wavVar(wmtsa)
wavVar()所属R语言包：wmtsa
Discrete wavelet variance estimation
离散小波方差估计
译者：生物统计家园网 机器人LoveR
描述----------Description----------
The discrete wavelet variance is a useful alternative to the spectral density function (SDF) and is seen as an octave-band regularization of the SDF. The wavelet variance decomposes the variance of certain stochastic processes on a scale-by-scale basis, and thus, is very appealing to the analyst studying physical phenomena which fluctuate both within and across a wide range of scale.
离散小波方差谱密度函数（SDF）是一个有用的替代，被看作是一个倍频程的正规化自卫队。小波方差分解的某些随机过程的方差的规模，通过规模的基础上，因此，是非常有吸引力的分析师研究在国内和跨越广泛的规模波动的物理现象。
By definition, the wavelet variance involves an averaged energy summation of MODWT wavelet coefficients. While DWT wavelet coefficients can also be used, the statistical properties are inferior to those of the MODWT wavelet variance. See the references for more details.
根据定义，的小波方差涉及一个MODWT小波系数的平均能量求和。虽然也可用于DWT的小波系数的统计特性不如那些的的MODWT小波方差。有关详细信息，请参考相关手册。
The MODWT Wavelet Variance
的MODWT小波方差
Let N be the the number of samples in a time series X(t), L be the length of the wavelet filter, L(j)=(2^j-1)(L-1)+1 be the equivalent filter width at level $j$ in a MODWT, and tau(j)=2^(j-1) be the scale of the data at level j for j=1,...,J. Then the unbiased wavelet variance is defined as
让N是一个时间序列中的样本数X(t)，L的小波滤波器的长度，L(j)=(2^j-1)(L-1)+1是等效的滤波器在水平宽度$ j $的在一个MODWT，和tau(j)=2^(j-1)规模的数据级jj=1,...,J。不带偏见的小波方差被定义为
where d(j,t) are the MODWT coefficients at level j and time t, and Mj=N - L(j) + 1. The unbiased wavelet variance estimator avoids so-called boundary coefficients which are those coefficients subject to circular filter operations in a discrete wavelet transform. The biased estimator is defined as
其中d(j,t)MODWT的系数级j时间t和Mj=N - L(j) + 1。小波方差的无偏估计避免了所谓的的边界系数，这些系数是在离散小波变换的圆形过滤操作。有偏估计被定义为
The DWT Wavelet Variance
DWT小波方差
The DWT can also be used to calculate wavelet variance estimates, but is not preferred over the MODWT due to its poor statistical properties. Let N(j)= floor(N/2^j) be the number of DWT wavelet coefficients at level j, and L'(j)=ceiling((L-2)(1-2^(-j))) be the number of DWT boundary coefficients at level j (assuming N(j) > L'(j)). Then the DWT version of the unbiased wavelet variance is defined as
DWT可也可以用于计算小波方差的估计，但还没有由于其较差的统计性质在MODWT优选。让我们N(j)= floor(N/2^j)DWT小波系数的数量级j和L'(j)=ceiling((L-2)(1-2^(-j)))是在水平的DWT边界系数j（假设N(j) > L'(j)）。然后，公正的小波方差的的DWT版本的定义为：
where d(j,t) are the DWT coefficients at level j and time t. Similarly, the DWT version of the biased wavelet variance is defined as
d(j,t)的j和时间t的小波系数。同样，DWT版本的偏见小波方差被定义为
用法----------Usage----------
position=list(from=1,by=1,units=character()), units=character(),
documentation=character(), sdf=NULL, sdfargs=NULL,
参数----------Arguments----------
参数：x
a vector containing a uniformly-sampled real-valued time series.
一个向量，包含均匀采样的实值的时间序列。
参数：documentation
a character string used to describe the input data. Default: character().
一个字符串用来描述输入data。默认值：character()。
参数：n.fft
a positive integer (greater than one) defining the number of frequencies to use in evaluating the SDF. The frequencies are uniformly distributed over the interval [0, Nyquist] ala f=[0, 1/P , 2/P, 3/P, ..., (n.freq-1)/P] where P=2*(n.freq-1)/sampling.interval. Only used when the input SDF is not NULL. Default: 1024.
