# 2007Nx

2007 N 10 12 :

uҁFZhenisbek Assylbekov (LEw)

uځFRate of Convergence of Multinomial Log-likelihood Ratio Statistic to Chi-square Distribution

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Pearson's chi-square test is one of the most popular tests in statistical applications. It is based on Pearson's chi-square statistic. In 1972 Yarnold showed that distribution function of k -dimensional multinomial chi-square statistic converges to chi-square distribution with (k -1) degrees of freedom at the rate O (n -(k -1)/k). In my Master's Thesis I considered multinomial log-likelihood ratio statistic which is close to Pearson's chi-square statistic but is not identical with it. It was proved that the distribution function of three-dimensional multinomial log-likelihood ratio statistic converges to chi-square distribution with two degrees of freedom at the rate O (n -2/3).

2007 N 7 27 :

uҁF{ qbq (En)

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Browne (1984) ɂĂꂽ ADF (Asymptotically Distribution-Free) 蓝vʂpU\Ɋւ錟ɂčlĎ蓝vʂ̋A z̓JCQ敪zɕz邱ƂmĂ邪Cϑl̎ Ƃɂ́CW{x傫ꍇłJCQߎ̐xȂ ƂmĂD{\ł́CɁCU\`\̏ꍇɂ āCẢł̌蓝vʂɊւQߓWJ𓱏oČʂ𗘗p ߎ̉ǂɂčl@D

2007 N 7 13 :

uҁFe (LEw)

uځF𖞂 α-resolvable BIB design ̑ݐ

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α-resolvable BIB design ɂubN b ̉ẺǂɂāCBIB design ̃p[^̐𗘗p邽߂ɁC(αCv -1)=1 Ƃ𖞂ꍇɂĂ̍l@sĂD̍l@ɂāCubN b ̉Eub ≥2(v -1)+tvƗ\zDCur =k +λvƂ𖞂ꍇ݂̂l@̑ΏۂƂĎcDŁC(αCv -1)=1 r =k +λ ƂQ̏𖞂 α-resolvable BIB design ̃p[^ɂĂ̍l@i߂D design ɂ α-resolvable Ƃ\͍lCp[^݂̂ɒڂƂC\zsub ≥2(v -1)+tv𖞂Ȃ BIB design ̗Ⴊ݂D design ̂̂PɂāC\l邱Ƃɂ α-resolvable łȂƂƂłDɁC(αCv -1)=1 r =k +λ ƂQ̏𖞂 design ɂāCp[^̓ts߂ɁC λ ̒lŒ肵ȂCdesign ̑ݐɂĂ̍l@sD̍l@ɂC\zƂub ≥2(v -1)+tv𖞂Ȃ α-resolvable BIB design ݂Ƃ̃p[^n𔭌邱ƂłD

2007 N 6 22 :

uҁFHc qV (LEw)

uځFwʉtA@Ƃ̉

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{񍐂ł͑wʉtA@̌_ǂ@ЉD wʉtA@̓f y =ƒ(β1'x, β2'x, …, βn'x, ε) 肵Ƃ β1, β2, …, βn 𐄒肷̂ł邪CN֐ ƒ Ώ̂łƂɂ β1, β2, …, βn ̐ɎsƂ_D ̉ǖ@Ƃď] y ̒lɂĂ݂̂őwʉĂƂɉCewƂɎ听͂sāC̎听̒lɂ肳ɑwו@ĂClV~[VlXȍl@sƂɂāC̎@Lł邱ƂD

2007 N 5 11 :

uҁF{ Ís (BEw@)

uځFω_fɑ΂`hbƂ̉p

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nf[^ɂāC𐶂ݏo\sςłƂ ͋HłCǂ̎_iω_jłȂ炩̕ω ݒ荞񂾃fiω_fj́C܂܂ȕ ŕKvƂȂDω_Ӗp[^͒ʏ̃p [^Ƃ͐قȂCω_f߂ɂ͓ȓv _KvƂȂD{\ł͂̂CvIfI ̂߂̊{c[ł`hbiԒrʋKjɏœ_ āCω_f̂`hbʏ̂`hbƈقȂ邱Ƃ݂D āĈ`hbÓȕω_fIC܂Ó ω𐄒肷邱Ƃ𐔒lł߁CŌɂoσf[ ^ւ̓Kp݂D

2007 N 4 27 :

uҁF W (LEHw)

uځFMichalski ̗Ԗ

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uMichalski̗Ԗv(Michalski train problem)Ƃ́C R. S. Michalski1977N̘_Œ񎦂̂ŁC Ytt@C ̐}̂悤ȃCX gŕ`ꂽus̗ԁvƁus̗ԁv̗ႪƂCus ̗ԁvƁus̗ԁvʂ邽߂̃[CƂ łD MichalskíCeԂ̏ԂLŕ\CL̑gݍ킹ɂ郋[ ̐؁CJԂƂŁC[@܂D ̂悤Ȍ́CuA[_v (inductive inference) ƌĂ΂ClHm \̏dvȕłC݂̎_݂ƁCf[^}CjǑ ƍl邱Ƃł܂D ̃Z~i[ł́Čl̎n܂ɏỏ̖ƁC 𔭒[ɂlŏ̌Ƃ̍܂CPbiHjȂ 炨bƎv܂D