# estimation

1. ### graduating multi-decrement tables

I need to construct a multi-decrement table and I've had much success withestimation of crude rates, but now I feel that I need to graduate the rates as well as project certain rates forward for states that have not yet materialised in my data. Is there anybody that can direct me to some good...
2. ### Statistical inference

Hi there, I would like to ask a couple of basic questions: 1. What is the difference between estimation and hypothesis testing? I mean are they two options for inference? or estimation of the parameters comes first and then we apply the hypothesis testing? 2. How can I determine what is...
3. ### Nonlinear least squares method and its assumptions

I know that when estimating and using ordinary least squares, irregular terms have to be iid N(0, σ2 ). Now I want to use nonlinear least squares method for estimations. Are there any specific conditions that irregular terms have to fullfill? Or do they have to be still iid N(0, σ2 )? Thank...
4. ### Systematic component variation

The appendix of the paper of [McPherson et al (1982) contains a derivation of the systematic component variation SCV. I understand the derivation with exception of the first step. Here are the premisses: O_i: observed cases in region i E_i: expected cases in region i \lambda_i...
5. ### Estimating location of lower tail

Say I have a sample, assumed from a Normal Distribution. I want to find a confidence interval for this parameter: L = \mu - \alpha * \sigma where \alpha is a known constant. I guess I should use the estimator: \bar{x} - \alpha*s But what standard error should I use? Just for...
6. ### estimating expected value of a difficult cost function.

suppose i want to compute the following expectation: E = \int C(x)f(x)dx where x follows a known pdf f(x) from which we can easily draw samples, and C(x) is a function that is very difficult to compute for given x. As a result, i can not solve the integral analytically or numerically. Suppose...
7. ### Poisson/Gamma model (empirical Bayes), prior distribution parameters calculation

Hello everyone, I want to calculate the α and β estimates of the prior (Gamma) distribution for the Poisson/Gamma model based on the Empirical Bayes method, however I cannot find any closed-form equations from literature. Any idea? Thank you in advance for your help!
8. ### Estimating the Average and Standard Deviation with Missing Data

I need a way to shows me how the parameters of PDF, log-normal in this case, can be estimated based on a set with missing data points at the tail end of a sample. For example, Consider we had 20 numbers with specified μ and σ, and then missed two largest number of them. How do we can estimate...
9. ### Regression analysis(?) for multiple independent variables

Hello all, Apologies for posting an elementary query, but my stats is very rusty. Not looking for an explicit solution, necessarily, just a pointer in the right direction. (And if I've posted to the wrong sub-forum, I'd be grateful for suggestions.) I have N records. Each contains M real...
10. ### Easy question regarding SEM in lisrel

Hey all, I'm running a full SEM in lisrel and I'm having an issue. Below is the code. The issue is namely this: I specified Lambda Y as full and fixed, and then freed my 6 relevant parameters (1,1; 2,1; 3,2; 4,2; and 5;3). HOWEVER, Lisrel is only estimating LY(2,1) and LY(4,2) and the rest...
11. ### Parameters estimation.

It is known that a sample consisting of the values 12, 11.2, 13.5, 12.3, 13.8 and 11.9 comes from a population with density functionf (x, α, β) = ( β/ \α ) (1 /x ^{ β +1}), for x>=1, α>0, β>0. Estimate the values of α and β. Here I have two parameters, and values, do I have to derive first...
12. ### Finding a UMVUE for variance of normal distribution

Let 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 \bar X is the sample mean and S^2 is the sample variance. Then assuming that (\bar...
13. ### Inference using simulated quantile function

I generated a quantile function \hat X using Monte Carlo simulation. The random variable I simulate is the mean value of 5 draws from an i.i.d. range statistic Y. I.e., I have Y(\sigma) \sim \sigma F(), and I simulated the value of X(\sigma=1) \sim \sum_{1}^{5} y(1)_i / 5. Is it valid for...
14. ### Biased and un-biased estimators.

I am working with the Rayleigh-distribution and note that on Wikipedia they say that s^2 = 1/(2N) sum x_i^2 is an unbiased estimator of sigma^2. Now they also say that s = sqrt(s^2) is a biased estimator of sigma. How can this be?? If one is unbiased, why isn't the other one? I mean, you...
15. ### joint probability with conditional

Hello, What is P(A|B, C)? I have a dataset and I want to estimate the mutual information of A|B and C. The formula for mutual information is Sum_A|B Sum_C p(a|b, c) log( p(a|b, c) / p(a|b) p(b) ) da db I'm looking for a formula for p(a|b, c) Many thanks in advance Xavier
16. ### obtaining an unbiased estimator for the min: x_(1)

How would I go about finding an unbiased estimator for the minimum order statistic for a given PDF and distribution. Example: f(x|theta)=e^-(x-theta) for x > theta found my MLE to be X_(1), the MIN(X_i). Setting my theta_hat = X_(1) and plugging in to n*f(x)*[1-F(x)]^(n-1) I obtain...
17. ### Bootstrap and more

Hi guys, I've 2 questions:
18. ### Introduction to Estimation(need help with terms)

Which of the following definitions is incorrect? Estimation It is a process by which sample data is used to estimate or approximate the value of an unknown population parameter. The estimate can be expressed as a single value, known as a point estimate, or a range of values, known as an...
19. ### Unbiased Estimator.

the radius of a circle is measured with an error of measurement which is distributed normal with mean 0 and variance \sigma^2,\sigma^2 unknown.Given n independent measurements of the radius , find an unbiased estimator of the area of the circle. By using *Maximum Likelihood Estimator* I found...
20. ### VAR or VECM with I(1) and I(0) series

Hello, I am trying to estimate macroeconomic data with VAR. I have a system of 5 equations. 3 of the series are I(1) while 2 are I(0). I have a few questions in estimation: i) can I estimate a VAR with first differences of the three integrated series, and levels of the other two which have no...