Q:

Checked and Unchecked Exceptions and design thoughts

Lets say have this immutable record type:
public class Record
{
    public Record(int x, int y) {
        Validator.ValidateX(x);
        Validator.ValidateY(y);
        X=x;
        Y=y;
    }

    public final int X;
    public final int Y;

    public static class Validator {
        public void ValidateX(int x) { if(x < 0) { throw new UnCheckedException; } }
        public void ValidateY(int y) { if(y < 0) { throw new UnCheckedException; } }
    }
}

Notice it throws an unchecked exception.  The reason is because this is a object that is used quite often and it is inconvenient to have to deal with a checked exception.  
However, if this object is in a class library where it may be used to validate user inputs (or some other external input).  Now it's starting to sound like it should be a CHECKED exception, because the inputs are no longer up the to programmer.
Thoughts everyone?  should i make checked or unchecked, or are there better design for this?
UPDATE:
my confusion is coming from this scenerio:  normally Record would be used like this:
Record r = new Record(1,2);
OtherObj o = new OtherObj(r);

there it's up to the programmer, so unchecked exception is ok.
However when you get parameters for Record from a user you want to validate them right? so you might call 
Record.ValidateX(inputX);
Record.ValidateY(inputY);

There it might throw a checked exception because inputs are no longer controlled?
Sorry, I normally wouldn't be too concerned with this (personally I think unchecked is fine). but this is actually a problem in a homework and I want to get it right lol.
UPDATE(2):
I starting to think what I need is for ValidateX to throw a checked exception because it is typically what would be used if user input is involved.  In that case we could ask the user for input again.  However, for the Record constructor, it will throw checked exception because constructing a Record with invalid arguements is an API violation.  The new code would look like this:
public class Record
{
    public Record(int x, int y) {
        try
        {
            Validator.ValidateX(x);
            Validator.ValidateY(y);
        }catch(CheckedException xcpt) { throw new UnCheckedException(xcpt.getMessage()); }
        X=x;
        Y=y;
    }

    public final int X;
    public final int Y;

    public static class Validator {
        public void ValidateX(int x) throws CheckedException { if(x < 0) { throw new CheckedException; } }
        public void ValidateY(int y) throws CheckedException { if(y < 0) { throw new CheckedException; } }
    }
}

Now the programmer can validate the parameters before passing them to the Record class. If the does not then it's a API violation and an unchecked exception is thrown.
How does this sound?!

A:

Notice it throws an unchecked
  exception. The reason is because this
  is a object that is used quite often
  and it is inconvenient to have to deal
  with a checked exception.

No, I think the reason you throw an unchecked exception here is because it involves a violation of contract on the part of the user of that API, and not an exceptional condition during the normal functioning of that method. See the Java SDK's use of NullPointerException, IllegalArgumentException, etc., which are RuntimeExceptions because they represent a violation of contract.

A:

Bloch, item 58: Use checked exceptions
  for recoverable conditions and runtime
  exceptions for programming errors.

If the user of your class is able to avoid the problem by using the API correctly (including not passing in values that are documented to be invalid) then it's a programming error, so throw an InvalidArgumentException.

A:

You should never validate user input with an unchecked exception. Exceptions are normally checked because that way you can not forget to handle the exceptions. 
Validating parameters used in an api is a completely different kind. These should be unchecked, because otherwise you'll end up adding try/catch to every function call. Whenever a method is passed an invalid argument, this is surely a programming error. The normal way is to throw an IllegalArgumentException or NullPointerException (or any other that suits your needs).
In api calls leave the checked excpetions for

Validations you promise to the caller of the api
Expected exceptional conditions (requested file doesn't exist, write failed etc)

Besides the above, recoverability is also important for deciding for a checked or unchecked exception. If you can never recover (which is normally the case in a programming error) you can (or should?) take the unchecked exception.
Preferably don't write code that doesn't meet the above guidelines. For you that would mean that you have to write a function that returns a boolean or checked exception when using to validate user input, and an unchecked exception when validating input parameters to your functions. Of course your can and should use the same function to validate the exceptions, just wrap the one that returns a boolean or checked exception:
public boolean validateX(int x)
{
     return x > 0;
}

private void validateParameter(int x)
{
     if (validateX(x))
     {
         throw new IllegalArgumentException("X is invalid");
     }
}

This is a bit more work, but it will give you the best of both worlds. By making the validate parameter function private you can ensure you don't accidentally use it outside of your class. Of course you can also put the if(validateX(x)) ... part inside your constructor.

