This is actually happened with my mom when she was nearly 10-11 years of age in a village of Bihar.
The house in which they lived was very big with 6-7 rooms around and in the middle of the house there was no roof. It was open. At night, my mom along with her other siblings used to sleep outside in that part of house on a cot. A big peepal tree was also there and it was wide open middle section in between the house. They always used to close the main gate before they slept and there was no chance of a theif or any intruder coming inside the walls after 11:00pm.
One full moon night, my mom slept on cot which was nearly 2-3 meters away from that peepal tree. She woke up early morning that day around 4-5 am.
As she opened her eyes, to her amazement, she saw a man in his 40's wearing white clothes- kurta, dhoti wearing a white turban around his head standing under the peepal tree. His face, hand & legs everything was pure white and shining. He was standing still and looked like a statue. He was staring at my mom.
My mom was frozen and trembling with fear. At first she thought to wake up her elder sister but she was too scared to move and tell her. She shut her eyes as tightly as she could and slept.
In the morning she told this to her siblings who said it might be a dream while her parents ignored.
My mom says she has no other memory of her childhood so clear. She still remembers the white man's face, clothes and the turban he wore.
She never experienced anything after that but still wonders who was that man!