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1
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1answer
19 views

positive price coefficient after instrumentation in demand estimation

I need to complete an assignment for Industrial Organization course where one of the tasks is to estimate a discrete choice demand model. This means I basically need to estimate a linear model: ...
0
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0answers
7 views

Difference estimation VS estimation of the mean [on hold]

What is difference estimation? How does difference estimation differ from estimation of the mean?
-1
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2answers
40 views

$X \sim N(0, \sigma_1^2)$, $Y \sim N(0, \sigma_2^2)$, $U = X+Y$. What are $E[X|U], E[Y|U]$?

$X \sim N(0, \sigma_1^2)$, $Y \sim N(0, \sigma_2^2)$, $U = X+Y$. What are the values of $E[X|U], E[Y|U]$? I understand $E[X|U] + E[Y|U] = U$, but I'm not sure how to move forward...
0
votes
0answers
33 views

Likelihood and sufficient statistics

a)Find the maximum likelihood estimador for $a$ in the density $f(x;a)=\frac{2}{a^2}(a-x)I_{(0,a)}(x)$. b)Is it a sufficient statistics? I did $$\prod f(x;a)=\prod \frac{2}{a^2}(a-x)I_{(0,a)}(x)$$ ...
1
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0answers
35 views

Sufficient statistics, continuous distribution

Let $X_1,X_2,..,X_n$ be a random sample from the density $$f(x;\theta)=\theta x^{-2}I_{[\theta,\infty]}(x)$$ a)Is $T_1=min[X_1,...,X_n]$ a sufficient statistics? My doubt here is the right way to ...
2
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1answer
37 views

Sufficient Statistics, normal distribution

Let X be a single observation from $N(0,\theta)$. $(\theta=\sigma^2)$ a)Is X a sufficient statistics? b)Is |X| a sufficient statistics? What I did ...
-1
votes
1answer
61 views

Slutsky's Theorem to show convergence to Standard Normal Distribution

We are given $W_n = \frac{\bar{X}-\lambda}{\sqrt{\bar{X}/{n}}}$ and need to show it converges to a standard normal distribution. EDIT: The square root in my original post did not extended over the ...
1
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1answer
16 views

Finding z-scores from z table relating to confidence intervals

I'm having trouble finding the proper $z$ score so that I can find the $99\%$ confidence interval. $\bar{x} = 6.01231$. with an $s$ of $1.96833$ and $n$ of $26$, and I got $2.575$ for ...
1
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0answers
14 views

Probability of selecting exactly 2 members of a group of 7, out of 35 people, if 3 people are picked

There are 7 friends A, B, C, D, E, F, and G that belong to a classroom of 35 students. Three students are chosen from the 35. What the probability that exactly two of the group of friends is chosen? ...
1
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1answer
24 views

Modeling different lag structures

I know there are various information criteria that can be used to compare model specifications, including those with different lag structures. I can easily compare the Akaike Information Criterion ...
1
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0answers
6 views

R-Studio summary page independent variable percent [on hold]

What in R Studio's summary of data shows percent of the independent variable if the dependent Variable is 0? For instance, my Y axis is an independent variable and my question is asking if the ...
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0answers
5 views

Understanding the Precision-Recall breakeven point in ranking

Consider an IR system that retrieves all document and rank them in order of relevance. Now, we can calculate Precision and Recall at each rank. Does the breakeven point (recall=precision) always ...
1
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0answers
33 views

Set the seed to a specific number?

i'm quite new to stata and statistics, and I have some questions I hope some of you can answer. My first question is regarding "seed". I have a assignment where i'm asked to use 300 repetitions and ...
0
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0answers
7 views

Self-study (Expectation Maximization on Bivariate Normal Distribution)

I see this example is also "classic", and I am attempting to understand how to approach it. I have an iid sample drawn from a bivariate normal distribution with mean vector ($\mu_1, \mu_2$) and ...
3
votes
1answer
41 views

Variance of a product of Bernoulli with another distribution

This is probably a stupid question, so my apologies if this is too simple. I have a distribution X, now I play the following game: I toss a coin, if it falls on a head, I get nothing, if it falls on ...
3
votes
1answer
18 views

Variance Reduction calculate

If $\phi(x)=\frac{e^x-1}{e-1}I_{[0,1]}(x)$, use the variance reduction techniques: Importance Sampling, Antithetic Variables, Control Variates.Compare the methods and check which provides the greatest ...
3
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1answer
28 views

Convergence of standardized means of a Bernoulli variable / CLT

The Question Consider a binary random variable X that satisfies: $Pr(X = 0) = \theta \ \ \ $ and $Pr(X = 1) = 1−\theta $ for $\theta \in (0, 1)$ an unknown parameter. Suppose an i.i.d. sample of size ...
0
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0answers
35 views

