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  • User error: missing stream in "getFormat" via ARC2_Reader in _sparql_request() (line 92 of /home/jcorneli/beta/sites/all/modules/sparql/sparql.module).
  • User error: missing stream in "readStream" http://planetmath.org:8890/sparql?query=%0APREFIX+msc%3A+%3Chttp%3A%2F%2Fmsc2010.org%2Fresources%2FMSC%2F2010%2F%3E+PREFIX+skos%3A+%3Chttp%3A%2F%2Fwww.w3.org%2F2004%2F02%2Fskos%2Fcore%23%3E+PREFIX+dct%3A+%3Chttp%3A%2F%2Fpurl.org%2Fdc%2Fterms%2F%3E+PREFIX+local%3A+%3Chttp%3A%2F%2Flocal.virt%2F%3E+SELECT+%3Flabel+WHERE+%7B+GRAPH+%3Chttp%3A%2F%2Flocalhost%3A8890%2FDAV%2Fhome%2Fpm%2Frdf_sink%23this%3E+%7B+msc%3A97D40+skos%3AprefLabel+%3Flabel+FILTER+langMatches%28+lang%28%3Flabel%29%2C+%22en%22+%29+%7D%7D via ARC2_Reader in _sparql_request() (line 92 of /home/jcorneli/beta/sites/all/modules/sparql/sparql.module).
  • User error: Socket error: Could not connect to "http://planetmath.org:8890/sparql?query=%0APREFIX+msc%3A+%3Chttp%3A%2F%2Fmsc2010.org%2Fresources%2FMSC%2F2010%2F%3E+PREFIX+skos%3A+%3Chttp%3A%2F%2Fwww.w3.org%2F2004%2F02%2Fskos%2Fcore%23%3E+PREFIX+dct%3A+%3Chttp%3A%2F%2Fpurl.org%2Fdc%2Fterms%2F%3E+PREFIX+local%3A+%3Chttp%3A%2F%2Flocal.virt%2F%3E+SELECT+%3Flabel+WHERE+%7B+GRAPH+%3Chttp%3A%2F%2Flocalhost%3A8890%2FDAV%2Fhome%2Fpm%2Frdf_sink%23this%3E+%7B+msc%3A26C99+skos%3AprefLabel+%3Flabel+FILTER+langMatches%28+lang%28%3Flabel%29%2C+%22en%22+%29+%7D%7D" (proxy: 0): Connection refused in ARC2_Reader in _sparql_request() (line 92 of /home/jcorneli/beta/sites/all/modules/sparql/sparql.module).
  • User error: missing stream in "getFormat" via ARC2_Reader in _sparql_request() (line 92 of /home/jcorneli/beta/sites/all/modules/sparql/sparql.module).
  • User error: missing stream in "readStream" http://planetmath.org:8890/sparql?query=%0APREFIX+msc%3A+%3Chttp%3A%2F%2Fmsc2010.org%2Fresources%2FMSC%2F2010%2F%3E+PREFIX+skos%3A+%3Chttp%3A%2F%2Fwww.w3.org%2F2004%2F02%2Fskos%2Fcore%23%3E+PREFIX+dct%3A+%3Chttp%3A%2F%2Fpurl.org%2Fdc%2Fterms%2F%3E+PREFIX+local%3A+%3Chttp%3A%2F%2Flocal.virt%2F%3E+SELECT+%3Flabel+WHERE+%7B+GRAPH+%3Chttp%3A%2F%2Flocalhost%3A8890%2FDAV%2Fhome%2Fpm%2Frdf_sink%23this%3E+%7B+msc%3A26C99+skos%3AprefLabel+%3Flabel+FILTER+langMatches%28+lang%28%3Flabel%29%2C+%22en%22+%29+%7D%7D via ARC2_Reader in _sparql_request() (line 92 of /home/jcorneli/beta/sites/all/modules/sparql/sparql.module).
  • User error: Socket error: Could not connect to "http://planetmath.org:8890/sparql?query=%0APREFIX+msc%3A+%3Chttp%3A%2F%2Fmsc2010.org%2Fresources%2FMSC%2F2010%2F%3E+PREFIX+skos%3A+%3Chttp%3A%2F%2Fwww.w3.org%2F2004%2F02%2Fskos%2Fcore%23%3E+PREFIX+dct%3A+%3Chttp%3A%2F%2Fpurl.org%2Fdc%2Fterms%2F%3E+PREFIX+local%3A+%3Chttp%3A%2F%2Flocal.virt%2F%3E+SELECT+%3Flabel+WHERE+%7B+GRAPH+%3Chttp%3A%2F%2Flocalhost%3A8890%2FDAV%2Fhome%2Fpm%2Frdf_sink%23this%3E+%7B+msc%3A12-00+skos%3AprefLabel+%3Flabel+FILTER+langMatches%28+lang%28%3Flabel%29%2C+%22en%22+%29+%7D%7D" (proxy: 0): Connection refused in ARC2_Reader in _sparql_request() (line 92 of /home/jcorneli/beta/sites/all/modules/sparql/sparql.module).
  • User error: missing stream in "getFormat" via ARC2_Reader in _sparql_request() (line 92 of /home/jcorneli/beta/sites/all/modules/sparql/sparql.module).
  • User error: missing stream in "readStream" http://planetmath.org:8890/sparql?query=%0APREFIX+msc%3A+%3Chttp%3A%2F%2Fmsc2010.org%2Fresources%2FMSC%2F2010%2F%3E+PREFIX+skos%3A+%3Chttp%3A%2F%2Fwww.w3.org%2F2004%2F02%2Fskos%2Fcore%23%3E+PREFIX+dct%3A+%3Chttp%3A%2F%2Fpurl.org%2Fdc%2Fterms%2F%3E+PREFIX+local%3A+%3Chttp%3A%2F%2Flocal.virt%2F%3E+SELECT+%3Flabel+WHERE+%7B+GRAPH+%3Chttp%3A%2F%2Flocalhost%3A8890%2FDAV%2Fhome%2Fpm%2Frdf_sink%23this%3E+%7B+msc%3A12-00+skos%3AprefLabel+%3Flabel+FILTER+langMatches%28+lang%28%3Flabel%29%2C+%22en%22+%29+%7D%7D via ARC2_Reader in _sparql_request() (line 92 of /home/jcorneli/beta/sites/all/modules/sparql/sparql.module).

