Model with rank as the dependent variable? I have a dataset with n records. The input features are f1, f2, f3 ... fm, and the dependent variable (output) is just the rank (not any type of scores).

What type of model should I build so that I can use the model to predict the rank of a new dataset? I suppose I could build a linear regression by assuming the dependent variable is just the rank (i.e. score = rank), but I am wondering if there is a better model or approach for this problem. Thanks!
Leaving aside any discussion of algorithms and statistics, you cannot predict a rank of an object without context. Are you supposed to rank it relative to your current rows, or in relationship to other new rows? For ranking algorithms based on features, you would usually want to assign an arbitrary score and then sort by it and assign ranks accordingly.