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    Empirical Survivor Function (esf)

    From page 26, chapter 2 of the reference "Tableman, M., & Kim, J. S. (2003). Survival analysis using S: analysis of time-to-event data. CRC press", I have found the definition of the empirical survivor function (esf) is S(t) = (number of individuals > t)/n . But from page 80, chapter 3 of...
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    Parametric vs. Nonparametric.

    Suppose a researcher estimated a parameter in parametric way with correct distributional assumption. Another researcher estimated the same parameter in non-parametric way. Will there any difference of accuracy (bias) in estimation in these two situations?
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    Kaplan-Meier Estimate

    Let T_i is the survival time for individual i (i=1,2,\ldots, n) and C_i be the time to censoring. Let U_i=\min(T_i,C_i). And \hat S(U_i) is the Kaplan-Meier estimator for the censoring distribution. Suppose R_i and Z_i are two indicator functions. Also,p is a probability. Consider the following...
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    Specifying the initial values of likfit function of geodata in R

    I have a geostatistical data. For analysis, I am using `geoR`. I want to estimate the parameters. But `likfit` or `variofit` function requires initial values for the covariance parameters: \sigma^2 (partial sill) and \phi (range parameter). But I can't guess the initial values for my data...
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    Restricted Maximum Likelihood (REML) Estimate of Variance Component.

    Let, \mathbf y_i = \mathbf X_i\mathbf\beta + \mathbf Z_i\mathbf b_i+ \mathbf\epsilon_i, where \mathbf y_i\sim N(\mathbf X_i\mathbf\beta, \Sigma_i=\sigma^2\mathbf I_{n_i}+\mathbf Z_i \mathbf G\mathbf Z_i'), \mathbf b_i\sim N(\mathbf 0, \mathbf G), \mathbf\epsilon_i\sim N(\mathbf 0...
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    Differentiation Involving Determinant.

    I have to compute the following differentiation : \frac{\partial}{\partial\sigma^2}\det[\mathbf X_{p\times n}'(\sigma^2 \mathbf I_{n}+\mathbf Z_{n\times q}\mathbf G_{q\times q}\mathbf Z_{q\times n}')^{-1}\mathbf X_{n\times p}], where \sigma^2 is a scalar, \det denotes determinant, \mathbf...
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    Showing Left Side to Right Side.

    Let \mathbf x is a (p\times 1) vector, \mathbf\mu_1 is a (p\times 1) vector, \mathbf\mu_2 is a (p\times 1) vector, and \Sigma is a (p\times p) matrix. Now I have to show -\frac{1}{2}(\mathbf x-\mathbf\mu_1)'\Sigma^{-1}(\mathbf x-\mathbf\mu_1)+\frac{1}{2}(\mathbf...
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    Defining Contrast Matrix

    In the book Applied Longitudinal Analysis, 2nd Edition there is an example in the chapter "Marginal Models: Generalized Estimating Equations (GEE)" in "Muscatine Coronary Risk Factor Study" sub-section. I am illustrating it below : Let Y_{ij}=1if the i^{\text{th}} child is classified as obese...
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    Hypothesis difficulty

    Let Y_{ij}=1 if the i^{\text{th}} child is classified as obese at the j^{\text{th}} occasion, and Y_{ij}=0 otherwise. The marginal probability of obesity at each occasion follows the logistic model log\frac{\Pr(Y_{ij}=1)}{\Pr(Y_{ij}=0)}=...
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    R: Date Calculation

    Let I have some data against time : time <- seq(ISOdate(2007,7,1,0), ISOdate(2008,4,5,23), by = "1 hour") y <- rnorm(n = length(time)) dat <- data.frame(time = time, y = y) Now I am trying to create another variable `day_index` which will take value 1 for 2007-07-01...
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    Is Sea Level Rise Data from NOAA an Areal Data?

    I am working on sea level rise and I collected the data from NOAA. In the "meta", they describe the data is obtained by : Hourly : three-point Hanning filter centered on the hour Daily : 119-point convolution filter (Bloomfield, 1976) centered on noon applied to the hourly data with...
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    R warning : the condition has length > 1 and only the first element will be used

    I have data like following : year month day y 2007 7 1 3845 2007 7 2 3756 2007 7 3 3564 . . . 2007 7 31 3478 2007 8 1 3245 2007 8 2 3764 . . . 2007 8 31 3123 . . . 2008 12 31 3890...
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    Difficulty in Selecting Thesis Topic

    I am a graduate student. I have a 6 credit thesis and I am interested in the field of longitudinal and Bayesian. My supervisor said me to choose my topic. But I am not understanding if I choose a topic how can I know what is the scope (further extension) of this topic because I can't only...
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    Unique Solution.

    Is the following statement true that : "To get unique solution of each parameter in a model, number of equations must be greater than or equal to the number of parameters." ??? Regards.
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    Does Imposing a Constrain Make a Method More Powerful?

    Suppose we have 100 patients in a randomized trial. 50 of them are in treatment group and the rest are in placebo group. This is a longitudinal study so that we measure the response from each individual at four different periods: baseline, week 1, week 4, and week 6. Now suppose we have good...
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    Defining Contrast Matrix

    Suppose I have a binary Covariate X which is defined as X = \begin{cases} 1, & \text{if treatment group} \\ 0, & \text{if placebo group} \end{cases} The model is \mathbb E[Y] = \beta_0 + \beta_1X, where Y is a continuous random variable. If X=0, then \mathbb E[Y] =...
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    Calculating the amount of underestimation

    Coverage rate for a parameter is 91.2%, and the nominal coverage rate is 95%. If the confidence interval is based on asymptotic standard normal, then the amount of coverage 91.2% implies that the standard errors for the parameter is estimated about 15% too small. Because z* value used to make a...
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    Simple Algebraic Calculation about underestimation

    In a findings, it is found that the non-coverage rate for the second-level intercept variance is 8.9%, and the non-coverage rate for the second-level slope variance is 8.8%. Although the coverage is not grotesquely wrong, the 95% confidence interval is clearly too short. The amount of...
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    Are Unbiasedness and Accuracy of the estimates, all to determine the sample size?

    For determining sample size , why is to focus on the unbiasedness and accuracy of the estimates ? Are this two properties, unbiasedness and accuracy of the estimates, all to determine the sample size ? In a simulation study of multilevel model, authors chose that combination of sample size...
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    Calculating Overall Relative Bias

    I am in some trouble to understand how is to calculate the overall relative bias. In this link, there are results of overall relative bias in "Parameter estimates" sub-section under "Results" section. There they mentioned that : Could you please explain me how did they calculate it? I had...