Questions tagged [statistical-inference]

The area of statistics that focuses on taking information from samples of a population, in order to derive information on the entire population.

2,476 questions
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Test for equal means

I have a control experiment and an experiment. In these two experiments, I can detect different peptides. The presence of the peptides in the experiment is measured by determining the concentration of ...
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Is the following always true: $\mbox{Var}[\mbox{Range}(X_1,\cdots,X_n)] = O(n^{-B})$ with $0\leq B \leq 2$?

Here $X_1,\cdots,X_n$ are i.i.d. The two extremes $B=0$ and $B=2$, and the standard case $B = 1$ are illustrated in the picture below. For the reference, see here.
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Proving independence between Beta estimated and Delta in OLS

I know that in ordinary least squares $b$(beta estimated) and $\delta^2$(variance estimated) are independent, but how do I prove that?
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Why wont the mean height of 70 fall under 99.7 percent when using formula: mean+/-3(SD)

Sample problem: In general, the mean height of women is 65″ with a standard deviation of 3.5″. What is the probability of finding a random sample of 50 women with a mean height of 70″, assuming the ...
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How easy is it to create false evidence for a biased coin?

I have a biased coin which comes up heads with probability $p$. I know the value of $p$, but I want to falsely claim that the coin has a different probability of heads, $q$, where $q > p$. To ...
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In the categorial regression using the logit link function, the estimated coefficients are used to calculate the odds ratios or the ratio between two odds, that is, the model is interpreted through ...
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Finding the UMVUE of $\frac{1}{\lambda}$

I have been given the pdf: $$f_X (x; \lambda) = \left(\frac{\lambda}{\pi}\right)^{\frac{1}{2}} x^{-\frac{3}{2}} e^{-\frac{\lambda}{x}}$$ with support $x>0$ and $\lambda>0$. I am asked to ...
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Confusion with Gauss Markov

Consider the the linear regression model Yi = β xi + ei , where the numbers x1, . . . , xn are known, the independent random variables e1, . . . , en have the N(0, σ 2 ) distribution, and the ...
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Why is the KL divergence the number of bits required to represent the error of an estimator?

I am familiar with several interpretations of the KL divergence, last week I heard of a new one, mentioned in a lecture on probabilistic graphical models. It was stated kind of offhandedly, so I hope ...
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If $X_i \sim U(\theta-\frac{1}{2};\theta+\frac{1}{2})$, show that $[X_{(1)},X_{(n)}]$ is a confidence interval
Let $X_1,...X_n$ random sample from $f(x;\theta)=I_{[\theta-\frac{1}{2};\theta+\frac{1}{2}]}(x)$. a) Show that $[X_{(1)},X_{(n)}]$ is a confidence interval for $\theta$. b) Compute the ...