The type T is not generic; it cannot be parameterized with arguments <?> error in a generic function

I want to create a generic function that takes any Map & a String key, if the key is not present in the map, then it should create a new instance of the Value Type (which is passed) & put it in the map & then return it.

Here is my implementation

public <T> T getValueFromMap(Map<String, T> map, String key, Class<T> valueClass){
    T value = map.get(key);
    if (value == null){
        try {
            value = valueClass.newInstance();
        } catch (InstantiationException e) {
            // TODO Auto-generated catch block
            e.printStackTrace();
        } catch (IllegalAccessException e) {
            // TODO Auto-generated catch block
            e.printStackTrace();
        }
        map.put(key, value);
    }
    return value;
}

It works if I use it with a normal (not generic) List as the value type,

Map<String,List> myMap;
List value = getValueFromMap(myMap, "aKey", List.class) //works

but not with generic type lists

Map<String,List<String>> myMap;
List<String> value = getValueFromMap(myMap, "aKey", List.class) //does not work

Also if I try to make Map<String, T> map parameter generic by changing it to Map<String, T<?>> it complains that the type T is not generic; it cannot be parameterized with arguments <?>

Can the generic parameters be themselves made generic?

Is there any way to create function with above mentioned requirements?

~Update

Thanks for all the insightful answers everyone.

I have verified that the accepted solution works for any value type with this code

    Map<String, Map<String, List<String>>> outer = 
            new HashMap<String, Map<String,List<String>>>();

    Map<String, List<String>> inner =