# 加载中...

Johannine
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ICM sources

always pretends to be reversed

George

Study Space

(2012-07-02 11:56)

# 我覺得是時候重新寫一些東西了。

(2010-03-07 13:15)

### 杂谈

I am so much delighted to read the economist.com's recent editorial to unmask the myth of sex disproportion in China: Gendercide, the world wide war on baby girls.

Conventional thinking many blame illiteracy of parents, poverty and the controvertial one-child policy for the sex disproportions in China. Thanks to the economist.com, these opinions have turned out to be distorted, with sound statistical backgrounds.

Based on prudent analysis and cautious data display, the article has successfully demonstrated that conventional thinking may be

(2010-02-24 15:04)

### 杂谈

http://www.economist.com/debate/debates/overview/166?source=hptextfeature

(2009-11-13 23:51)

### 杂谈

In the quantile longitudinal model proposed by Koenker, he tried to base the L1 norm on the L2 norm of mean regression. The difficulty is to decide the penalty term reflecting the random effect part: using the L1 norm penalty term, the structure of a pilot covariance matrix can not be used. Then I started to think: why not use the eigenvalue?

Eigenvalue and eigenvector decomposition may be the most charming part of matrix algebra, it compresses the information in an N*N-dimension space into N dimensions, such as the spectral decomposition, which was applied in signal transmission adapted to our television before the advance of digital technology. In fact, it drives all the classical multidimensional analysis techniques, the Primary Component Analysis, Partial Least Squares Regression, Factor Analysis, Independent Co

(2009-11-13 22:04)

Draw a line on a balloon. Draw a circle on it as well. Stretch and twist the balloon in what ever direction you like, without breaking it. Whatever figure you create, the line remains a line, and the circle remains a closed area. There are no breaks.

Such categorizes the idea of continuity. The surface is continuous because:

(2009-11-13 21:22)

### 杂谈

Ratio estimation is an important topic more than in sampling survey literature. In microeconomics, the marginal effect is indeed ratio statistics. In medical industry, the cost-effectiveness ratio also interests researchers, since in practice we not only take into consideration of whether a certain medicine can cure a disease, but also how much the cost entails in the treatment. A treatment with high economical cost may not be applicable.

Turn back to the statistical literature behind. For all conditions we consider the estimation of R=X/Y, where X and Y are both random variables. In sampling survey R is only an intermediate variable, the real interest is estimating X, therefore Y is chosen with a relatively small variance. Thus, in estimation we neglect the variance of Y, and the formula is rather simple.

(2009-08-19 19:43)

The world of mathematics is a marvelous creation by nature, and discovered by human intelligence. Although various elements have identified themselves by various symbols and formulas, their essence is inevitably homogeneous once and again.

For example, when we study calculation we learn how to add, minus, multiple and devide numbers. Such operator as '+','*','-'and '/' are first applied in the space of real variables. Then we move on to study matrix algebra, l

(2009-06-08 22:32)

### 杂谈

In sampling theory, the ratio estimator is an important statistics. Since it implements information of the assistant variable, whose population distribution is more easily obtained, the sampling variance is greatly reduced. However, the theoretical variance of a ratio estimator is hard to get, and many statisticians approximate the estimation by neglecting the variance of the denominator part of the estimator.  This method inevitably leads to an underestimation of the variance estimation. It is argued that if the sample size is large enough this approximation is quite feasible. In this article I carry out a strict Monte-Carlo experiment of a sampling instance. Both theoretical variance and estimation using the approximation is calculated, and I find that even with a small sample size the approximation is quite close to the real value. Further discussion is presented, demonst

(2009-03-31 08:43)

### 数学

The Nine Chapters of Mathematical Art, an ancient Chinese mathematical work, already shed some light on the characteristics on the Hilbert Space. The Gougu Theorem mentioned in this book actually coincides with the Parseval Formula held in the two dimensional Euclidean space.  Time series analysis deals a lot with distances between random variables, and such distances are defined in a special type of Hilbert space: the square integrable functions on a probability space. Although in linear time series regressions the algorithm simulates that of the least square linear regression, in linear regression the variables are defined directly on the Euclidean space, while in time series calculation the application of distances in Euclidean space only approximates distances in the previous square integrable function space. The spectral analysis is based upon an isomorphism between two types of Hilbert spaces, using an Ito integrati

(2009-03-12 15:31)