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

learn more… | top users | synonyms (1)

1
vote
0answers
20 views

Geometric proof of partical correlation with pythagoras theorem [on hold]

Please help me with my statistics lesson. I need to prove the partical correlation formula with the definition and the pythagoras theorem. The definition (partical correlation): ...
0
votes
0answers
20 views

R Commander: how to test correlation across all variables? [on hold]

If I want to test correlation between two variables I would run the following command in R: ...
0
votes
0answers
23 views

What does make SVM a “soft computing” method?

Soft computing is defined in [1] by the capability of "operating with uncertain, imprecise and incomplete information in a manner that reflects human thinking". So, based on my limited understanding, ...
0
votes
0answers
9 views

References for Combine Seasonal Period in Seasonal Time Series

I'm in a middle writing my thesis. I got confused for find the references which said period of seasonal could be chosen from the small period which already containing another periods. Here is my ...
0
votes
0answers
14 views

Calculate state change probability

I am having telco order management data and need to calculate the probability of each order going through different stages. data is like this: Order No; product_type; time spent in step1; time ...
3
votes
0answers
32 views

Expectation of a conditional density

I'm trying to figure out why the following equation holds: $$f_{Y}(y) = E(f_{Y|X}(y|X))$$ I have sort of "worked out" the RHS to be: \begin{align} f_{Y}(y) &= E(f_{Y|X}(y|X)) \\[5pt] ...
0
votes
1answer
22 views

Algorithm to determine a point in time series data, after which probability of increase in value is very low

I am working with dataset which contains number of movie tickets sold per day. This is basically a count of total number of tickets sold, for a particular movie, for each day after its release date. I ...
0
votes
0answers
6 views

How to calculate sample size for testing H0: Y is related to X by a sigmoidal function?

I'm assuming I would need to specify a given functional form and conditional standard deviation for Y at each X. That would give me some parameters to be estimated and I would need to set a threshold ...
1
vote
1answer
41 views

Interchanging limit and derivative for CDFs

Let $F_{\theta}(x)$ denote a cumulative distribution function indexed by the parameter vector $\theta$. Given this definition is the following equation correct (and if so under which conditions)? ...
5
votes
2answers
125 views

For least squares estimation, what is the difference between using the estimator $\hat{\beta} = X^{T}Y$ vs $\hat{\beta} = (X^{T}X)^{-1}X^{T}Y$

For least squares estimation, the estimator $\hat{\beta} = X^{T}Y$ is an unbiased estimator while $\hat{\beta} = (X^{T}X)^{-1}X^{T}Y$ is also an unbiased estimator given that $X$ is well-defined. Is ...
3
votes
1answer
39 views

Is it possible to determine how many effects I can estimate in a least squares problem just by looking at the correlation matrix?

I currently have a model matrix $X$ with $6$ columns, which is being used for a factorial design problem, with each column associated with an effect. The ultimate goal is to be able to estimate as ...
0
votes
3answers
68 views

Express correlation matrix of $X$ in terms of $X^{T}X$ (in the OLS context)

In least squares estimation where $Y = \beta X$, how can we find the correlation matrix of $X$ in terms of $X^{T}X$? It seems that $X^{T}X$ is very close in structure to the correlation matrix, but ...
-1
votes
0answers
43 views

Convergence in distribution and degenerate random variable

Let $\{Y_n\}$ be a sequence of random variables with an associated sequence of CDFs $\{F_n\}$ given by : $$F_n(y) = \begin{cases} 0 & \textsf{for}&y <0 \\ (\frac{y}{\theta})^n & ...
0
votes
0answers
10 views

Distribution of samples from a uniform distribution [duplicate]

Let's say we are taking $n$ samples from a uniform distribution, that spans from $0$ to $1$. According to the central limit theorem, the mean of the $n$ samples will follow a normal distribution with ...
0
votes
0answers
27 views

Is my graph extraordinary excessive graph (positive excess) ? [closed]

My graph shows the following distribution of values. (the scale ist from 1-5) 1=0 2=0 3=7 3,5=7 4=8 4,5=15 5=20 So there is no curve. But it is increase abruptly however. Does anyone know, of the ...
1
vote
1answer
48 views

Percentage interpretation of negative values when you can't use log transformation

I have a data set of 5 indicators of the stock market. 2 of the indicators have negative values: e.g. they range from say -50 to 100. After running a regression I would like to be able to compare the ...
0
votes
1answer
49 views

data normalization after dimension reduction for classification

The classifier is KNN or RBF-SVM. After doing dimension reduction (e.g., PCA, LDA or KPCA, KLDA), does it need to do normalization before classification? In LIBSVM ...
1
vote
0answers
15 views

What mean to use in odometer calculation based on model?

