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Talk:Multivariate normal distribution

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In the subsection titled "Bivariate case", the notation ' is used twice. But that notation has not been previously defined and, in fact, is not used in the other sections of the article. Its meaning should be clarified. SometimesRPC 18:44, 8 January 2024 (UTC)
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three references to an SSRN preprint. The preprint is based on a student's Honors thesis (see link in section 4.3 of the preprint). There's presumably nothing wrong with the preprint but it might be preferable to cite more authoritative sources. Eldacan
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Previously the PDF said covariance matrix Σ had to be positive-definite. I fixed it to PSD for covariance matrix. I would also say symmetric but the article on PSD includes symmetric as part of the definition so I'll use that definition.
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The reference discusses this within the context of estimation, which IMO complicates the statement unnecessarily. It seems more consistent to remove the reference and cite the Knowledge article's own section.
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Ok I misunderstood - it needs to be invertible thus positive definite to write down the PDF in that form, otherwise it is like zero variance
90: 645: 253: 587: 431: 278: 81: 58: 604: 566:{\displaystyle \operatorname {E} (X_{1}\mid X_{2}=x_{2})=\mu _{1}+\rho {\frac {\sigma _{1}}{\sigma _{2}}}(x_{2}-\mu _{2})} 33: 198: 177: 430:
and then provides a reference . However, the cited reference is just a formulation of the statement of the
284: 39: 421:{\displaystyle y(x)=\operatorname {sgn}(\rho ){\frac {\sigma _{Y}}{\sigma _{X}}}(x-\mu _{X})+\mu _{Y}.} 73: 52: 21: 89:
on Knowledge. If you would like to participate, please visit the project page, where you can join
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Formula for the limit of the isoline ellipsis' major axis in the bivariate case
86: 233: 218: 281:" states a formula for the limit of the major axis of isoline ellipses as 184: 142: 15: 442: 325: 287: 85:, a collaborative effort to improve the coverage of 565: 420: 309: 432:conditional expectation of the bivariate normal 272: 192:This page has archives. Sections older than 8: 605:"Linear least mean-squared error estimation" 212:Infobox PDF requirement on covariance matrix 612:Lecture notes course on applied probability 598: 596: 47: 554: 541: 526: 516: 510: 498: 482: 469: 456: 441: 409: 393: 372: 362: 356: 324: 296: 288: 286: 592: 49: 19: 202:when more than 4 sections are present. 7: 310:{\displaystyle |\rho |\rightarrow 1} 79:This article is within the scope of 38:It is of interest to the following 651:Top-importance Statistics articles 443: 14: 603:Wyatt, John (November 26, 2008). 196:may be automatically archived by 147: 99:Knowledge:WikiProject Statistics 72: 51: 20: 656:WikiProject Statistics articles 252:User 174.168.4.26 has recently 119:This article has been rated as 102:Template:WikiProject Statistics 560: 534: 488: 449: 399: 380: 353: 347: 335: 329: 301: 297: 289: 248:More authoritative references? 1: 93:and see a list of open tasks. 