Mathematical theory of statistics, concerned with formal definitions and general results.

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3
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1answer
113 views

What do vertical bars mean in statistical distributions?

What do the vertical bars mean in the first and third formulae? $$v_i|z_i=k,\mu_k\sim\mathcal{N}(\mu_k, \sigma^2)$$ $$P(z_i=k)=\pi_k$$ $$\pi|\alpha\sim \text{Dir}(\alpha/K1_K)$$ $$\mu_k\sim ...
1
vote
1answer
21 views

Doubt on interpretation of Neyma-Pearson lemma

In my book: $\mathbf{X}=(X_1,\ldots,X_n)$ $f(\mathbf{x})$ is the joint density, where $f$ is either $f_0 \text{ or } f_1$. Suppose we want to test $H_0: f=f_0$ or $H_1: f=f_1$. The test, whose test ...
1
vote
1answer
29 views

Geodesic distance and mean

My data-set consists of points in globe. Suppose a User visits locations $l_1,l_2,\dots l_n$ (each location in $(lat, long)$ in the city with probability $p_1,p_2,\dots,p_n$ and I want to calculate ...
1
vote
1answer
262 views

Which is kernel similar gaussian kernel?

I must find a kernel that statisfies as follows: In the my reference paper, the author suggest gaussian kernel that is The purpose of that kernel is that it will take a weight for each points ...
1
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2answers
59 views

Limiting joint distribution of estimators; Functional Statistics; Influence curves;

Let $X_1,...,X_n$ iid r.v. with distribution F, with mean $\mu$ and median $\theta$.Assume that $Var(X_i)=\sigma^2$ and $F'(\theta)>0$. If $\hat{\mu}_n$ is the sample mean, and $\hat{\theta}_n$ the ...
2
votes
1answer
44 views

$E(X_i \cdot I(X_j>\theta))$, where theta is the median?

Let $X_1, ..., X_n$ be iid with a distribution F. Let $\theta$ be the median of F. What is the value of $E(X_i \cdot I(X_j>\theta))$? If $i\neq j$, then $E(X_i \cdot I(X_j>\theta))= 1/2 \cdot ...
0
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0answers
29 views

How to convert daily variances to a monthly volatility and then annualize it?

I work out the conditional variance using a GARCH model based on daily returns as follows: ...
1
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1answer
14 views

Get Characteristic Function from MGF? [duplicate]

I've been calculating characteristic functions and MGF's and was wondering whether we can always get the characteristic function simply by substituting $it$ instead of $t$ in the resulting equation. ...
1
vote
1answer
28 views

Convergence of Gini index

Let $\theta(F)=2\int^1_0(t-q_F(t))dt$, where $\displaystyle q_F(t)=\frac{\int_0^tF^{-1}(s)ds}{\int_0^1F^{-1}(s)ds}$. For discrete distributions I'm assuming that $F^{-1}(s)=\inf\{x:F(x)=s\}$ (the ...
0
votes
0answers
10 views

Is the AUC for dataset (A union B) between the AUC of dataset A and the AUC of dataset B?

Consider you have a binary classifier which you tested on dataset AB=A union B. Assume that the several Area Under the Curve metrics for the three datasets are: AUC(A), AUC(B), and AUC(AB). Without ...
0
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0answers
7 views

Approaches to Subsampling to exceed a Population Mean

I've studied a large amount of Probability & Statistics, but I'm embarrassed to say I've forgotten too much of it. Would appreciate any pointers anyone has about this: I have a set of about 360 ...
1
vote
1answer
36 views

Joint density of first r order statistics

Let $X_i \sim^{iid} F$ for $i=1,...,n$, where $F$ is a continuous distribution. I want to find the pdf for $X_{(1)},X_{(2)},..., X_{(r)}$, with $r\leq n$. We know that $f_{X_{(1)},X_{(2)},..., ...
-2
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0answers
14 views

The percent of members in a random sample that have an equal chance of being selected: [closed]

The percent of members in a random sample that have an equal chance of being selected: 0%, 33%, 50%, or 100%
2
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0answers
44 views

Birthday “Paradox” — with a different perspective

Background: Many people are familiar with the so-called Birthday "Paradox" that, in a room of 23 people, there is a better than 50/50 chance that two of them will share the same birthday. In its more ...
0
votes
1answer
23 views

How can I statistically formulate football player attributes similar to Football Manager games or footballdatabase.eu?

