I did a quick simulation of that circuit, and a few things popped out that are strange.
First, under DC conditions: the base of Q2 charges up to 98% of the input voltage (15V) through the RC divider between R2+R4 and R5. This is 14.7V. With Q2 'on', the output should sit at a constant VBE drop below that, or about 14V.
If there is 1V of ripple on the input (superimposed on the 15V), when the input voltage drops to 14V, the base is still held at 14.7, however the emitter is still at 14V, so the collector voltage drops down towards 14V, since it can move faster than the base. This turns on the base to collector diode, causing a spike downwards in the base voltage until the base node discharges back down to below a diode drop. This cycle repeats, leaving a very noisy output as Q2 switches on and off.
I think if you want to use this circuit with any significant ripple on the input (any ripple in excess of a junction diode threshold), then the base voltage needs to be lowered, so that worst case, the base will always be at least less than a diode drop to the collector. Raising R2 and R4 up to 6.8K, causes the output to lower to 13V, giving 1V of margin to 1V of input ripple. After raising R2 and R4 up, I see a clean output and about 70dB of attenuation from input to output (or it converts 1V of input ripple into 3mV of output ripple).