588:09:19, 26 January 2024 (UTC) 646:C-Class Statistics articles 672: 277:The article's subsection " 264:Notation in Bivariate case 242:21:22, 29 March 2022 (UTC) 227:20:53, 29 March 2022 (UTC) 259:08:15, 20 July 2023 (UTC) 118: 67: 46: 567: 422: 311: 199:Lowercase sigmabot III 82:WikiProject Statistics 28:This article is rated 568: 423: 312: 440: 323: 285: 621:on October 10, 2015 105:Statistics articles 563: 418: 307: 34:content assessment 532: 378: 206: 205: 171: 170: 139: 138: 135: 134: 131: 130: 663: 631: 630: 628: 626: 620: 614:. Archived from 609: 600: 572: 570: 569: 564: 559: 558: 546: 545: 533: 531: 530: 521: 520: 511: 503: 502: 487: 486: 474: 473: 461: 460: 427: 425: 424: 419: 414: 413: 398: 397: 379: 377: 376: 367: 366: 357: 316: 314: 313: 308: 300: 292: 201: 185: 162: 161: 151: 143: 125:importance scale 107: 106: 103: 100: 97: 76: 69: 68: 63: 55: 48: 31: 25: 24: 16: 671: 670: 666: 665: 664: 662: 661: 660: 636: 635: 634: 624: 622: 618: 607: 602: 601: 594: 550: 537: 522: 512: 494: 478: 465: 452: 438: 437: 405: 389: 368: 358: 321: 320: 283: 282: 275: 266: 250: 214: 197: 186: 180: 156: 104: 101: 98: 95: 94: 61: 32:on Knowledge's 29: 12: 11: 5: 669: 667: 659: 658: 653: 648: 638: 637: 633: 632: 591: 562: 557: 553: 549: 544: 540: 536: 529: 525: 519: 515: 509: 506: 501: 497: 493: 490: 485: 481: 477: 472: 468: 464: 459: 455: 451: 448: 445: 417: 412: 408: 404: 401: 396: 392: 388: 385: 382: 375: 371: 365: 361: 355: 352: 349: 346: 343: 340: 337: 334: 331: 328: 306: 303: 299: 295: 291: 279:Bivariate case 274: 271: 265: 262: 249: 246: 245: 244: 213: 210: 208: 204: 203: 191: 188: 187: 182: 178: 176: 173: 172: 169: 168: 158: 157: 152: 146: 137: 136: 133: 132: 129: 128: 121:Top-importance 117: 111: 110: 108: 91:the discussion 77: 65: 64: 62:Top‑importance 56: 44: 43: 37: 26: 13: 10: 9: 6: 4: 3: 2: 668: 657: 654: 652: 649: 647: 644: 643: 641: 617: 613: 606: 599: 597: 593: 590: 589: 585: 581: 577: 573: 555: 551: 547: 542: 538: 527: 523: 517: 513: 507: 504: 499: 495: 491: 483: 479: 475: 470: 466: 462: 457: 453: 446: 435: 433: 428: 415: 410: 406: 402: 394: 390: 386: 383: 373: 369: 363: 359: 350: 344: 341: 338: 332: 326: 318: 304: 293: 280: 270: 263: 261: 260: 255: 247: 243: 239: 235: 231: 230: 229: 228: 224: 220: 211: 209: 200: 195: 190: 189: 175: 174: 167: 164: 163: 160: 159: 155: 150: 145: 144: 141: 126: 122: 116: 113: 112: 109: 92: 88: 84: 83: 78: 75: 71: 70: 66: 60: 57: 54: 50: 45: 41: 35: 27: 23: 18: 17: 623:. Retrieved 616:the original 611: 578: 574: 436: 429: 319: 276: 267: 251: 215: 207: 193: 153: 140: 120: 80: 40:WikiProjects 640:Categories 625:23 January 96:Statistics 87:statistics 59:Statistics 166:Archive 1 580:M hoehle 154:Archives 194:90 days 123:on the 30:C-class 36:scale. 619:(PDF) 608:(PDF) 254:added 627:2012 584:talk 238:talk 234:Wqwt 223:talk 219:Wqwt 342:sgn 115:Top 642:: 610:. 595:^ 586:) 552:μ 548:− 524:σ 514:σ 508:ρ 496:μ 463:∣ 447:⁡ 434:: 407:μ 391:μ 387:− 370:σ 360:σ 351:ρ 345:⁡ 317:: 302:→ 294:ρ 240:) 225:) 629:. 582:( 561:) 556:2 543:2 539:x 535:( 528:2 518:1 505:+ 500:1 492:= 489:) 484:2 480:x 476:= 471:2 467:X 458:1 454:X 450:( 444:E 416:. 411:Y 403:+ 400:) 395:X 384:x 381:( 374:X 364:Y 354:) 348:( 339:= 336:) 333:x 330:( 327:y 305:1 298:| 290:| 236:( 221:( 127:. 42::

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Archive 1
Lowercase sigmabot III
Wqwt
talk
20:53, 29 March 2022 (UTC)
Wqwt
talk
21:22, 29 March 2022 (UTC)
added
08:15, 20 July 2023 (UTC)
Bivariate case
conditional expectation of the bivariate normal
M hoehle
talk
09:19, 26 January 2024 (UTC)


"Linear least mean-squared error estimation"

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