Im trying to figure out what would be considered a valid calculation. Imagine I have a dataset that looks like that: ...
1
vote
1answer
32 views

On One-to-One Functions of Complete Statistics

Why is a one-to-one function of complete statistic also complete? How might you go about proving this?
3
votes
1answer
22 views

On the proof of admissibility of constant estimators under squared loss

The question concerns the discussion in Wasserman, All of Statistics, Section 13.6. He defines: An estimator $\hat{\theta}$ is inadmissible if there exists another rule $\hat{\theta}'$ such that ...
1
vote
1answer
54 views

Limiting distribution of $\frac{\sqrt{n}\left(\bar{X_n}-\mu\right)}{\sqrt{\bar{X_n}}}$ from mean of Gamma$\left(\mu,1\right)$?

Given $\bar{X_n}$ is mean of random sample with size $n$ from Gamma distribution with parameter $\alpha=\mu$ and $\beta=1$. I wanna find the limiting distribution of ...
0
votes
0answers
15 views

What statistical test should I use to compare the binary outcome of two groups (with pre- and post- test)?

I have two groups of people: experiment group and control group. People in each group accepted pre-test and post-test. The outcome of the tests is binary: "good" or "bad". In other words, each people ...
1
vote
0answers
26 views

Show that weighted least squares estimator for a specific model is not consistent

Here is the background for this problem: $\qquad\qquad\qquad$ $Y_{1},...,Y_{n}$ iid $N(\mu,c^2\mu^2)$, $\,\,$ $c^2$ known. $\,$ The problem is as following: Consider the above model. Define ...
0
votes
1answer
10 views

Is there a framework for reinforcement learning with states and actions in the same domain?

In reinforcement learning, there are states, actions, initial states, terminal states, a progress function and a reward function. Is there a theoretical framework or setting where states and actions ...
3
votes
0answers
25 views

Does the UMVUE have to be a minimal sufficient statistic?

I'm studying point estimation and I have found this question that seems pretty tricky to me. If $T$ is a minimal sufficient statistic for $\theta$ with $E(T) = \tau(\theta)$, can you say that $T$ ...
0
votes
0answers
7 views

Significant change over time between categories

I am trying to establish whether change over time is significant at an archaeological site. Basically, there are seven different time periods (lets call it A-G) and in each time period there are six ...
2
votes
1answer
53 views

How should I calculate the variance of a circular random variable?

Consider the following function being the PDF of a circular random variable (orientation angle from the zenith) ...
0
votes
0answers
31 views

How to compare PCA with KPCA for dimension reduction?

Both linear principal component analysis (PCA) and kernel principal component analysis (KPCA) are unsupervised dimension reduction methods. I have a dataset with $4000$ training samples and $40000$ ...
1
vote
0answers
110 views

Pooled Variance for Dependent $t$-test statistic?

I'm looking into finding a way to calculate Cohen's $d$ for correlated samples. Assuming pooled variances, we end up getting $$\text{SE}\left( \Delta \text{ of means}\right) = ...
1
vote
1answer
33 views

Random unit vectors in $\mathbb{C}^n$ and $\mathbb{R}^{2n}$

Suppose $\mathbf{u}\in\mathbb{C}^n$ is a complex random vector with circular symmetry, uniformly distributed on the unit complex $n$-sphere, so we have $\|\mathbf{u}\|=1$. In other words, $\mathbf{u}$ ...
4
votes
1answer
122 views

Marginal normality and joint normality

Let $X$ and $Y$ be two independent standard normally distributed random variables $N(0,1)$ .If we define a new random variable $Z$ such that : $$Z = \begin{cases}X & \text{if} &XY > ...
5
votes
1answer
62 views

Compute $E\left[ \Phi \left(X \right) \Phi \left(Y \right) \right]$ for a bivariate normal distribution

Assume that $X$ and $Y$ follow the bivariate normal distribution with correlation coeffcient $\rho > 0$, zero means and scale parameters equal to one. I am looking for an elegant way to compute ...
1
vote
1answer
16 views

Derivation of formula for sample size of finite population

I found here the formula for computing the sample size $n$ of a finite population $N$ $$ n = \frac{n_\infty}{1 + \frac{n_\infty - 1}{N}} $$ where the sample size for an infinite population $n_\infty$ ...
1
vote
0answers
24 views

calculating PMI for co-occurrences of words

I am in the process of building a question answering system. I am interested in calculating the PMI for words $x$ and $y$ occurring within 5 words of each other in a document. I have the formula and ...
0
votes
0answers
8 views

Count of the biggest bin in histogram, C#, sharp [migrated]

I want to make histogram of my data so, I use histogram class at c# using MathNet.Numerics.Statistics. ...
0
votes
0answers
23 views

What are the correct ways to check if a variable is significant?

