Geodesic
The squared error of the estimate of a multidimensional normal density function by the sample data
Teoriâ veroâtnostej i ee primeneniâ, Tome 14 (1969) no. 1, pp. 151-155 Cet article a éte moissonné depuis la source Math-Net.Ru

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It has been proved in [2] that the distributions of the variables $$ n\int_{R^k}[p(x)-p^*_n(x)]^2\,dx $$ converge as $n\to\infty$ to the distribution of the sum of two independent quadratic forms. In the paper the distributions of these quadratic forms are obtained. 
@article{TVP_1969_14_1_a17,
     author = {G. M. Maniya},
     title = {The squared error of the estimate of a~multidimensional normal density function by the sample data},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {151--155},
     year = {1969},
     volume = {14},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1969_14_1_a17/}
}
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G. M. Maniya. The squared error of the estimate of a multidimensional normal density function by the sample data. Teoriâ veroâtnostej i ee primeneniâ, Tome 14 (1969) no. 1, pp. 151-155. http://geodesic.mathdoc.fr/item/TVP_1969_14_1_a17/