一个正整数（大于1）限定的数目的频率使用在评估自卫队。均匀地分布在该频率的时间间隔[0，奈奎斯特]丙氨酸F = [0，1 / P，2/3 / P，P，...，（n.freq-1）/ P]，其中P = 2 * （n.freq-1）/ sampling.interval。仅用于输入SDF是不是NULL的。默认值：1024。
参数：n.levels
the number of decomposition levels. Default: the maximum level at which there exists at least one interior wavelet coefficient.
的分解级别的数目。默认值：在其中存在的至少一个内部的小波系数的最大电平。
参数：position
a list containing the arguments from, by and to which describe the position(s) of the input data. All position arguments need not be specified as missing members will be filled in by their default values. Default: list(from=1, by=1, units=character()).
list包含的参数from, by和to描述的位置（S）输入data。所有的位置参数需要被指定为缺少的成员将被填充，它们的默认值。默认值：list(from=1, by=1, units=character())。
参数：sampling.interval
sampling interval of the time series. Default: 1.
采样间隔的时间序列。默认值：1。
参数：sdf
a spectral density function of the process corresponding to the input time series. This input must be a function whose first argument is f (representing frequency). At a minimum, the SDF must be defined over frequencies [0, Nyquist] where Nyquist=1/(2*sampling.interval). Additional arguments that are needed to calculate the SDF should be passed via the sdfargs parameter. This argument is used only for calculating mode 2 EDOF. If the EDOF mode 2 estimates are not desired, specify this this argument as NULL and the EDOF mode 2 and corresponding confidence intervals will not be calculated. See the mutilsSDF function for more details. Default: NULL.
谱密度函数的过程中，对应于输入的时间序列。该输入必须是一个函数的第一个参数是f（即频率）。至少，日本自卫队必须定义在奈奎斯特频率[0，]Nyquist=1/(2*sampling.interval)。应通过sdfargs参数传递额外的参数所需要的计算自卫队。该参数仅用于计算模式2 EDOF。如果EDOF模式2估计不理想，指定这个参数NULL和EDOF模式的2和相应的置信区间将不会被计算。请参阅mutilsSDF功能的更多详细信息，。默认值：NULL。
参数：sdfargs
a list of arguments passed directly to the SDF function ala do.call. Default: NULL (no additional arguments).
参数列表直接传递到SDF功能阿拉的do.call。默认值：NULL（没有额外的参数）。
参数：units
a string denoting the units of the time series. Default: character() (no units).
一个字符串，表示的时间序列的单位。默认值：character()（无单位）。
参数：wavelet
a character string denoting the filter type. See wavDaubechies for details. Default: "s8".
一个字符串，表示过滤器的类型。见wavDaubechies的详细信息。默认值："s8"。
参数：xform
a character string denoting the type of wavelet transform: "modwt" or "dwt". Default: "modwt".
表示一个字符串类型的小波变换：的“modwt”或“载重吨”。默认值："modwt"。
值----------Value----------
an object of class wavVar.
对象类wavVar。
参考文献----------References----------
D. B. Percival and A. T. Walden, Wavelet Methods for Time Series Analysis, Cambridge University Press, 2000.
参见----------See Also----------
实例----------Examples----------
## create sequence [＃创建序列]
x <- make.signal("doppler")
## perform a time independent wavelet variance [执行时间独立的小波方差]
## analysis [＃分析]
vmod <- wavVar(x)
## plot the result [＃图的结果]
plot(vmod, pch=15, title="Wavelet Variance of Doppler")
## calculate wavelet variance estimaates for the [＃计算小波方差estimaates，]
## ocean series and calculate EDOF mode 2 [＃海洋系列和计算EDOF模式2]
## estimates and corresponding 95 percent [估计和相应的95％]
## confidence intervals [＃置信区间]
vocean <- wavVar(ocean, sdf=oceansdf, wavelet="d6")
## summarize the results [＃总结的结果。]
plot(vocean, edof=1:3)
summary(vocean)
转载请注明:出自 生物统计家园网(http://www.biostatistic.net)。
注：
注1：为了方便大家学习，本文档为生物统计家园网机器人LoveR翻译而成，仅供个人R语言学习参考使用，生物统计家园保留版权。
注2：由于是机器人自动翻译，难免有不准确之处，使用时仔细对照中、英文内容进行反复理解，可以帮助R语言的学习。
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发表于 2012-10-1 22:57:34