I've conducted a series of computational experiments varying a set of discrete parameters. I see on the figures that some of the parameters don't affect the result in any consistent way and look like ...
-1
votes
2answers
49 views

$\mathbb{P}(A_1)≤\mathbb{P}(A_1)$ in Boole's inequality ($n=1$) proof?

Why does this proof use $≤$ in the $n=1$ (induction base case) case for Boole's inequality, when in fact it's an equality? That is, why claim, $\mathbb{P}(A_1)≤\mathbb{P}(A_1)$, when it should be a ...
0
votes
1answer
19 views

Question on Integrating Over Joint Probability

Let us say that we have a joint probability density denoted as $$P(x_1,x_2,...,x_n)$$ If we are trying to find the probability that every $x_i$ is greater than $0$, is it correct to say that the ...
1
vote
1answer
37 views

How to do this transformation $Y= g(x) \sim \mathcal U(0,2)$?

If $X$ is a continuous random variable with probability density function $f_X(x)=2(1-x)$ for $0 < x < 1$, find the transformation $Y=g(X)$ such that the random variable $Y\sim \mathcal U(0,2)$.
3
votes
1answer
43 views

Hypothesis testing for the (Pearson) correlation coefficient

I don't understand why we have to assume ρ=0 in to get the probability density function? If I say null hypothesis p is something like 0.3, I can still use the probability density function, can't I?
2
votes
1answer
29 views

Boosted Trees: Objective Function clarification

Reading through this overview of boosted trees, I'm having trouble understanding how the second line was derived. $$ Obj(t)=\sum_1^n{loss(y_{i} - \hat{y}_i^{(t)})} + \sum_1^t{\Omega(f_i)} \\ = ...
1
vote
0answers
43 views

How can I determine whether a change is statistically significant ONLY based on confidence intervals and points of estimate?

The table above shows the proportions (%) of a given country's population that have experienced theft from vehicles each year along with respective confidence limits. How can I tell if a change ...
-2
votes
0answers
18 views

Obtaining distribution function for positive linear combination of independent random variables with Poisson distribution [duplicate]

Let $X_1,X_2,...,X_n,Z$ be i.i.d poisson random variables,respectively with mean $\lambda_i$ and $\lambda$ where $"n"$ is definite, $c_i\geq 0$. Assume all the parameters $\lambda_i$'s and $\lambda$ ...
0
votes
1answer
35 views

Probability of winning and losing match in a group of five teams?

We are conducting a tournament in our office. For that purpose we have made groups and each group is comprised of five teams. Each team will play four matches with each other. Now we have to pick top ...
1
vote
0answers
19 views

Sampling property for linear regression estimation

Least Squares Estimation for linear regression is that, $$\hat{\beta} = (X^{T}X)^{-1}X^{T}y$$ Also, it is easy to see that, $$\hat{\beta} \sim \mathcal{N}(\beta, (X^{T}X)^{-1}\sigma^2)$$ If we assume ...
3
votes
1answer
41 views

Non parametric density estimation

In general it's possible to estimate a given multivariate density function $f(x)$ using some non-parametric methods such as kernels or histogram. What are the conditions on a function $g$ such that ...
1
vote
2answers
31 views

Proving that weighted probabilities lie in the range 0 to 1

How to prove that: $$P_{avg} = \dfrac{w_{1}P_{A} + w_{2}P_{B} + w_{3}P_{C}}{w_{1} + w_{2} + w_{3}}$$ lies between 0 and 1, where $P_{i}$ corresponds to probability scores and $w_{j}$ are real ...
0
votes
0answers
6 views

Can I treat my ordinal data as categorical, and use those results to corellate with a 5 point likert scale?

I have recently been reading about business ethics and have undertaken a research project concerning interest in ethical consumption. I am rusty on my stats so I am desperate to get to the bottom of ...
0
votes
0answers
18 views

Estimating residual variance with covariance matrix and mean vector

I'm currently working on estimating a multiple regression solely with the covariance matrix and the mean vector. The example I'm working with gives the following formulas for the bivariate case of ...
0
votes
0answers
6 views

Delayed Trend Following?

Example 1. Let's say there are two Exchanges, one in London second in China. People tend to say: Hey, it seems like the London exchange is 'following' China exchange with some delay. It doesn't have ...