0
votes
1answer
25 views

Does consistent estimators have in-variance property?

If $(T_n)$ is a sequence of consistent estimators of a parameter $\theta$ ( i.e. for every $ \epsilon >0$ , $\lim_{n \to \infty} P [ \space |T_n -\theta|< \epsilon ]=1$ ) , then is it true that ...
0
votes
1answer
19 views

Testing a hypothesys about a survey?

A survey of $61, 647$ people including questions about office relationships. Of the respondents, $26$% reported that bosses scream at employees. Use a $.05$ significance level to test the claim that ...
0
votes
1answer
24 views

Hypothesis Testing, P-value, T-test Statistic, Confidence Interval

I am writing a report for my class project. I am taking statistics and I am REALLY panicking with the results I have in my report. I do not think my calculations for t-test statistic or confidence ...
0
votes
1answer
27 views

Is difference between two sets of measurements significant?

Consider the following experimental setting: I have two machines $m_0$ and $m_1$ of which I would like to know which one performs better. For this I have set up an experiment to measure the time it ...
0
votes
2answers
34 views

Biased MLE estimate of mean (expectation)

Please give an example of p.m.f. or p.d.f. , the maximum likely-hood estimate of whose mean (expectation) is a biased estimator . Thanks
1
vote
1answer
29 views

Variance- covariance matrix

Consider $H$ denotes hat matrix and $e$ denotes residual. In the book Applied regression Analysis by Draper/Smith, it is written that : $\mathbb V(e_i)$ is given ...
0
votes
1answer
30 views

Confidence Interval for Regression Coefficient ,$\beta$

In the book 'Applied regression Analysis' by Draper/Smith, it is written that : Obtain individual $100(1-\alpha)\%$ confidence interval for the various parameters separately from the formula ...
0
votes
1answer
24 views

Calculating optimum values of $u$ and $m$ from $\mathbb V(\bar {y_2}\prime)=\frac{S_2^2(n-u\rho^2)}{n^2-u^2\rho^2}$

I have to find optimum sample size in sampling on two occasions. Suppose that the samples are of the same size n on both occasions. In selecting the second sample, $m$ of the units in the first ...
0
votes
1answer
23 views

How do I convert non-normal distribution to a normal distribution?

I have the below graph I drew using histogram in Excel but when I got my data and graphed it, certainly it is not a normal distribution. My assignment required me to gather some data and draw normal ...
0
votes
1answer
32 views

Mantel-Haenszel $\chi_1^2$ statistic

I was doing a particular example from the book Epidemiologic Research by Kleinbaum(example 15.6) and didn't understood some basic statistical aspect. ...
0
votes
0answers
20 views

Statistics on a column of values

I have a class project that I am working on as an engineering student but the course is probability and statistics so I don't really know how to make sense or use of what I am learning so I thought of ...
0
votes
1answer
26 views

A question about $\chi^2$ distribution

Ok, i have a question but i start with a definition first so that one can get the context. (All variables in question have the same variance and under $H_0$ which we are considering - they have the ...
0
votes
1answer
34 views

Method of moments for Beta $(\alpha_1,\alpha_2)$ distribution

I am trying to solve for the first two moments of a Beta$(\alpha_1,\alpha_2)$ distribution. We know that the first moment is equal to: $\mu_1 = \frac{\alpha_1}{\alpha_1+\alpha_2}$ and the second ...
2
votes
4answers
124 views

Is it true that $\mathbb E[{\frac{X}{Y}]}={\frac{\mathbb E[X]}{\mathbb E[Y]}}$?

If $X$ and $Y$ are both random variables, does it hold $$\mathbb E\left[\frac{X}{Y}\right]={\frac{\mathbb E[X]}{\mathbb E[Y]}}$$ ??
-1
votes
0answers
21 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 ...
1
vote
1answer
16 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 ...
1
vote
1answer
27 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
19 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
20 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
34 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
19 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
27 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} = ...
-1
votes
0answers
23 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
31 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
23 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
1answer
26 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
19 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
36 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
38 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
23 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
1answer
19 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
30 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 ...
1
vote
1answer
31 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
25 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
54 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
37 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
1answer
15 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
146 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
24 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
22 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
21 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
28 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
15 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
18 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
32 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 ...