I have collected player match history statistics like runs, shoots, passes and such. I would like to come up similar attribute values (psychical, mental, technical) to Football Manager game or ...
0
votes
0answers
10 views

What is $C_{pk}$(test) $-\ C_{pk}$(reference)?

I have a process under test (approximately normal distributed), and I have calculated $C_{pk}$ (a process capability index) for this process. These values are compared to reference values which are of ...
-2
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0answers
45 views

I need help about my statistics homework [closed]

The average number of mosquitoes in a stagnant pond is 60 per square meter with a standard deviation of 16. If 9 square meters are chosen at random for a mosquito count, find the probability that the ...
-4
votes
0answers
23 views

I need help finding the variance for this problem [closed]

Find the variance for the values of n and p when the conditions for the binomial distribution are met. n=700 p=.85 a. 89.25 b. 595 c. 9.4 d. 105
1
vote
1answer
58 views

Should a Poisson regression be carried out with only 3 data points?

I'm trying to test the relationship between the number of adults counted and the percentage heather cover over 3 areas. The data looks like this: ...
0
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0answers
27 views

How to represent bayesian loss function in binary classification

I am studying classification using linear regression . Now, I want to map it in Bayesian regression. Let talk about binary classification using linear regression again. Assume that I have a set ...
3
votes
1answer
120 views

Is it possible to statistically test relationships between counts and percentages?

I have counted adult butterfly numbers over 3 areas and would like to compare these counts with the percentage heather cover on each of the 3 areas. Is this possible? My data looks like this (the ...
6
votes
2answers
153 views

Deriving the bivariate Poisson distribution

I've recently encountered the bivariate Poisson distribution, but I'm a little confused as to how it can be derived. The distribution is given by: $P(X = x, Y = y) = ...
2
votes
0answers
119 views

Question about Dynkin Lehmann Scheffe Theorem

I'm self-studying for an examination, and I would like to understand how to use the Dynkin Lehmann Scheffe theorem for an applied question. I am using Bickel and Doksum's "Mathematical Statistics" ...
2
votes
1answer
47 views

Bounded expectation implied bounded conditional or vice versa?

If $\mathrm{E}\left(X\right)<\infty$ does that imply $\mathrm{E}\left(X|Y\right)<\infty$? How about vice versa? I'm thinking if we condition on an event (say $Y>2$) then if we have ...
3
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0answers
23 views

The distribution of a sufficient statistic

If I understand correctly, a distribution in the exponential family... $$\underline X\sim f_{\underline\theta}(\underline x) = exp\{\sum\limits_{i}\eta_i(\underline\theta)T_i(\underline ...
4
votes
1answer
48 views

Hyper-volume of the $\alpha$ contour of a multivariate Gaussian

I'm looking for the assymptotic ($n\rightarrow \infty$) value of (the log of the determinant of) the covariance of the $\alpha$% of observations with smallest Eucledian distance to the origin in a ...
5
votes
2answers
69 views

Convergence in distribution of sum implies marginal convergence?

Let $X_n, X, Y$ be random variables such that $X_n + cY \stackrel{d}{\rightarrow} X + cY $ for every positive constant $c$. Prove that $X_n \stackrel{d}{\rightarrow} X$. I know if only we have joint ...
0
votes
0answers
47 views

How can i show mathematically Partial Least Square Regression is better than other Ordinary Least Square Regression?

I want to develop techniques for attribute selection (important independent variable X) using Partial least square 2 regression(PLS2R) for a large data sets .Initially i tried using multivariate ...
0
votes
0answers
17 views

How to calculate the standard deviation from a normalised value?

I have 2 data sets (I have more but for simplicity lets say I have 2). Data 1 0.15239652 0.145848036 0.175981261 Data 2 0.417902092 0.342696648 0.354871141 I ...
0
votes
0answers
11 views

How to treat “Missing Value Analysis” test results (problems)

I have a problem with Missing Value Analysis. I am using SPSS version 20. I am trying to test whether missing values are at complete random. As I know in order to ensure missing values are completely ...
0
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0answers
22 views

MPE and MAPE averages

I am a computer science graduate with a minor in mathematics, however it has been a long while since taking any statistical courses. I am looking at calculating the Mean Percent Error and Mean ...
2
votes
1answer
102 views

What loss function can I use for linear classification?

