0
votes
0answers
16 views

What is sampling with unequal probabilities without replacement

sampling without replacement: i know if my sample size is $n$, and if $i^{th}$ unit is drawn then we will not replace the unit in the population , so that in my next draw i can get any unit except ...
0
votes
0answers
9 views

“Approximation” of a maximum likelihood confidence set

I have some trouble constructing the "approximate" set, how can it be defined or calculated? Suppose that three characteristics in a large population can be observed according to the following ...
0
votes
0answers
18 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
17 views

UMVUE using complete and sufficient statistic

Let $X_1,X_2,...,X_n$ be a random sample from a normal distribution with mean $\mu$ and variance $\sigma^2$. I showed that $(\bar X,S^2)$ is jointly sufficient for estimating ($\mu$,$\sigma^2$) where ...
0
votes
0answers
19 views

Maximum Likelihood estimators in linear models

Consider two simple linear models. $y_{1j}=\alpha _1+\beta_{1}x_{1j}+\epsilon_{1j}$ and $y_{2j}=\alpha _2+\beta_{2}x_{2j}+\epsilon_{2j}$ , $ j=1,2,...,n>2$ where $ ...
1
vote
1answer
27 views

Finding UMVUE for Poisson distribution using Rao Blackwell

Let ${X_1,X_2,... ,X_n}$ be a random sample from a Poisson distribution with parameter $\lambda$.Let $\gamma(\lambda)=P(X<=1)$. Find UMVUE for $\gamma(\lambda)$. This is my attempt: First I ...
1
vote
0answers
16 views

Draw and compare the likelihood using R

The following shows the heart rate (in beats/minute) of a person, measured throughout the day: 73, 75, 84, 76, 93, 79, 85, 80, 76, 78, 80. Assume the data are an iid sample from ...
0
votes
0answers
17 views

What is the problem with this model parameter estimation algorithm?

In a statistical model with parameters $\theta$ and unobserved laten variables $Z$, the model likelihood is $$L(\theta;X)=Pr(X|\theta)=\sum_ZPr(X,Z|\theta)$$ The standard way to estimate $\theta$ ...
0
votes
0answers
21 views

Parameter estimation of Lorenz system (nonlinear dynamical system)

My problem is as follows. I have to estimate parameters of Lorenz system using given data. Lorenz system is described by following system of ODEs: $$ \frac{dx}{dt} = \sigma(x-y) \\ \frac{dy}{dt} = ...
0
votes
0answers
21 views

learning phenomena in bayesian technique

I have identified using bayesian method for my auto tagging application. I am dealing with user facebook post. Post belongs to ...
1
vote
1answer
29 views

Question about Logistic Regression - 7

I am currently studying Logistic Regression. I am facing a problem with understand the sentence in the red circle below. I am trying to figure out what he/she means by the sentence. Please let me have ...
0
votes
0answers
21 views

Question about Logistic Regression - 6

I am studying Logistic Regression and I have come across to understating the paragraph below. I kind of can understand, but it makes me confused when I read the sentence in the red circle, "It also ...
0
votes
0answers
21 views

Question about Logistic Regression - 2

How should I tell the difference between those two formulas in the circles below. I am studying logistic regression and I have faced two different formulas from two different documents. I don't know ...
0
votes
1answer
18 views

Question about Logistic regression-1

As I am currently studying Logistic regression, but I am still new to this. I have encountered a sentence and a word below in red circles that I can only image but not with my own clear ...
2
votes
2answers
34 views

Question about Logistic Regression - 4

I am currently studying on logistic regression. So I have found a document on the Internet explaining about it. Somehow, it explains Bernoulli distribution in the beginning and I am having a problem ...
0
votes
1answer
37 views

Whether or not $X_1$,…,$X_n$ are independent and exchangeable

For some n = 1,2,..., let $Y_1$,...,$Y_{n+1}$ denote iid real-valued random variables. Define $X_j$ = $Y_j$$Y_{j+1}$, $\hspace{10mm}$j=1,...,n a) Are $X_1$,$X_2$,...,$X_n$ independent? b) Are ...
4
votes
3answers
45 views

Question about English sentences in statistics?

Can somebody help me interpreting the red circled sentences in planer English? I understand "We view $y_i$ as a realization of a random variable $Y_i$ that can take the values of one and zero" but ...
0
votes
1answer
12 views

Multiplying a binary predictor variable with another predictor variable.

