New answers tagged

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"A" point estimator doesn't have to be the "best" point estimator that takes into account all the information. So you can just take the mean of the sample, this is a point estimator of $\lambda$.


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svycontrast computes "linear or nonlinear contrasts of estimates produced by survey functions (or any object with coef and vcov methods)." That is, it takes the estimates that it is given and computes functions of them. It does not do anything with the individual data -- it does not even see the individual data (in general). When you do svycontrast(a, ...


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Note that this would be a beta distribution such as the one in here with $\alpha = \theta$ and $\beta = 1$. First, consider that $E[x] = \int_0^1x\theta x^{\theta-1} dx= \theta \int_0^1x^\theta dx=\frac{\theta}{\theta+1} x^{\theta+1}|_0^1 = \frac{\theta}{\theta+1}$. Then you can find $\hat{\theta}$ using the method of moments such that $\frac{\hat{\theta}}{...


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1 Your equation number 5 should be $$\hat{y}_t(\theta)=\varphi_t \theta + \hat{y}_{t-1} \qquad \text{for} \,\, t=0, 1, 2,\dots$$ instead of $$\hat{y}_t(\theta)=\varphi_t \theta + y_{t-1} \qquad \text{for} \,\, t=0, 1, 2,\dots$$ 2 Also you compute the derivative $\varphi$ based on the matrix that contains values of $S, I ,R, D$ that are the observed ...


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What you have here is a set of two simultaneous equations with two unknowns. Assuming that the explanatory variable in the regression is not constant (so that the design matrix has linearly independent columns), these equations have unique explicit solutions. (The solution for the slope coefficient is given in the linked notes you gave.) The explicit ...


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Coefficient estimates depend on which independent variables (i.e. the $x_i$'s) you include in your regression (not the coefficients explicitly). Which independent variables you include impacts how the 'terrain' of the cost function (i.e. the error sum of squares) looks, and hence where the minimum of the cost function occurs. The parameters are estimated ...


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Notation. Let $\pi = P(\text{Disease})$ be the prevalence of the disease in the population and $\tau = P(\text{Pos Test})$ be the proportion testing positive. For the test, let $\eta = P(\text{Pos}|\text{Disease})$ be the sensitivity and $\theta = P(\text{Neg}|\text{No Disease})$ be its specificity. Also, given test results, let $\gamma = P(\text{Disease}| ...


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Summary: Yes, a balanced block design have to be connected. You say you get different answers from different sources. If we are to discuss this, you must give references to those different sources with conflicting answers! Your reference is Theory of Block Designs by Aloke Dey. I do not have access to that, but to the newer INCOMPLETE BLOCK DESIGNS here ...


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Adding to Xiaomi answer, here is the derivation, using Leibnitz rule: $\require{cancel} \frac{\partial \rho}{\partial \delta} = \int_{-\infty}^{\delta}\pi(\theta|x)d\theta - \int_{\delta}^{\infty}\pi(\theta|x)d\theta \\ \frac{\partial^2 \rho}{\partial \delta^2} = \pi(\delta|x)\cdot1 - \cancel{\pi(\delta|x)\cdot0} + \cancel{\int_{-\infty}^{\delta}0d\theta} -...


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The mathematical definition of an unbiased estimator is: $E[u(X_1, X_2,\dots,X_n)]=\theta$. In English, this formula means that the expected value of a statistic, generally given as $u(X_1, X_2], \dots, X_n)$, equals the parameter (of the population) value. While a parameter has a single (probably unknown) value, a statistic has a distribution of values (...


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You are mixing up some ideas I think. In the case of inferential statistics, you can never know the population parameter but you can estimate it using a sample. The one sample you take is but one of an infinite set of possible samples you might have. The distribution of those infinite sample means is usually normally distributed. But the mean of the one you ...


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Death rate Using death rate may work when people that die have most likely acquired the virus locally. However, for the moment, many people die because they acquired the virus during a visit to another area, or because they got it from another person that acquired the virus abroad. Thus this death-rate based number is not very accurate unless the virus ...


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It seems that there is a blog post that also deals with this question. If you have deaths in your region, you can use that to guess the number of true current cases. We know approximately how long it takes for that person to go from catching the virus to dying on average (17.3 days). That means the person who died on 2/29 in Washington State probably got ...


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The usual setting for estimating a joint pdf, is of having paired observations, say a sample of the form $(x_1, y_1), (x_2, y_2), \dotsc, (x_n,y_n)$. Then we can do business. If you have less than that, you should tell us more about your context, and why ... There are many possibilities. If you know your two variables are independent, then the marginals ...


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You (null) model is $X \sim \mathcal{Binom}(5,p)$ and to estimate $p$ you just sum up the number of boys, the number of children and divide. In R: xs <- 0:5 Ns <- c(34, 128, 233, 267, 144, 55) boys <- sum(xs*Ns) children <- 5*sum(Ns) phat <- boys/children Then you want to test if the distribution really is binomial, that is, thatbthe ...


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The bias of an estimator $\hat \theta_n$ of a parameter $\theta^0$ is defined as $$B(\hat \theta_n) = E(\hat \theta_n) - \theta^0,$$ where the $n$ subscript indicates that the estimator is a function of the sample size. It follows that the distribution of the estimator is a function of the sample size, meaning that, in general, for each different $n$ the ...


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