included in hierarchical regression?

I would like to perform hierarchical regression in which all variables are based on previous research/theory. But when I perform Pearson correlations, I found that some variables did not correlate to ...
0
votes
8answers
596 views

Does the presence of an outlier increase the probability that another outlier will also be present on the same observation?

**Edit: (10/26/13) More clear (hopefully) mini-rewrites added at the bottom** I'm asking this from a theoretical/general standpoint - not one that applies to a specific use case. I was thinking ...
11
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1answer
154 views

Is there a statistical application that requires strong consistency?

I was wondering if someone knows or if there exists an application in statistics in which strong consistency of an estimator is required instead of weak consistency. That is, strong consistency is ...
0
votes
1answer
190 views

Theoretical expected value and variance

Let $X$ be a random variable having expected value $\mu$ and variance $\sigma^2$. Find the Expected Value and Variance of $Y = \frac{X−\mu}{\sigma}$. I would like to show some progress I've made so ...
1
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0answers
34 views

Modelling with multiple-valued variables

I am about to start out analysis of a microbiological data set (ETEC: enterotoxic echerichia coli in children with diarrhea). The variables refer to the ETEC, not to the children. Some of the ...
2
votes
2answers
143 views

How do we understand the relationship between independent probabilities and real-world independence?

From what I have come to understand, the events A and B are considered independent for purposes of probability theory when $$ p(A \cap B) = p(A) \cdot p(B) $$ Now, supposing I flip two coins. I ...
0
votes
0answers
40 views

Frequency of data: is quarterly data better than half-year data? Why?

Hi have a dataset which I constructed using quarterly observations (from bank accounts). I could have also used half-year or yearly data, but I chose quarterly because I thought that higher frequency ...
4
votes
1answer
48 views

What is the name/relevant details of this exponential-family related structure?

Suppose that $X$ comes from an exponential family $$ p_\theta(x) = h(x)\exp(\theta x - A(\theta)), $$ and that, conditional on $X$, $Y$ also comes from an exponential family of the form $$ ...
3
votes
2answers
125 views

Similarity theory: Testing whether dimensions are separable or integral

Note: I'm not referring to linear separability. I've found the interesting comment in Edelman, Shahbazi: "Renewing the respect for similarity" that for integral dimensions, Euclidean distance is ...
2
votes
0answers
213 views

Improving an unbiased estimator using the Rao-Blackwell theorem [closed]

Given data following a Bernoulli distribution $Y_1,...Y_n \sim B(1,p)$, we want to measure $\theta = \text{Var}(Y_1)$ I found this unbiased estimator $S^2 = \frac{\sum{(y_i-\bar{y}})^2}{n-1}$ I need ...
1
vote
1answer
32 views

How to analyse data from the same group where some people have opted out and data is anonymous?

I have a peculiar situation, I am conducting research and had a group of students participate in it. I had them scored on (property) $X$ and say $n_1$ people participated. After an intervention, I ...
1
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0answers
37 views

Partials of PDF with no closed form solution

I need to estimate partial derivatives for all N parameters denoted $\theta_{N}$ of a probability density function(PDF) $\mathcal{f}$. This PDF $\mathcal{f}$ has no closed form solution and is ...
2
votes
2answers
2k views

How do you Interpret RMSLE (Root Mean Squared Logarithmic Error)?

I've been doing a machine learning competition where they use RMSLE (Root Mean Squared Logarithmic Error) to evaluate the performance predicting the sale price of a category of equipment. The problem ...
3
votes
1answer
105 views

Question regarding Bonferroni correction

Prove the following version of the Bonferroni inequality- $$P\left(\bigcap_{i=1}^kA_i\right)\ge1-\sum_{i=1}^kP(A_i^c)$$ When creating simultaneous confidence interval, what are $A_i$ and $A_i^c$? ...
2
votes
1answer
73 views

What is the name of the theory (if there is one) that states lottery winners are more likely to tell others about their lottery entry?

I've previously read about a theory that I remember (correctly or not) being called the "Winning Lottery Theory" which is essentially the following: An individual hears about disproportionately ...