Is it completely valid, to have an equation with a certain amount of variables, where two of the variables multiply each other? For example, I want to have an equation $Y = B_0 + B_1X_1 + B_2X_2 ...
0
votes
1answer
22 views

Question about Logistic Regression - 5

Can somebody give me a clear explanation about logistic regression in bold below? Logistic regression can be binomial or multinomial. Binomial or binary logistic regression deals with situations in ...
0
votes
0answers
11 views

Predictions on the statitistical series [migrated]

I'm in need to summarize possible approaches (as well as their pros and cons) to the problem of statistical series prediction. It's pure theoretical question, an example below was given only for ...
0
votes
1answer
17 views

Understand the English paragraph on association rule.

I am currently studying Association Rule Pattern Mining. I am reading the explanation on wikipedia about it. Somehow, I feel like I have a problem in understanding the paragraph below. Can somebody ...
0
votes
1answer
29 views

Is the sum of predicted y values equal to the sum of actual y values?

Say I have a set of points Y and I want to accuratly predict the values of Y by using three variables X1,X2,X3. Hence my equation is Y=intercept + C1*X1 + C2*X2 + C3*X3 After performing linear ...
0
votes
0answers
33 views

interpretation of ANOVA using RStudio

This is my first post so go easy on me... So I have this table as 'tomato' and I have come up with some linear models to try out which are given below... however I don't know how to interpret the ...
1
vote
1answer
30 views

Difficulty in understanding statistics and inference

I have a random variable, X, with cdf $F$ and pdf $f$. I want to estimate a parameter of $F$, say mean, $\mu$. So what do I do? I construct an estimator, $Y_n$, with several random variable X1, ...
0
votes
1answer
22 views

Calculating Inflection Point in Real World Data

I can think of a few ways to get a good grasp of this problem from an experimental perspective, but I'm looking for a more general explanation that can be applied to different situations. If this ...
0
votes
1answer
39 views

Sampling error with weighted mean

I am studying statistics and I am wondering when it comes to standard error or a sampling if the calculation changes when there are weights added. I have a weighted mean: $$\mu_{w} = ...
0
votes
2answers
34 views

Why is there a difference between a population variance and a sample variance

Sorry if this answer is simple but I was wondering why is there a difference between a population variance and a sample variance? I understand The variance is calculated as: $$\text{Var} = ...
0
votes
1answer
10 views

Weighted variance of a small sample

I am trying to calculate the variance of a small sample. I have the data: ...
1
vote
0answers
28 views

which statistics to use? [migrated]

I have a medical research in which i have two set of data 1) control group [ people who have no ailment] 2) study group [ people who have some particular ailment] Within each category there are ...
1
vote
1answer
14 views

What are the properties of the CDF when two variables are independent?

More specifically, if $X$ and $Y$ are independent variables then does $F(X,Y) = F_1(X)F_2(Y)$? Where $F(X,Y)$ is the joint CDF of $X$ and $Y$ and $F_1(X)$ and $F_2(Y)$ are the marginal CDFs of $X$ and ...
0
votes
2answers
136 views

How to find the following integration

Let $X_1, \cdots, X_n$ be $iid$ normal random variables with unknown mean $\mu$ and known variance $\sigma^2$. How to find $E[\Phi(\bar X)]$, where $\bar X:=\frac{\sum_{i=1}^nX_i}{n}$, please? I guess ...
1
vote
0answers
21 views

A variant of Hoeffding's Inequallity

I'm new to concentration inequalities and I have a question related to Hoeffding's inequality. Let $X_1 ~ \dots X_n$ be a set of i.i.d random variables, s.t. $E[X_i] = \mu$, $Var[X_i] = \sigma^2$, ...
0
votes
1answer
21 views

Is it a wrong expression for the local log-likelihood of logistic regression?

