JPG files use 8 bits per color per pixel (I've never heard of any camera that uses the alleged 12-bit-per-color-per-pixel extension) and is a compact way of storing images.
RAW files are huge but have the full image data from the image sensor which is likely to be more than 8 bits. (judging from recent DSP specs I would assume 12 bit ADCs are the norm... but how would you actually find out how many bits a particular camera provides?)
Is there anything similar to JPG which stores the file in a form that allows lossy compression for high spatial frequencies, but has more dynamic range than 8 bits?
Answer
It's going to be difficult to answer your question without knowing in what simalarities do you wish your image format to share with Jpeg?
Compression Ratios? Universal Support on the web? Camera support?
JPEG2000 has support for 48-bit depths (though in practice only 24 are common). It also supports both lossy and lossless compression, so you can tailor your size savings.
DNG is widely used as a lossless format (there IS lossy compression support), but does offer roughly 40% size savings because of lossless compression, allowing you to get better size management, while still maintaining most of the qualities of a RAW image.
PNG is also lossless, but has more universal support on the web, and up to 16bits per channel color depth.
By and large however, RAW/DNG are kept/edited, while JPEG is used for web.
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