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estimator

Let X1,X2,…,XnsubscriptX1subscriptX2normal-…subscriptXnX_{1},X_{2},\ldots,X_{n} be samples (with observations Xi=xisubscriptXisubscriptxiX_{i}=x_{i}) from a distribution with probability density function f(X∣θ)fragmentsffragmentsnormal-(Xnormal-∣θnormal-)f(X\mid\theta), where θθ\theta is a real-valued unknown parameter in fff. Consider θθ\theta as a random variable and let τ⁢(θ)τθ\tau(\theta) be its realization.

An estimator for θθ\theta is a statistic ηθ=ηθ⁢(X1,X2,…,Xn)subscriptηθsubscriptηθsubscriptX1subscriptX2normal-…subscriptXn\eta_{{\theta}}=\eta_{{\theta}}(X_{1},X_{2},\ldots,X_{n}) that is used to, loosely speaking, estimate τ⁢(θ)τθ\tau(\theta). Any value ηθ(X1=x1,X2=x2,…,Xn=xn)fragmentssubscriptηθfragmentsnormal-(subscriptX1subscriptx1normal-,subscriptX2subscriptx2normal-,normal-…normal-,subscriptXnsubscriptxnnormal-)\eta_{{\theta}}(X_{1}=x_{1},X_{2}=x_{2},\ldots,X_{n}=x_{n}) of ηθsubscriptηθ\eta_{{\theta}} is called an estimate of τ⁢(θ)τθ\tau(\theta).

Example. Let X1,X2,…,XnsubscriptX1subscriptX2normal-…subscriptXnX_{1},X_{2},\ldots,X_{n} be iid from a normal distribution N⁢(μ,σ2)Nμsuperscriptσ2N(\mu,\sigma^{2}). Here the two parameters are the mean μμ\mu and the variance σ2superscriptσ2\sigma^{2}. The sample mean X¯normal-¯X\overline{X} is an estimator of μμ\mu, while the sample variance s2superscripts2s^{2} is an estimator of σ2superscriptσ2\sigma^{2}. In addition, sample median, sample mode, sample trimmed mean are all estimators of μμ\mu. The statistic defined by

1n-1⁢∑i=1n(Xi-m)2,1n1superscriptsubscripti1nsuperscriptsubscriptXim2\frac{1}{n-1}\sum_{{i=1}}^{{n}}(X_{i}-m)^{2},

where mmm is a sample median, is another estimator of σ2superscriptσ2\sigma^{2}.

Defines: 
estimate
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Definition
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Owner: CWoo
Added: 2004-12-10 - 01:25
Author(s): CWoo

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(v6) by CWoo 2013-03-22
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