Monte Carlo Integration, Importance Sampling

Suppose I want to apply Importance Sampling in the following integral $$\int_X h(x)f(x)dx=\int_X h(x)\frac{f(x)}{g(x)}g(x)dx$$ where $f(x)$ is a probability density function, so I need another ...
1
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0answers
15 views

Understanding Zipf's law calculation for probability of a word

So, I am analyzing a a corpus of ~1,000,000 words and I am trying to understand how I can use Zipf's law. I found on some textbook slides the following formulas: $$f_r = c/r$$ $$p_r = k/r $$ where ...
1
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1answer
68 views

How to find the normalizing constant for a distribution of unbounded support?

The probability density of a random variable is $$f(x) = ax^2 e^{-kx} ;k\gt0,0\le x\le \infty$$ What is the value of $a$? I understand that first we'll have to take the integral of the function ...
0
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0answers
6 views

What are pro-cons of Wilcoxon signed ranks when compared to sign-test on information retrieval

I have to judge whether a search engine A retrieves better results than B. I have the average precision of each for 10 different queries. I run both sign-test and Wilcoxon signed-tanks test. Now, the ...
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0answers
19 views
+50

Collaborative filtering using a linear model

Consider I have a set of movies and a set of users ($A$,$B$,$C$,$D$) and a matrix with related scores (I can have gaps in this matrix). Consider a linear regression model where a specific user A's ...
0
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0answers
76 views

Show $∫_0^t X(t,s)dB(s)$ is a Gaussian random variable $Y(t)$ [duplicate]

Show that if $X(t)$ is non-random (does not depend on $B(t)$) and is a function of $t$ and $s$ with $\int_0^t X^2(t,s)ds<\infty$, then $\int_0^t X(t,s) dB(s)$ is a Gaussian random variable $Y(t)$. ...
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0answers
194 views

Show that $\int_0^t X(t,s) dB(s)$ is a Gaussian random variable $Y(t)$ [closed]

Show that if $X(t)$ is non-random (does not depend on $B(t)$) and is a function of $t$ and $s$ with $\int_0^t X^2(t,s)ds<\infty$, then $\int_0^t X(t,s) dB(s)$ is a Gaussian random variable $Y(t)$. ...
2
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1answer
34 views

Model to predict categorical outcome from continuous and categorical variables

I have to fit a model to test whether Learning (1=learned, 0=failed) depends on lizard sex (M or F), Lizard SVL (snout-vent length), or an interaction of the two. I am new to both R and this website. ...
1
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2answers
27 views

Hypothesis testing statstics

The management of a fast-food restaurant claims only 50% of its customers read the nutritional labels attached to the containers of its products. A random sample of 92 people were surveyed and asked ...
0
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1answer
44 views

How to test a hypothesis about the mean based on an assumed normal distribution?

The entrance onto a major bridge in New York City was engineered to accommodate an average of $3800$ vehicles per hour. However, a random sample of nine observations gives an average of ...
2
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2answers
40 views

Check my proof regarding convergence in probability

I got a bit confused during the end of this proof so I am asking for a check. Take $$Y(n) = \begin{cases} 1 &\mbox{with probability} \ 1 -p_n \\ n & \mbox{with probability} \ p_n \end{cases} ...
3
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0answers
55 views

Bayesian Analysis of Box-Cox Transformation

This problem is problem 5 in Chapter 7 of Bayesian Data Analysis, 3rd edition. Consider the Box-Cox transformation: $y_i^{(\lambda)} \sim \mathcal{N}(\mu, \sigma^2)$ where $y_i^{(\lambda)} = ...
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0answers
13 views

How can I express $D_{m,n}$ as a distribution free statistic in terms of $d_l$

Consider 2-sample problem with m and n observations from the mutually independent, absolutely continuous populations $F_X$ and $F_Y$, respectively, define 2-sided kolmogorov-smirnov statistics ...
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0answers
21 views

How do I plot an abline() when I don't have any data points (in R) [migrated]

I have to plot a few different simple linear models on a chart, the main point being to comment on them. I have no data for the models. I can't get R to create a plot with appropriate axes, i.e. I ...
3
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2answers
66 views

Significance of stats on t-test problem

Hi there, I am trying to perform a visual analysis of significance on these stats. Other information provided is the Standardized motor skills test score [M = 100, SD = 15], not sure if this is ...
2
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1answer
57 views

Can you show that $\bar{X}$ is a consistent estimator for $\lambda$ using Tchebysheff's inequality?

