Sequential Probabilistic Ratio Test for the Scale Parameter of the P -Norm Distribution

We consider a series of independent observations from a P -norm distribution with the position parameter μ and the scale parameter σ . We test the simple hypothesis H 0 : σ = σ 1 versus H 1 : σ = σ 2 . Firstly, we give the stop rule and decision rule of sequential probabilistic ratio test (SPRT). Secondly, we prove the existence of h σ which needs to satisfy the specific situation in SPRT method, and the approximate formula of the mean sample function is derived. Finally, a simulation example is given. The simulation shows that the ratio of sample size required by SPRT and the classic Neyman–Pearson N − P test is about 50.92 % at most, 38.30 % at least.

Partial Derivative Estimation for Underlying Functional-Valued Process in a Unified Framework

We consider functional data analysis when the observations at each location are functional rather than scalar. When the dynamic of underlying functional-valued process at each location is of interest, it is desirable to recover partial derivatives of a sample function, especially from sparse and noise-contaminated measures. We propose a novel approach based on estimating derivatives of eigenfunctions of marginal kernels to obtain a representation for functional-valued process and its partial derivatives in a unified framework in which the number of locations and number of observations at each location for each individual can be any rate relative to the sample size. We derive almost sure rates of convergence for the procedures and further establish consistency results for recovered partial derivatives.

After notes on self-similarity exponent for fractal structures

Previous works have highlighted the suitability of the concept of fractal structure, which derives from asymmetric topology, to propound generalized definitions of fractal dimension. The aim of the present article is to collect some results and approaches allowing to connect the self-similarity index and the fractal dimension of a broad spectrum of random processes. To tackle with, we shall use the concept of induced fractal structure on the image set of a sample curve. The main result in this paper states that given a sample function of a random process endowed with the induced fractal structure on its image, it holds that the self-similarity index of that function equals the inverse of its fractal dimension.

Status and Transformation Measures of the Roof of Existing Residential Buildings

Flat roof wildly exists in early built residential buildings in most of China cities. Flat roofs have many shortcomings such as sample function, large energy consumption and lacking features. Through researching of existing housing roofing, analysis the measures and advantages of transformation of flat roof to pitched, expounding the technology prospects of transformation of flat roof to pitched.