Best way to document anonymous objects and functions with jsdoc

You can use @callback or @typedef.

/**
 * @callback arrayCallback
 * @param  {object} element - Value of array element
 * @param  {number} index   - Index of array element
 * @param  {Array}  array   - Array itself
 */

/**
 * @param {arrayCallback} callback - function applied against elements
 * @return {Array} with elements transformed by callback
 */
Array.prototype.map = function(callback) { ... }

You can document stuff that doesnt exist in the code by using the @name tag.

/**
 * Description of the function
 * @name IDontReallyExist
 * @function
 * @param {String} someParameter Description
*/

/**
 * The CallAgain method calls the provided function twice
 * @param {IDontReallyExist} func The function to call twice
*/
exports.CallAgain = function(func) { func(); func(); }

Here is the @name tag documentation. You might find name paths useful too.