In page 206 of the book 'Elements of statistical learning', the author wrote: The local log-likelihood for this $J$ class model can be written $\sum_{i=1}^NK_\lambda (x_0, ...
0
votes
1answer
19 views

Consequences of violation of independence assumption in ANOVA test

Can you please explain me what is the consequences of violation of independence assumption in ANOVA test? I couldn't visualize it. Does Cochran Theorem relates to ...
0
votes
1answer
25 views

P-P plot and Q-Q plot

How to draw P-P plot and Q-Q plot manually ? I have looked at different site and they explained in various way, such as one said for p-p plot in X-axis there is residual in ascending order and in ...
0
votes
1answer
28 views

Existence of Expectation

Question: Let $X_1$, $X_2$, and Z denote independent, real-valued random variables. Assume that $Pr(Z=0) = 1 - Pr(Z=1)$ = $\alpha$ for some $0 < \alpha < 1$. Define $Y = \left\{ ...
1
vote
1answer
13 views

Confidence interval for difference in means

I need to obtain a 95% confidence interval for the indifference in the mean score overall I have the following data which states subject (A-L) and then Test and Retest A B C D E F G H I J K ...
0
votes
1answer
16 views

Chi square test, double counting?

We're testing whether three species are affected differently by some poison, getting this table (type/dead/alive/tot): A, 10, 20, 30 B, 16, 14, 30 C, 22, 8, 30 Under H0, we're expeting 16 to live ...
0
votes
1answer
31 views

Cross-Validation

Does anyone understand the paragraph below? The paragraph comes from Cross-valiation explanation at wikipedia. "It can be shown under mild assumptions that the expected value of the MSE for the ...
0
votes
1answer
17 views

Is the statement: $p\left(\left.y\right|h^{-1}\left(\varphi\right)\right)=p\left(\left.y\right|\varphi\right)$ correct?

Say I have a likelihood function $p\left(\left.y\right|\theta\right)$ and I make the reparameterization $\varphi=h\left(\theta\right)$ using the bijective function $h$ with inverse $h^{-1}$. Then it ...
1
vote
1answer
31 views

Doubts on Bayes hypothesis test

I meet one problem on hypothesis testing in statistic theory. "Assume given the probability spaces $(X,S,\mu_i)$, $i=1,2$. $H_i$, $i=1,2$, is the hypothesis that $T$ is from the statistical ...
0
votes
1answer
53 views

Better estimators with absolute function pdf

I have some pdf $f(x|\theta) = (\theta/2) ^ {|x|} \cdot (1 - \theta) ^ {(1 - |x|)}$ where $x = -1, 0, 1$, and $0 \le \theta \le 1$. I found the MLE of theta by denoting $n_{-1}$ the number of ...
1
vote
1answer
22 views

Decompose a sum of Gaussian curves

I have a data set with 2 different curves in a .csv file. Both curves are a sum of Gaussian curves and I'd like to be able to decompose these curves into their substituent addends: ...
0
votes
0answers
15 views

Calculating person-time

Suppose that an investigator wants to measure the incidence rate of high blood pressure in the $1997-98$ freshman class of a university. Assume that there were $1000$ entering freshmen and that this ...
1
vote
1answer
17 views

Uncertainty on an estimator

Well first I want to say that I have a very weak background in stats/probability but I still hope that the question I want to share with you makes sense. I have a set of binary (coming from a set of ...
0
votes
1answer
11 views

Statistics Sample requirements

In statistics , a sample should be random, have a sample size less than one-tenth of the population and be normally distributed for it to be viable for simple statistical analysis. I understand fully ...
3
votes
1answer
63 views

Normalization for Chi square test

The formula for the Chi-Square test statistic is the following: $\chi^2 = \sum_{i=1}^{n} \frac{(O_i - E_i)^2}{E_i}$ where O - is observed data, and E - is expected. I'm curious why it depends on ...
2
votes
4answers
49 views

The Objectivity of Statistical Testing

I have a very generic question about applied statistics. Suppose, to make things simple, we have a biased coin with probability $p$ of landing heads. We want to determine if our coin is truly fair - ...
0
votes
0answers
29 views

Proving a statistic is sufficient and NOT complete

Let X be a single observation from the distribution , $P(X=x)= \begin{cases} \theta, & \text{if $x$ =-1} \\ (1-\theta)^2\theta^x, & \text{if $x =0,1,2,3,...; 0<\theta<1$} \\ ...
0
votes
0answers
44 views

Sufficient statistic for normal distribution

Let X from a Normal distribution $(\theta,1)$. a) Find a sufficient statistic for $\theta$. b)Is $S_n^2$ sufficient for $\theta$ My answer for part a) The joint p.d.f= $1 \over (2\pi)^{n/2}$$e^{{-1 ...