I have a question about loss function in bayes classification. Let see similar case of loss function in linear classification: Given data $(x,y)=${$(x_1,y1)....(x_n,y_n)$} is map to label $T=${-1,1}. ...
0
votes
0answers
6 views

Problem with calculating the avarage power of a vector? [migrated]

I am calculating the average power of a vector. I would like to compare it the final expression with the simulation. However, they are not equal. Please help me to point out which steps are wrong. ...
0
votes
1answer
50 views

How to compare models from different but related datasets?

I'm building regression models on four the different but related data set and at the end, I want to test the significance of models. Since my models are built in a different data set, it's not ...
0
votes
0answers
36 views

Chi-square test for one group

I'm struggling with this problem. For the analysis of my test, I was instructed to use chi-square test for one group. I use Statistica and everywhere I try to do this I need the expected values​​, ...
1
vote
1answer
29 views

What are the assumptions of linear regression (both simple and multiple)

I know this is a basic question, but I get slightly different answers everywhere I look, a quick example is that I learnt at Uni that the errors of the dependent variable have to be normally ...
5
votes
4answers
407 views

Calculating PDF given CDF

I know that the PDF is the first derivative of the CDF for a continuous random variable, and the difference for a discrete random variable. However, I would like to know why this is, why are there ...
0
votes
1answer
48 views

Anomaly detection using exponential weighted moving average

I would like to detect anomaly using exponential weighted moving average. I don't have series of data points. All I have is EMA(t-1) and the data point of the current time(t) DP(t). From these data, ...
0
votes
1answer
23 views

Alternatives to absolute error?

Let me explain my scenario in which I need to calculate absolute error. Lets say the X is the actual value. And X' is the value of X with some error 'e'. So X' = X + e'. Lets say i = 1 to 10000. I ...
0
votes
0answers
36 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 ...
0
votes
0answers
15 views

Let $f(x)$ be the density of $X$. What is $\lim_{n\rightarrow \infty}\mathrm{E}_X[nf(X+n)]$?

The expectation can be written as $\mathrm{E}_X[nf(X+n)] = \int_{-\infty}^\infty nf(x+n)f(x)\,\mathrm{d}x$. The expectation relies on the speed of tail $f(x+n)$ goes to $0$. I posted a related ...
0
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0answers
16 views

Regression line fit for linearly increasing data with manual reset

I've a linearly increasing time series dataset of a sensor with value ranges between 50 to 150 on which I've implemented a simple linear regression algorithm to fit a regression line, and I'm ...
1
vote
2answers
196 views

Estimate ARMA coefficients through ACF and PACF inspection

I know that this is probably a question that's been asked plenty of times, but i haven't seen an answer that's both accurate and simple. How do you estimate the appropriate forecast model for a time ...
2
votes
1answer
34 views

How to combine distributions

If I have two continuous distributions $f(x)$ and $g(x)$, there are several mathematical ways to combine $f$ and $g$ to get new distributions. Which correspond to what statistical interpretation? For ...
0
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0answers
8 views

What kind of statistical method is recommended to compare ratio in pre-test and post-test

I want to compare two different ratios. When this ratio is close to 1 it shows the better stability in the body. Would you please guide me that which statistical test is better for this situation? ...
5
votes
2answers
64 views

How would one formally prove that the OOB error in random forest is unbiased?

I have read this statement many times but have never come across a proof. I would like to try to produce one myself but I'm not even sure on what notation to use. Can anyone help me with this?
0
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0answers
2 views

Which test to find out whether EC50s in my three dose-response relationships are different or not?

I injected three different cRNAs constructs (construct A,B and C) into oocytes and the oocytes expressed the respective cRNAs as respective ion channels (ion channel A,B and C). My aim was to test ...
3
votes
3answers
50 views

Bias of estimating a Ratio?

I would like to know why 1/N * Summation of(y/x) is a worse estimator than average of y divided by average of x. This is in the context of constructing an estimator of a ratio where the ratio would ...
-1
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0answers
14 views

to test the difference between 3 vaules [closed]

I measured half maximal effective concentration (EC50) of three different RNA construct and I want to test whether they are statistically significance or not. Which test should I use?