Recent content by Jeffack

Sorry about that. You are correct: ##y## is a n-by-1 vector, where n is the number of observations. ##x_1, x_2,...x_{14} ## are all n-by-1 vectors. ##y_i## is the ##i##th element of vector ##y##. ##x_{n,i}## is the ##i##th element of vector ##x_n##. The problem should have been written as...

I am doing a nonlinear least squares estimation on a function of 14 variables (meaning that, to estimate ##y=f(x)##, I minimize ##\Sigma_i(y_i-(\hat x_i))^2## ). I do this using the quasi-Newton algorithm in MATLAB. This also gives the Hessian (matrix of second derivatives) at the minimizing...

Thanks for your reply on this. I realized that I didn't type in one condition (which is the one that really complicates things): 6) ##f''(x)<0##. This combined with (2) means that ##f'(x)## approaches 0 as ##x## approaches ##\infty##. The goal is to have ##A## determine how long the function...

I am trying to create a function of A and x which has the following properties. A is a scaling parameter that determines the shape of the function. I write the function below in f(A,x) form 1) f(A,1)=1 always 2) For all x>1, 0<f ' (x)<1 3) As A approaches some upper bound (which could be...

I had an idea. This could be way off base, but here goes... I'm going to simplify everything here by using an additive error term (rather than multiplying by e^\eta ). For the simple two-stores-in-a-zip example, the actual data-generating-process is: R_{1}=\eta_{1}+r_{1}...

I'm attempting to minimize the sum of squares. So, if there were 3 stores and I observed them all, I would minimize \eta_{1}^{2}+\eta_{2}^{2}+\eta_{3}^{2} . If, instead, stores 2 and 3 are aggregated together, I think that I need to minimize \eta_{1}^{2}+\{\mathrm{some\ approximation\ of\...

Thanks again for all your help on this. To answer your questions... Yes, I have panel data, so I have data for multiple zip codes over multiple months. Yes, that's what I'm trying to do. I'm summing the error over each month and each location. If I knew each store's revenue (which I don't)...

Thanks for the help thus far. The short answer is that, given observed R and predicted r for each location, I would like to estimate \eta_{1}^{2}+\eta_{2}^{2}+...+\eta_{N}^{2} , where N is the number of stores in that location. The more explanatory answer is that I am trying to...

You're correct about the "estimation" vs "calculation" comment. Regarding your question at the end, I am assuming that r is the same for each store within an area (I use zip codes as my area). In other words, my model spits out a single predicted revenue number for each zip code. Example...

Yes. If they are summed, I know how many stores are included in the group.

I have a model in which, for each store, predicted revenues are perturbed by a multiplicative shock: R = e^\eta r where r is predicted and R is observed. \eta is mean zero. I can find \eta as follows: \ln( r) - \ln( R) = \eta . I'm summing the squares of the \eta's. However, there are...

Thanks for your help. The variables are definitely correlated. Now I just need to figure out how to generate the random variables.

I think that, based on the CDF, the variables are dependent, correct? The conditional density of ##x_2## depends on the value of ##x_1##.

Hi, I'm an economics graduate student doing some work on a nested logit model. I am trying to generate random variables that follow the following CDF: F(x_1, x_2) =\textrm{exp}[ -(e^{-2x_1}+e^{-2x_2}) ^{1/2}] (This is an extreme-value distribution) With a single random variable, I...