This question was taken from a practice exam in my statistics course. Given a random sample $X_1, X_2, ... X_n$ from a Poisson distribution with mean $\lambda$, can you show that $\bar{X}$ is ...
2
votes
1answer
41 views

Pointwise convergence of the cdf of normal random variables

For a sequence $X_1, X_2, \dots $, Let $F_n(x)$ denote the cdf of $X_n$. Suppose our sequence is $X_n \sim N(0,n) $ then for all $x$ the point-wise limit of $F_n(x)$ is $\frac{1}{2}$. How would one ...
0
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1answer
16 views

Blocks in a given numeric vector [closed]

Given a sequence of integers: 1,1,2,3,1,3,4,5,6,2,2,2,7. It is required to report the no. of occurrences of each integer {1,2,3,4,5,6,7} but block-wise. Block-wise means an integer occurring in the ...
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2answers
58 views

Kernel of a Normal Distribution

From Wikipedia , The kernel of a probability density function (pdf) or probability mass function (pmf) is the form of the pdf or pmf in which any factors that are not functions of any of the ...
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0answers
31 views

University of London Past Paper help [closed]

Hey this is my third year trying to pass my stats exam, I simply have a bad block when it comes to statistics and need some help. I'm trying to do a 2014 past paper and so far the only thing i can do ...
0
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1answer
30 views

Autocorrelation or Serial Correlation

Autocorrelation is also known as serial correlation . Why is the terminology serial used ? Is there anything unserial or ...
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2answers
44 views

Correlation Coefficient for lag $k$ in Time Series Data

Formula of Pearson Correlation Coefficient is : $$r_{xy}=\frac{\sum_{i=1}^{n}(x_i-\bar x)(y_i-\bar y)}{\sqrt{\sum_{i=1}^{n}(x_i-\bar x)^2}\sqrt{\sum_{i=1}^{n}(y_i-\bar y)^2}}$$ In Time series ...
1
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2answers
111 views

Multivariate Data

There is a built-in data set USArrests data in R software . ?USArrests We use this ...
0
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1answer
10 views

Deriving Confidence Interval from pivotal statistic

Using the pivotal statistic $T = \frac{Y ̄ −μ}{s/\sqrt{n}}$ derive the $(1 − α)100%$ confidence interval for the mean $μ$, where a random sample of size $n$ is taken from a very large population and ...
3
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1answer
44 views

Control Variates, Monte Carlo integration

Exercise: Calculate $P(N>2.5)$ where $N$~$N(0,1)$ through simple monte carlo integration, and then use control variables to reduce the variance of my estimator. I did ...
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0answers
34 views

Why are these formulas for the variance equal?

I am trying to understand why the simple bootstrap procedure does not work, but for now I would like to know why we can we write $s^2_n = \frac{1}{n} \sum^n_{i = 1} X^2_i - (\bar{X}_n)^2$ ? This is ...
4
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1answer
102 views

Variance reduction technique in Monte Carlo integration

I have some trouble understanding the variance reduction method called "Antithetic variables": Suppose that the integrand is $g(x)=x^2$ and the reference density $f(x)=e^{-x}I_{[0,\infty]}$ is ...
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0answers
21 views

Regression analysis of Distance Covered by a football player [closed]

I am supposed to create a regression analysis project to my Econometrics class. The dependent variable would be Distance Covered per game by a player and the indipendent variables would be the ...
0
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2answers
37 views

Expected number of trials

Consider independent trials, each of which is a success with probability p and derive the expected number of trials needed to obtain k consecutive successes by (a)conditioning on the time of the ...
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0answers
13 views

Finding MLE by factor analyzing the correlation matrix

In the book "Applied Multivariate Statistical Analysis" written by Johnson and Wichern, they have mentioned that the MLEs ($\hat{L_z}$) are obtained from the the correlation matrix $R$ by inserting ...
0
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2answers
15 views

A step of a proof regarding the Nadaraya-Watson estimator

Let the data be $(y_i , X_i) $ where $y_i$ is real valued and $X_i$ is a q-vector. The regression function for $y_i$ on $X_i$ is $g(x) = E(y_i | X_i = x)$, we can write this as: $$y_i = g(X_i) + ...
7
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1answer
181 views

Generating Binomial Random Variables with given Correlation

Suppose I know how to generate independent Binomial Random Variables. How can I generate two random variables $X$ and $Y$ such that $$X\sim \text{Bin}(8,\dfrac{2}{3}),\quad Y\sim ...
1
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0answers
34 views

Regression with percentage change?

As the education rating of a Canadian city decreases by $1\%$, the crime rating will change by ___ (make sure you include the negative sign if warranted) The line of the equation I found to be ...